Fall 2004 US 311 Packet Copyright by Michael Newton Keas & Kerry Magruder • Wood Science 119C • Phone 878-2098
Table of Contents and Course Schedule Reading is due on the date under which it is listed • Study guides are located on indicated pages Wednesday August 25: First Day Orientation .............................................................................4 Monday August 30......................................................................................................................5 Syllabus, Fall 2004, US 311, Oklahoma Baptist University .....................................................5 Student Information Sheet.......................................................................................................8 Lab 1: Cowboy Astronomer (Planetarium). Read ASAP! ......................................................10 The Rose: An Exercise in How We Experience the World ....................................................14 Science and Faith ..................................................................................................................19 Basic Celestial Phenomena (BCP) Unit 1: Introduction .........................................................32 Wednesday September 1 ...........................................................................................................42 BCP Unit 2: Daily and Zodiacal (Sidereal) Motion................................................................42 Monday Sept. 6, Labor Day (do lab this week)..........................................................................64 Lab 2: Place in Space (Planetarium) ......................................................................................64 Wednesday September 8 ...........................................................................................................66 BCP Unit 3: Synodic Patterns ...............................................................................................66 Monday September 13 ..............................................................................................................82 Lab 3: Babylonian Show & The Planets (Planetarium) ..........................................................82 Cosmic Dimensions: Past and Present ...................................................................................84 Chaisson: Pages 0-1, 10-16 (read study guide in Packet first) ................................................92 Danielson: Pascal, Chesterton: Pages 195-197, 347-349........................................................93 Wednesday September 15 .........................................................................................................95 Privileged Planet: Introduction & Ch. 1: Wonderful Eclipses ................................................95 Monday September 20 ............................................................................................................ 103 Lab 4: Africa Show, Precession, Exam Review (Planetarium)............................................. 103 Chronology ......................................................................................................................... 105 Ancient Greek Astronomy................................................................................................... 106 Danielson: Ptolemy and Proclus: Pages 68-77..................................................................... 122 Wednesday September 22 ....................................................................................................... 124 Presocratic Science ............................................................................................................. 124 Danielson: Hebrew and Greek Worldviews: Pages 1-30...................................................... 134 Monday September 27 ............................................................................................................ 137 No Required Lab: Try to Finish Extra Credit Skywatch....................................................... 137 Plato and Aristotle: Two Worldviews that Shaped Science.................................................. 137 Danielson: Plato and Aristotle: Pages 31-42 ........................................................................ 145 Danielson: Cicero: Pages 50-57........................................................................................... 146 Danielson: Boethius, Maimonides, Dante, Oresme, Cusanus: Pages 80b-96 ........................ 147 Exam 1 Study Guide ........................................................................................................... 158 Wednesday September 29: Exam 1 ......................................................................................... 160 1
Monday October 4 .................................................................................................................. 161 Lab 5: Flat Earth (Room 214), Flat Earth Show (Planetarium). Do Pre-Lab Before Lab! ..... 161 Chaisson, pages 25-34a: Copernican Revolution ................................................................. 171 Copernicus.......................................................................................................................... 171 Danielson: Copernicus: 104-117 ......................................................................................... 178 Kepler’s New Astronomy.................................................................................................... 182 Danielson: Calvin, Kepler, Brahe: 122-131, 163-165, 169-172............................................ 191 Wednesday October 6 ............................................................................................................. 193 Chaisson, pages 34b-41: Scientific Revolution.................................................................... 193 Galileo ................................................................................................................................ 193 Newton ............................................................................................................................... 206 Monday October 11 ................................................................................................................ 219 Lab 6: Copernican Show (Planetarium), New Astronomy (Rm 214). Pre-Lab Before Lab!.. 219 Privileged Planet, Ch. 11: The Revisionist History of the Copernican Revolution ............... 231 Danielson: Galileo, Campanella: Pages 145-154, 173-177................................................... 235 Wednesday October 13 ........................................................................................................... 237 Chaisson, Ch. 2: Light and Matter....................................................................................... 237 Monday October 18 (no lab this week).................................................................................... 238 Chaisson, Ch. 4: The Solar System...................................................................................... 238 Wednesday October 20 ........................................................................................................... 239 Chaisson, Ch. 5: Earth and its Moon ................................................................................... 239 Monday October 25 ................................................................................................................ 240 Lab 7: Distances of Celestial Objects .................................................................................. 240 Chaisson, Ch. 6: The Terrestrial Planets.............................................................................. 254 Wednesday October 27 ........................................................................................................... 255 Privileged Planet: Chemistry, Blue Dot, p. 32-40a, 81-101.................................................. 255 Monday November 1 .............................................................................................................. 261 Lab 8: Galileo’s Inclined Plane. Do Pre-Lab Before Lab!.................................................... 261 Chaisson, Ch. 9: The Sun .................................................................................................... 275 Wednesday November 3 ......................................................................................................... 276 Chaisson, Ch. 10: Measuring the Stars ................................................................................ 276 Exam 2 Study Guide ........................................................................................................... 276 Monday November 8: Exam 2 ................................................................................................ 277 Lab 9: Archimedes’ Principle. Do Pre-Lab Before Lab! ...................................................... 277 Wednesday November 10 ....................................................................................................... 294 Chaisson, Ch. 14: The Milky Way Galaxy .......................................................................... 294 Monday November 15 ............................................................................................................ 295 Lab 10: Privileged Planet Film............................................................................................ 295 Privileged Planet, Ch. 7: Star Probes (p. 127b-140) ............................................................. 295 Privileged Planet, Ch. 8: Galactic Habitat............................................................................ 297 Wednesday November 17 ....................................................................................................... 302 Chaisson, Hubble’s Law (p. 420-426a)................................................................................ 302 Chaisson, Ch. 17: Cosmology ............................................................................................. 302 Monday November 22 (no lab this week) Optional Skywatch Lab Due Monday ..................... 303 Privileged Planet, Ch. 9 & 10: Big Bang & Fine-Tuning (selected pages)............................ 303 Wednesday November 24: Thanksgiving ................................................................................ 308 2
Monday November 29 ............................................................................................................ 309 Makeup Quizzes for Whole Semester.................................................................................. 309 Lab 11: Foucault Pendulum................................................................................................. 309 Chaisson, Ch. 18: Life in the Universe ................................................................................ 320 Wednesday December 1.......................................................................................................... 321 Privileged Planet, Copernican & Anthropic Principles, p. 247-274...................................... 321 Monday December 6............................................................................................................... 325 Lab 12: Galileo Film ........................................................................................................... 325 Privileged Planet, Ch. 15: Universe Designed for Discovery ............................................... 332 Wednesday December 8.......................................................................................................... 335 Privileged Planet, Ch. 16 & Conclusion, p. 313-335............................................................ 335 Final Exam Study Guide ..................................................................................................... 339 Extra Lab Activities ................................................................................................................ 341 Makeup Labs: Video Reports .............................................................................................. 341 Extra Credit Lab: Skywatch ................................................................................................ 344 Old Exam Copies.................................................................................................................... 357
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Wednesday August 25: First Day Orientation US 311 • Dr. Mike Keas • Wood Science 119C • Phone 878-2098 • Email:
[email protected] Pop Quizzes: 20% Lab Reports: 5%
Exam 1: 20% Exam 2: 20%
Final Exam: 35% Extra Credit Lab: 1%
Extra Credit Final Exam Essay: about 2%
Important Things to Understand about this Course • How this course fits into the Unified Studies program: follow the evidence wherever it leads • New this year: Chaisson text, history of science content reduced to 8 days, outdoor lab = EC • How are labs more important than the 5% lab report value suggests? • The “three R’s” of this class: R______________, R______________, R______________ Required Supplies • Test forms (buy bundle of 10 near Nat Sci texts in bookstore) • Miller Planisphere (with Nat Sci texts in bookstore) • Three ring binder in which to place Course Packet Supplies for Optional Extra Credit Lab (Outdoor Skywatch) • Protractor with rotating arm (with Nat Sci texts in bookstore) • Flashlight (perhaps purchase at Big-K or Walmart) What to Do or Know Before the Next Class Period • Buy the readings & supplies and read the Syllabus & Schedule, Part 1, in the Course Packet • First required lab is in Planetarium by foyer pendulum next week • Find 1 or more class partners (need not be in same lab) & put on Student Information Sheet • Complete items due next class period for possible quiz as listed in class schedule in Packet To Request a Lab Switch: Tear off & hand in the form below • I will return this form to you next class period • If your request is granted, process the provided add/drop at Academic Center within 2 days ------------------------------------------------------------------Name: Phone No.: OBU Box No.: Circle Your Classification: Sophomore . . . Junior . . . Senior Graduation Date: Write “enrolled” by lab in which you are currently enrolled. Circle below & rank your 1st & 2nd lab choices (“enrolled” lab might be 2nd choice lab) Lab Time Index Dept. No. Sect. Credit T 7:30-9:20 0345 US L311 1 0 T 9:30-11:20 0346 US L311 2 0 T 12:30-2:20 0347 US L311 3 0 T 2:30-4:20 0348 US L311 4 0 R 7:30-9:20 0349 US L311 5 0 R 9:30-11:20 0350 US L311 6 0 (add this lab and get free gum today) F 12:00-1:50 0351 US L311 7 0 F 2:00-3:50 0352 US L311 8 0 Circle Reason:
1. Convenience/Social Reason
2. Other (specify in writing) 4
Monday August 30 Syllabus, Fall 2004, US 311, Oklahoma Baptist University Dr. Mike Keas, x2098,
[email protected], Office Hours (Wood 119C) Mon. 2-4 & Wed. 4-5 Pop Quizzes: 20% Lab Reports: 5%
Exam 1: 20% Exam 2: 20%
Final Exam: 35% Extra Credit Lab: 1%
Extra Credit Final Exam Essay: about 2%
How US 311/312 Contributes to the Unified Studies Program • Two-semester science sequence that builds upon all other Unified Studies courses • Emphasizes the laboratory, field and cultural-worldview settings in which theories are shaped • Explores the problems, methods and aims of science • Models how to follow the evidence wherever it leads (even if it goes against popular views) • Shows science connected to the everyday demands of practical reason and personal meaning • Analysis of chance, necessity and intelligent design as causes of natural events • Insights of US 311 apply to main current issues of US 312: genetics, origins and environment US 311 Course Description A survey for non-science majors of selected topics in the physical sciences such as planetary motion, mechanics, atomic theory, cosmology and astrobiology. Includes historical development, the scientific method, the relation of science to cultural context and contemporary issues. The planetarium simulates field experiences that complement lectures. We begin with the basic celestial phenomena that were recognized by the makers of Stonehenge (2800 B.C.) and the astronomers of ancient Babylon, continue with the development of physics and astronomy in ancient Greek culture, and follow the appropriation and transformations of these scientific traditions through medieval and modern times. The historical material of this course has been reduced to the equivalent of about eight class periods. The labs that are framed historically are mostly devoted to current science. Required Reading • Dennis Danielson, editor, The Book of the Cosmos (Cambridge, MA: Perseus, 2000) • Gonzalez & Richards, The Privileged Planet (Washington, DC: Regnery, 2004) • Chaisson & McMillan, Astronomy: A Beginners Guide to the Universe. 4th edition (Pearson, 2004) ISBN 0-13-100727-0 • Course Packet (located near several course supply items in the OBU bookstore) Class Attendance & Partners. Come to class ready to discuss readings and take pop quizzes. Packet study guides (and study guides built into the Chaisson textbook) focus your reading. Read study guides before and after each assigned reading; they often tell you to skip certain pages. Students absent for any part of a class period don’t qualify for quiz credit. Select a class partner who will take notes when you are absent. Exams & Quizzes. Exams and pop quizzes especially cover the material in the study guides. You may not take a quiz in a class section other than one in which you are enrolled. Your lowest 5
quiz score is automatically dropped (little “d” symbol on grade print out). There are three class exams, including a comprehensive final. Makeups are only for substantial reasons. Makeup quizzes are created at random from the course and are given near the end of the course (see Schedule). Within a week of a quiz you must provide me with a note explaining your absence. You may take a makeup exam only if you leave me a phone message or contact me in some other direct way on the day you missed an exam (or earlier). For any kind of makeup (quiz, exam, lab, etc.), you must personally contact me by phone, email, or otherwise. Email from anybody else, including the Nurse or Dean of Students’ office, is not sufficient. Test Form & Pencil Policy. Bring computer test form and a #2 pencil to each class for quizzes and class exams. You may borrow them from other students (not me). Part of your grade will reflect how well you follow exam/quiz instructions (avoid penalties). Labs. Labs are required and are assessed through participatory attendance (lab reports that are graded 100%/0%). The PreLab part of a lab (if it exists) must be completed before you arrive at lab. With prior permission you may attend a lab section other than the one in which you are enrolled (plan ahead if you must miss your usual time). Missing 10 minutes of lab results in no credit for that lab. Makeup labs are only for substantial reasons presented within 2 workdays of your lab day. See the makeup lab procedure in the Packet. Makeups do not exempt the requirement to learn the materials of the original lab. Makeup labs drop one letter grade per week they are late (they are due one week after missed lab). Labs and the Organization of the Course Packet • You signed up for a specific lab section that runs sometime Tuesday, Thursday, or Friday • Required labs are arranged in the course packet under the Monday of the week they run • Always bring your course packet to your lab (and lecture) section • Fill out a lab report during the lab time to get credit • Skywatch extra credit lab and makeup video labs are located near the end of the packet Optional Extra Credit Skywatch Lab. Skywatch extra credit lab is due the Monday just before Thanksgiving, but don’t wait till then because the weather might be bad the few weeks prior to the due date. Besides, the skywatch lab will help you a little on exam 1, so it makes sense to finish it before exam 1. Some activities require several observations separated by a few hours, so plan ahead and help others. Disabilities. Contact Student Services, GC 101, to discuss accommodations for this course. Cheating. Any assignment grade will be lowered two whole letter grades in the case of cheating.
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Student Information Sheet Name: OBU Box:
Phone:
YES, post my grades using my OBU student ID number: Sign your name here to say YES _____________________________ NO, you may NOT post my grades Sign your name here to say NO _____________________________ If you don’t sign the yes line above, you will need to make appointments to obtain grade information. •
I read the entire Course Syllabus, signed (your name): ___________________
•
Have you either purchased or have access to all the course materials? _____
•
What are your options if you don’t have a test form for an exam or pop quiz?
•
If you can’t attend your lab session a particular week, get permission to attend another one. I may have to turn you away if you show up unannounced to a lab in which you are not enrolled. Circle below which of the other labs fit your schedule so you can plan in advance for such weeks.
T T T T R R F F
7:30-9:20 9:30-11:20 12:30-2:20 2:30-4:20 7:30-9:20 1:30-3:20 12:00-1:50 2:00-3:50
Class Partner(s): you must have at least one class partner Name:
Phone:
Name:
Phone:
Copy this for yourself before handing in this sheet. 8
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Lab 1: Cowboy Astronomer (Planetarium). Read ASAP! General Notes about Labs and the Organization of the Course Packet • You signed up for a specific lab section that runs sometime Tuesday, Thursday, or Friday • Required labs are arranged in the Course Packet under the Monday of the week they run • Always bring your Course Packet to your lab (and lecture) section • If there is a pre-lab, then complete it before your lab time (there is no pre-lab for lab #1) • Fill out a lab report during lab time to get credit (the first report is on the next page) • The skywatch extra credit lab and makeup video labs are located near the end of the packet • Skywatch extra credit lab is due the Monday just before Thanksgiving, but don’t wait till then because the weather might be bad the few weeks prior to the due date. Besides, the skywatch lab will help you a little on exam 1, so it makes sense to finish it before exam 1. Special Planetarium Lab Rules (for all planetarium labs) • Bring Course Packet • Bring Miller Planisphere • No food or drink in the planetarium • Store your belongings under your chair
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Lab 1: Cowboy Astronomer Report • Name: _________________ Activity: “You’ve been kidnapped, so where are you?” Use a fist held at arm’s length for 10° 1. Two _________ stars on bowl of Big Dipper point to tip of Little Dipper’s handle = _______ 2. Stars appear to move ______________ around Polaris. Why is it called Polaris? __________ 3. Pre-Civil War slaves escaped north guided by a Big Dipper song. Why did they use the Big Dipper rather than the Little Dipper and Polaris? ___________________________________ 4. Orion’s belt almost touches the ___________ equator, which is ________ equator projected. 5. Why have most cultures recognized Orion’s stars as a constellation? ___________________ Celestial Globe 6. The celestial equator on this model is the _________________. Polaris is represented by the ____________________. These two items are ______ degrees apart. 7. Where on earth would it be impossible to see Orion’s belt? _____________ _____________ (Imagine shrinking earth to a tiny point in the model’s center to be get this answer). 8. If Orion’s belt is due north just above your horizon, then where are you? ________________ 9. Ancient Greeks called this plastic model the “sphere of ____________ stars” because they thought that all these stars actually are on a single sphere (not! but it appears so). Nature and Culture Analysis: Naturally there (N) or culturally constructed (C)? 10. Are most constellations primarily a product of nature or culture? NC? ____ 11. Polaris’ special star status (the reason we give it special attention)? NC? ____ Miller Planisphere: A Squashed Celestial Globe with a Viewing Window 12. The planisphere map of the heavens has a hole in the middle that represents _____________. As I rotate my planisphere, the stars visible in the window are those stars visible at a given time from 30° north ______________. 30° is close enough to Shawnee’s _____° to be useful. 13. Face north; hold planisphere upside down with its “north arrow” pointing north. Find the Big Dipper and put its bowl left of the “north arrow,” just touching western horizon. What time points at today’s date? ______p.m. Convert to daylight savings (+1 hour): ______p.m. 14. Planisphere Q: Big Dipper’s bowl will be hard to see tonight _____p.m. to _____a.m. Why (what horizon problems)? _____________________________________________________ 15. Planisphere Q: Orion’s viewing hours (next few days) are: ___________ to ___________ Oh My Stars! 16. Circumpolar constellations never ______ or _____. Which Dipper is circumpolar? Big/Little 17. Nearly circumpolar constellations: Cassiopeia (______ shape) Cepheus (__________ shape) 18. Winter Hexagon: 1. Rigel is _______’s foot, 2. Sirius (brightest star) is in CANIS ________, 3. Procyon is in CANIS ________, 4. Pollux/Castor are the twin stars of _______, 5. Capella is in AURIGA, which is a _______ shape, 6. Aldebaran is a red eye of a ______ (TAURUS). Extra Credit Skywatch: Ask for red cellophane to put on flashlight so night vision isn’t inhibited.
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The Rose: An Exercise in How We Experience the World Aim: Identify the levels at which we experience the world (prior to developing theories) What does science explain? Before we investigate the historical development of science, it is helpful to think a little about the different aspects of reality that various fields of science will try to explain. Throughout the course we will refer back to this activity, so please give it your best effort. The ideas and terminology introduced here will help you analyze any particular episode in the history of science. Imagine that you gave/received a beautiful red rose to/from a friend. In this event you and the rose reflect reality at more than one level. What do you experience? What dimensions or levels of reality are reflected in this event? Let’s identify some of these aspects or dimensions of reality by filling out Reality Table #1 on the following page (according to the directions below). Directions (Reality Table #1) 1. In the 1st column describe the rose as you might experience it. 2. In the middle column describe the rose in itself, to the extent necessary for us to experience it in the way that we actually do. 3. On any given row, fill out either the 1st or the 2nd column, but not both. 4. In the 3rd column assign a name to the aspect of reality described in a previous column. 5. Add as many rows as necessary, one for each aspect you can think of. 6. Hint: What might you say or think when you see, select, care for, or remember the rose? Aspects of Reality By reflecting in this way on the experience of giving or receiving a rose, we may identify a number of different aspects or dimensions of reality, as shown in the right hand column of Reality Table #1. o The aspects in the right hand column are not things; they are adjectives we may use to describe the different modes of our experience of any real thing. o We experience the reality of a rose in many modes or levels. o The name or description of each row in the right hand column is an abstracted dimension of our experience, an abstracted aspect of a much fuller reality. Study Questions for Reality Table #1 1. How would you rank the aspects of reality you identified? Are some preconditions of others (in order to have one in operation, must certain others also be in operation)? 2. Might this table be completed in different ways? 3. Might the aspects or dimensions be called by different names? 4. How can we know if we have a complete list, or if we need to add additional rows?
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Reality Table #1 Complete the following table according to the directions on the previous page. Then reflect on each the study question (previous page). Person Giving or Receiving a Rose “How much did it cost”?
The Rose Itself
“Ouch!”
Aspect or Dimension of Reality Economic Sensory
Number of petals
Quantitative (numerical)
When finished with the table and the Study Questions on the previous page, compare your reflections recorded in Reality Table #1 with Reality Table #2 on the next page. 15
Reality Table #2: Some Aspects/Dimensions of Pre-Theoretical Experience of Reality1 Person Rose “Thank you” (response of numinous awe) “With all my love” “This is your rose” “How beautiful!” “How much does it cost?” “I’ll communicate love with a rose.” “My love is like a red, red rose....” “I grew it in my own rose garden.” “It differs from other plants because of its fragrance and prickly stem...” “Mmmm” (nose); “Ouch!” (finger) Growing Synthesizing oxygen Matter, individuality Bends in the wind Location Number of petals
Aspect/Dimension Worshipful, meaningful Ethical Juridical Aesthetic Economic Social Linguistic Historical-cultural Logical, analytical Sensory Biotic Compositional Physical Kinematic (motion) Spatial Quantitative
In the first column, above the double line, are some aspects of the rose as we experience it. The rose is a passive object of our experience reflecting these dimensions of reality. In the second column, below the double line, are the aspects of reality in which the rose functions actively, where the rose is its own subject regardless of our experience—which is a pre-condition of our experience of any particular rose in the first place. Think for a moment about an object’s heaviness or weight. Independent of any particular theoretical explanation of weight (Aristotle’s, Newton’s, or Einstein’s), humans have a capability of perceiving heaviness. To which aspect of reality would you assign weight? (Choose from those listed in the right hand column). Make up your own mind before checking our answer in this footnote.2 What matters is not the precise way we construct a “reality table,” but that we recognize that each thing or event that we experience has diverse aspects that cannot be reduced to a single one. Reality is rich and multi-dimensional. Reality Table #3 (next page) shows how our awareness of multiple aspects of reality traces back to the history of science and culture. We will refer back to this table and the rose exercise on numerous occasions later in this course.
1
2
We have adapted this exercise of the rose, and the table of aspects of reality, from the twentieth-century philosopher of science Hermann Dooyewerd with the assistance of Kenn Herman and Roy Clouser. For an in depth analysis of the aspects of reality and their significance for both the philosophy of science and a Christian world view, see Roy Clouser, Myth of Religious Neutrality (Notre Dame, 1992). We locate weight in the “physical” aspect. “Weight” is one of the physical properties of things that are superadded to, or not considered by, the quantitative, spatial, and kinematic aspects.
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Study Questions for Reality Table #3 (below) 1. Are most sciences devoted to a single aspect of many things, or to a single thing under many aspects? 2. How does the emergence of new disciplines (as shown in the history of science) help us to distinguish new aspects of reality? 3. If the number of aspects and the boundaries between them are grasped through historical study of the development of disciplines, including through reflection upon the history of science, then how precarious is the claim that disciplines devoted to different aspects will never, and can never, entail overlapping domains of study (e.g., evolutionary biology and theology)? Reality Table #3 Aspect/Dimension Description Worshipful, Commitments, ultimate meaningful meaning, response to awe Ethical Love, values Juridical Justice Aesthetic Beauty, harmony Economic Use of money and talents Social Social relations Linguistic Symbolic communication Historical-cultural Formative, generational (capability to form capability new things from pre-existing ones)3 Logical, analytical Drawing distinctions
Sciences Theology, Metaphysics Ethics Jurisprudence Aesthetics, Art Economics Sociology Linguistics History, Historical Geology, Evolutionary Biology, Big Bang Cosmology Logic
Sensory4
Sensations, emotions
Psychology
Biotic
Life
Biology
Compositional
Combine parts to make new wholes Energy, matter Motion Magnitude, extension Discrete quantities
Chemistry
Physical Kinematic5 Spatial Quantitative
3 4 5
Physics Kinematics Geometry Arithmetic
Practices Worship, confessions, creeds, prayers, statements of ideals Moral reflection, counsel Courts, legislation Painting, music, architecture Business, banking Associations, interactions Using language (French, etc.) Explanation by means of reconstruction of contingent events (developments that could have been otherwise) Probing theories, classifying by creating distinctions, drawing abstractions Probing feelings, behavior. Aristotle’s animal soul Health, hygiene, conservation. Aristotle’s plant soul Aristotle’s mixts. An organic chemist makes an artificial dye Aristotle’s four elements Plato’s astronomy Euclid’s geometry Babylonian mathematics
This is a precondition for the higher levels of reality, and results in material and cultural artifacts that alter the conditions of existence in contingent (non-necessary) ways that might have been otherwise. As any rose gardener knows, the results of horticulture are quite contingent! The sensory aspect of reality covers the qualities and laws of both perception (touch, taste, sight, smell and hearing) and at least the rudiments of feelings that are directly elicited by perception (fear, happiness). The “kinematic” dimension is motion abstracted from matter and physical reality, without reference to force, energy or mass.
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The foregoing analysis of the dimensions of pre-theoretical reality is only tentative; the tables are constructed by reflecting empirically on actual experience, rather than by merely a priori (armchair) reason. We began with the example of the rose, but the identification of different aspects of reality ultimately rests upon a consideration of the historical development of separate scientific fields or subdisciplines, such as arithmetic, geometry, kinematics, and dynamics. The table is always subject to revision as more levels of reality are distinguished during the historical development of science. As suggested by Reality Table #3, properties and patterns found in each aspect of reality often correspond to a single field of science or are expressed in a number of similar practices. For example, the modern discipline of physics includes the study of the physical aspect of reality. Ancient Greek “natural philosophy” (= “physics”) at various times in different ways included within its domain not only the physical aspect of reality, but also such aspects as the quantitative, spatial, and even the biological aspect. Since the boundaries of the sciences devoted to one or more of these aspects (or a subdivision of an aspect) have changed through time, the exact list drawn up at any place or time must be tentative and provisional as well. On the other hand, not all sciences are defined by the aspect they study. A few sciences—(one might suspect, for the most part, immature disciplines?)—are devoted to a single class of things as seen under many aspects, rather than as seen under only one aspect. For example, medieval and early modern Theories of the Earth were devoted to the subject of the Earth, but under many aspects until the most fruitful aspects for inquiry were distinguished and recognized. Eventually Theories of the Earth transitioned into the modern discipline of geology that was devoted chiefly to the historical aspect of the Earth.
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Science and Faith Before you read this essay, look over the study questions that are found at the end of it to anticipate what you will learn. Then, as you read, take notes that answer those study questions. We will refer back to the issues raised here often in this class. We hope this course will be relevant to you by sharpening your ability to recognize and critique the assumptions that lie behind arguments in any cultural activity (such as the subject of your own major studies) —not just science. A Christian worldview in the arena of science (or any other academic discipline) bears no resemblance to a “Christian” nature poster that is superficially sanctified by the quotation of a Scripture verse in one corner. If integration were that easy, Christian bookstores could package it in a plastic wrapper, and no one would need to get it from a Christian university. Rather, integration of faith and learning in a liberal arts context must take place on a worldview level. To defend this claim, we offer a long connected argument below, in which numbered sentences indicate our claims or theses. Such sentences are placed where there are general changes of emphasis, and do not mark abrupt transitions between discrete sections. Come to class prepared to discuss our theses. All opinions are welcomed in this class! Thesis 1. No person engaging in science or any other kind of intellectual work can completely avoid the “imposition” of interpretative patterns that make sense of experience and data. No one can think theoretically or act intentionally without a worldview. The early modern astronomer Johannes Kepler is an illuminating example of the interplay between open self-criticism and worldview commitment. Kepler’s celestial laws, described in any modern physics textbook, were derived from a cosmological scheme based on a Christian Neoplatonism featuring the five regular solids of the Pythagoreans. Kepler’s diagram (left) shows the five regular solids in the Creator’s blueprint of the universe.
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The Five Regular Solids: For each regular solid, every face is identical (e.g., a square for the cube) and every angle is identical (e.g., 90° for the cube).6
Solid Face Number of Faces Tetrahedron Equilateral triangle 4 Cube Square 6 Octahedron Equilateral triangle 8 Dodecahedron Equilateral pentagon 12 Icosahedron Equilateral triangle 20 For complex worldview reasons, Kepler believed that music and astronomy needed to be unified on a theoretical level, and that these geometrical solids would enable him to do so. The imposition upon the cosmos of that now-refuted cosmological scheme enabled Kepler to see farther than any observations could then justify by themselves. Nor was that interpretative scheme abandoned by him as a result of Tycho’s observations. Indeed, Kepler never abandoned it. J. V. Field explains:7 The ‘perfected astronomy’ derived from Tycho’s observations led Kepler to modify the theory described in the Mysterium Cosmographicum. However, there was no need for any drastic modification of the theory, which Kepler clearly still regarded as intellectually satisfying, mathematically justified and in fairly good agreement with the observations. He believed that the differences between the theory and the observations 6
The Pythagorean solids and Kepler’s cosmology will be explained later in this course (you don’t need to memorize these details now!). Thanks Jim for the 5 regular solid images: http://www.jimloy.com/geometry/hedra.htm 7 Kepler’s Geometrical Cosmology, Chicago, 1988, p. 94.
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were real and must be explained, but they did not seem to him to be so large as to cast doubt upon the essential correctness of the theory. Kepler’s geometrical solids are representative of the complex relations between theory and observation that are manifest generally throughout the history of science. Historically, major astronomical discoveries have not resulted from the simple accumulation of positive facts or undeniable evidence. Rather, theory and observation have proceeded in a dialectic of mutual adjustment and, in many cases, theory (the imposition of explanatory patterns) has led observation rather than vice-versa. For another example, when he conceived the heliocentric cosmos, Copernicus’ aim was been merely to equal Ptolemy in mathematical power, not to account for new observations. Observations did not compel him to hurl the Earth into the heavens or move the Sun to the center. Copernicus’ De Revolutionibus (1543) included only 27 of Copernicus’ own “observations,” none of which were crucial to any of his major propositions, and many of which were sub-horizon phenomena (events that happen below the horizon can’t actually be observed —these manufactured “observations” were only intended to illustrate his theory). How would a “positivist advocate” of complete “open-mindedness” explain the fact that the first direct observational evidence of the rotation of the Earth was discovered by Foucault in 1851, nearly three centuries after Copernicus? Worldviews (and their religious cores) continue to play important roles in the natural sciences today, although often in more subtle ways. This subtlety results from the modern tendency to try to keep worldview and religious considerations at arms length from the practice of science (despite the continued and necessary role of worldviews in science). To the extent that worldview considerations are difficult to identify in science, they are like cranes used in the construction of a skyscraper (we owe this analogy to Steve Wykstra). Their role in construction is often forgotten once the building reaches a certain stage. In science, this stage corresponds to the process of explaining natural phenomena within a fairly stable theoretical framework. Many assumptions necessary for certain types of research in science, as reasonable as they may seem upon inspection, are not visible to scientists or to most others in their daily work within a particular research tradition. Modern science has not developed as a simple accumulation of theory-independent observations. One does not have to be a postmodernist or a relativist to insist that un-interpreted data or evidence simply do not exist—or at the very least, cease to exist as soon as they are talked about. Rather, in the formulation and selection of problems to address, and in the specification of criteria by which evidence shall be interpreted, scientists as human beings actively shape the conclusions of all inquiry. Theory-making in any academic discipline, like any field of science, necessarily entails in advance the existence of perspectives on the kind of thing one is investigating—perspectives which precondition the very “data” that could possibly “appear” to the investigator’s mind. It is a part of honest inquiry to acknowledge this. It is the same with teaching. Instructors make innumerable “judgments” in course design that constrain and precondition “whatever data might appear” in the classroom. The professional and ethical response to this inevitability is to ensure that questioning and debate are welcomed. This requires that as many of the major viewpoints as possible are made available to students, so that students can hear of minority views that they may wish to pursue. But just as importantly, an 21
instructor ought to identify and communicate to students his or her own principles of inquiry and his or her own theoretical perspectives on a given subject. This honesty and openness not only offers students a mature and informed scholarly example (one which they may choose to adopt or not), but immeasurably assists students in their critical evaluation of the bias inherent in the classroom. If done well, it provides a model of self-scrutiny in a personal dialectic that can further stimulate debate. On the other hand, if such open self-disclosure is not attempted at all, one falls back upon the pretense of an apparently unconditioned discovery-experience by means of “whatever data might appear.” The appearance of un-interpreted evidence and unfiltered experience is only an illusion that amounts to covert indoctrination or subtle manipulation, which however benign, is the antithesis of the ideal of a liberal arts tradition as fostering a selfexamined life. (We attempt this sort of self-disclosure in the present essay.) Both professors and students ought to have the freedom to develop and express informed opinions. To do so in a way that is in keeping with the tradition of the liberal arts is to lay all your cards on the table, to make explicit where you stand and the reasons for your stance, and to treat opposing stances as fairly as possible. It is futile, and therefore misleading, for a professor to try to hide his or her own perspective from students on matters central to the discipline. Students will be able to evaluate a professor’s instruction more critically and thoroughly if the professor makes plain where he or she is coming from. To attempt to remain neutral on organizing perspectives is itself to take some kind of position. As Huxley wrote in 1937: “It is impossible to live without a metaphysic. The choice that is given is not between some kind of metaphysic and no metaphysic: it is always between good metaphysic and a bad metaphysic.” (Ends and Means, p. 252.) Chesterton commented: “Men have always one of two things: either a complete and conscious philosophy or the unconscious acceptance of the broken bits of some incomplete and shattered and often discredited philosophy.” (The Common Man, p. 173.) A liberal arts education should not allow a teacher to foist one’s opinions on students, but it does require that a teacher open up the foundations of one’s opinions to examination, as well as the foundational notions that guide the interpretive strategies of the authors whose works are being read by the class. Professors also ought to encourage students to critically evaluate their own perspectives on the subject matter of the course. A liberal arts educated person is not someone who is uncommitted to any particular views on a subject (which amounts to another position in its own right), but rather one who holds his or her views in a self-examined manner. To claim to know truth is not antithetical to liberal arts education if one is willing to defend one’s claims in open dialogue. Thesis 2. Each participant in the liberal arts tradition of science legitimately seeks for integration between specialized disciplines (the quest for a unity of truth). For a modern application of holding examined views in a quest for a unity of truth, consider biologist Edward Wilson’s revealing rhapsody on evolution: “Guided by no vision, bound to no distant purpose, evolution composes itself word by word to address the requirements of only one or two generations at a time.” We would be disappointed if anyone were to suggest that Wilson offers an example of an unbiased researcher who has merely examined the evidence and thus come to whatever views he now holds. While Wilson is certainly able to avoid intellectual paralysis and to develop an ethic and a worldview, Wilson’s interpretation of biology and evolution is driven by his sociobiology program that intends to reduce every aspect of human culture (even religion) to our biological nature. We applaud Wilson’s conscious integration of 22
his materialistic worldview and his science. However, those who deny his sociobiology and its materialistic worldview components may legitimately impose different worldview patterns on the evidence in order to pose heretofore overlooked questions and uncover heretofore unsuspected evidence to make a rational case against Wilson’s integrated system of scientific beliefs. To do so would not be to change the subject from science to religion (or something else), but rather to engage in the same sort of activity as Wilson, but to do so from different presuppositions and to arrive at different conclusions that one thinks best interprets the relevant scientific data. Rather than a change in subject domain, this is merely a change in the intellectual formation of the same problem, and to different conclusions. For instance, one may conclude, as does biochemist Michael Behe, that the best available scientific evidence regarding life’s origin points to the injection of non-materialistic information (intelligent design) into DNA/RNA in order to have a minimal level of complexity that is characteristic of biological life. Such inferences to design constitute different answers to the same scientific questions that Wilson addresses (rather than an essential change in subject, as charged by those who cry out “but that’s not science”). To attribute some sort of privileged objectivity to scientific worldviews like Edward Wilson’s (at the expense of Michael Behe and many others) is contrary to the tradition of liberal arts endorsed here, where open criticism of one’s foundational assumptions is fostered or encouraged, and never ruled out of order (even with respect to scientific authority). There is much work to be done in science, and those (like Kepler, Wilson, or Behe) who inform their work with deep perspectives (not superficially sanctifying clichés) are likely to push farther along because of those “imposed” perspectives. Thesis 3. Faith and reason are closely related for all theorists at a deep presuppositional level (basic assumptions, often not consciously identified by the theorist). No one is without faith commitments, regardless of common claims to religious or worldview neutrality by scientists and other scholars. All reasoning involves faith commitments embodied in one’s first principles, and reciprocally, all faith involves reason. The two are not separable enough to merely talk about the need to integrate the two; more often the difficulty lies in identifying the hidden ways in which they are already dialectically related in one’s discipline or one’s thinking. All significant arguments (scientific and otherwise) involve many presuppositions. Faith and reason are not two independent sources of knowledge, but both spring from the heart, the essentially religious faculty referred to by scriptures as the seat of worldview commitments. Following the clear discussion by Roy Clouser in The Myth of Religious Neutrality, we may define “faith” or “religious belief” as a heart-deep response to what a person takes to hold the status of divinity. By “divine” we mean, “that which is able to exist on its own without depending on anything else” (this definition is consistent with traditional Western usage from Aristotle to Aquinas and thereafter... even William James agrees with us here, and it appears to be implicit within the Bible). In this sense one’s divinity could be Yahweh, matter/energy, Number, form, self, or almost anything else. “Idolatry” would be to attribute the status of divinity to anything that is not actually divine. If you feel uncomfortable defining religious belief as we have done, you are free to disagree. For the analytical purposes of this course, however, we will use these definitions to explain the role 23
of core assumptions (fundamental beliefs, central worldview components, whether you like calling them “religious” or not) in the practice of science. When we define a “religious belief” as a heart-deep response to what a person takes to hold the status of divinity, we are referring to the implicit and/or explicit “trust” that one places in one’s perception of the core or source of reality and the actions and thinking that proceeds from this trust. We are not over-intellectualizing “religious belief” because we recognize that someone’s godly grandma may very well not spend any of her life reflecting consciously over the “self-existence” of God. Yet her adoration of God presupposes a heart-deep response to what grandma takes to hold the status of divinity (even though she may not consciously recognize the core feature of “divinity” as “self- existence”). Review these definitions before reading further: • Religious Belief: a heart-deep response to what a person takes to hold the status of divinity. • Status of divinity: that which is considered able to exist on its own without depending on anything else for its being or character. Thus far, we have been arguing that we begin the life of the mind with some sort of religious belief (whether consciously held or not) about what holds the status of divinity (either a belief in the true divinity or in an idol) and how things are related to the divine. Those who believe in a false divinity undermine their ability to most fruitfully investigate nature to the extent that these core worldview assumptions are fleshed out in the principles and habits of mind that guide scientific research. Any attempt at explaining the world, when traced back to its roots, will entail some form of belief about that which can exist on its own (the ultimate, the nondependent). Even people who claim to have no belief about what is nondependent will at least unconsciously presuppose some such belief in order to have even the most rudimentary and fragmentary basis for making sense out of their own daily experience and the cosmos in which they live. Everyone presupposes some sort of divinity, whether consciously or not, in the way that they live out their lives and understand what occurs in daily experience. For instance, the role that God plays in my explanations of daily life (and science) as a Christian, is a role that everyone must, in actual practice, fill with something. If you fail to identify which conception of deity a person has embraced (due to cultural distance or deliberate evasion or something else), do not conclude that such an instance falsifies our thesis about the religious or worldview non-neutrality of all humans. Thomas Torrance, a leading Christian theologian with advanced expertise in science and philosophy, offers a penetrating analysis of the subtle and necessary role of belief in all human rationality: “science and belief are not to be treated as opposed to one another but rather as belonging to one another and as operating together in the acquisition of knowledge” (Facets of Faith and Science, volume 1, p. 152ff). And more forcefully, in this same essay on “Ultimate and Penultimate Beliefs in Science,” he writes (Facets, p. 154): ... it is irrational to contrast faith and reason, for faith is the very mode of rationality adopted by the reason in its fidelity to what it seeks to understand, and as such faith constitutes the most basic form of knowledge upon which all subsequent rational inquiry proceeds. There could be no rational inquiry, no reflective thought, without prior, 24
informal knowledge directly grounded in experience and formed through the adaptation of our minds faithfully to the nature of things.... At its root faith is the resting of our mind faithfully upon objective reality (that which really is, “the nature and truth of things”), with due consideration to human fallibility. But one’s informal knowledge directly grounded in experience (the nature of things as intuitively grasped before one attempts to go about explaining things in the world) is distorted by sin—our rebellion against God. For Christians, sin’s distorting affect is in the process of being corrected by the grace of God through Christ by the renewing of our minds. Although this does not mean that all of our thinking will be correct, it at least points us in the right direction when it comes to our core worldview components, which in turn affect all of our attempts to explain things that we encounter. For those who reject God’s offer of grace through Christ and thus necessarily (consciously or unconsciously) replace the true God with a substitute of some sort (and idol), this false attribution of divinity will distort that person’s “informal knowledge directly grounded in experience” and thus distort all other their attempts to explain things. Non-Christians can still discover truth (by God’s common grace to all humans) and Christians have historically appropriated massive amounts of such knowledge (hopefully with an attempt at a Christian critique). Consider, for instance, how a Christian perspective on mathematics might take shape and distinguish a Christian from a non-Christian mathematician. Although we can all laugh at the notion of there being a distinctively “Christian” proof for a mathematical theorem, we would fool ourselves if we were to write off all of mathematics as neutral with respect to the truth claims of Christianity. Foundational perspectives at the heart of mathematics—that is, at the presuppositional level in which faith-discipline integration takes place—deal with vital questions such as what it is that mathematical symbols represent, or whether mathematical expressions such as 1+1=2 are true (or necessary, which is a different question). Such issues remain hotly debated, and rightfully so, because they arise from clashes among different worldviews, that is they arise from each person’s worldview-mediated “informal knowledge directly grounded in experience.” Two examples will suffice. The Pythagoreans held to the divinity or self-existence of Number. To them, numerical entities were eternal and immutable. All objects in the universe depended, in their view, upon Number and the relations between numbers. A Pythagorean prayer to the number ten has been preserved: “Bless us, divine number, thou who generatest gods and men! O holy, holy tetraktys, thou that containest the root and source of eternally-flowing creation!” Before we all laugh because of the unexpected presence of religion in mathematics, let’s jump to Stephen Hawking (widely considered the greatest living physicist), who is searching on a quest as if for a holy grail to find a mathematical equation for the universe so compelling that, of itself, it could call the universe into existence. Hawking is not far from a Pythagorean-like perspective, and from a Christian worldview one would properly consider his (admittedly elegant) mathematical physics to be idolatrous, in that it implicitly attributes the status of divinity (selfexistence) to Number. A Christian critique of such perspectives would retain the truths of whatever Hawking and other theorists of the past have constructed mathematically about the world, but then recognize the absolute dependence upon God (Yahweh) of the quantitative aspect of reality (which mathematics especially deals with). 25
Current cosmological and biological origins issues, among others, also illustrate the presuppositional interplay of faith and reason. A typical position taken by a “secular” or socalled “neutral” university professor is methodological or philosophical naturalism (more often than not, without explicit discussion of the problem). Methodological naturalism supposes that religious beliefs, such as the possibility of direct acts of God, should not be considered in scientific inquiry. Philosophical naturalism entails the stronger stance that there is no such thing as the supernatural at all. In either case, research into questions of cosmological or biological origins is placed within an intellectual straightjacket by assuming before investigation that the answers must not entail supernatural components. Unfortunately, even historical research is affected by such a straightjacket, for methodological naturalism underlies many claims that certain forms of science were not scientific at all (e.g., Babylonian astronomy). The bias of methodological naturalism is a different and prior issue than whether one concludes, after inquiry, that natural causes were at work. A consistently thinking Christian theist may conclude that God only set up and sustains natural laws that give rise to life and its diversity, or that he directly created the basic types of organisms of Earth, or any position between. We encourage our students to explore these and other Christian options and we do not coerce nonChristian students to adopt views unrelated to their own faith-commitments. We attempt to follow God’s example of not forcing people to accept His grace in Christ in that we don’t coerce students to accept either “mere Christianity,” or our particular interpretation of the Christian perspective on the various areas of science and history that we deal with in class. Torrance (Facets, p. 134) skillfully summarizes such an understanding of the interplay of belief and reason in the operation of the mind (in science or any discipline) in his affirming synopsis of Michael Polanyi’s work (physical chemist—turned philosopher of science): Hence, he [Michael Polanyi] calls us to recognize fundamental belief or intuitive apprehension as the source of knowledge from which acts of discovery take their rise, for it is in belief that we are in direct touch with reality, in belief that our minds are open to the invisible realm of intelligibility independent of ourselves, and through belief that we entrust our minds to the orderly and reliable nature of the universe. Belief of this kind is a commitment to the compelling claims of truth over which we have no control [contrary to postmodernism] but in the service of which our human rationality stands or falls. Faith and rationality, intuition and reason, are from beginning to end intrinsically interlocked with one another. In short, it is not a matter of whether faith will inform reason, but rather which faith will inform reason! Indeed, the “fear of the Lord is the beginning of wisdom,” (the thesis of the book of Proverbs) or, as medieval scholars often expressed this, “we believe in order that we may understand.” Thesis 4. A liberal arts education in science is not contrary to Christian education. We have always maintained that Christians should “search out the unity of truth under the Lordship of Christ.” Is this inconsistent with a liberal arts education in science, because it violates honest free inquiry? On the contrary, we have shown above that no one can theorize without worldview pre-commitments; the Christian is not unique in this. Moreover, such precommitments are often productive, as with Kepler and Wilson. Flannery O’Connor, the 26
twentieth-century writer, pointed out that someone with a perspectival vision can hold their ground and not fall prey to fashionable but ephemeral ideas: “What kept me a skeptic in college was precisely my Christian faith. It always said: wait, don’t bite on this, get a wider picture, continue to read” (Habit of Being, p. 477). Nor does the presence of such pre-commitments close off inquiry by predetermining one’s conclusions; as O’Connor insisted, “Dogma is the guardian of mystery” (Habit of Being, p. 365). Yet cultural myths die hard. It is commonly believed that “centuries of Christian rejection of scientific approaches” are typified by belief in a flat Earth prior to Columbus, or by the priests’ refusal to look through Galileo’s telescope. We will explore the “flat-Earth myth” later, but the mythic Galileo anecdote requires a specific response. How many people in our culture have heard of this story? In contrast, how many know that two of the first defenses of Galileo were written by priests, Foscarini and Campanella? Moreover, Galileo was in Rome just one year after his telescopic discoveries, expressly at the invitation of the Jesuit astronomers of the Collegio Romano. The latter unanimously confirmed his discoveries and reported to the Pope that his “telescope” was reliable. Most opposition to its use came not from astronomers or priests, but from Aristotelian natural philosophers (= “physicists”) in the universities. These Aristotelian physicists were threatened by the mathematical approach to physics championed by Galileo. In addition, Aristotelian natural philosophers questioned the optical integrity of the instrument, in part because of the historical association of optics with magical illusions. Apparently modern perceptions of the history of science are not always fair or self-examined either. This is understandable, of course, given the arcane nature of the historical evidence and the prevalence of cultural myths about Galileo. What is more troubling than hasty simplifications such as “centuries of Christian rejection of scientific approaches” would be a modern “natural philosopher” refusing to acknowledge that we all look through perspectival, worldview telescopes. What matters most is whether one’s pre-commitments are explicitly identified and openly acknowledged, or whether they are concealed and left unexposed to the light of critical probing and examination. We are grateful to work for an institution that advertises itself as a distinctive Christian liberal arts university. We hope to live up to the expectations of those students who are attracted to this university partly on the basis of its Christian institutional identity. Our views are in keeping with the “principle objective” of helping students “mature intellectually, think critically, objectively, and independently, and develop sound judgments”8 and the equally important and noncontradictory aim of being concerned with “issues of faith, particularly those which bear upon the process of liberal education and the subject matter of [one’s] discipline.”9 George Marsden’s The Soul of the American University: From Protestant Establishment to Established Nonbelief (Oxford, 1994) analyzes Christian belief in the academy as part of the pluralistic situation we have described. According to Marsden, there was a “fatal weakness in conceiving of the [American] university as a broadly Christian institution.” This weakness centered on two assumptions: “its commitments to scientific [positivistic] and professional ideals and to the demands for a unified public life.” In this essay we have denied the positivistic 8 9
We understand "objectively" not in a positivist fashion but as holding critical and self-examined views. Faculty Handbook, 2.10 "Faculty Rights, Responsibilities, and Professional Ethics," page II-49, paragraph A.2. OBU Faculty Handbook, 2.10 "Faculty Rights, Responsibilities, and Professional Ethics," page II- 50, paragraph A.7.
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assumption of an allegedly neutral professional investigator, as well as the expectation of a uniform academic life (everyone reaching the same conclusions regardless of their presuppositions and worldview). Had we aspired to either of these two impossible ideals, we would have to concede that a Christian liberal arts education is obsolete, for the reasons Marsden explores. Many Historians Recognize that Christianity Contributed to the Progress of Science Not only can we argue that science is not religiously neutral, but a strong case can be made for the following positive ways in which Christianity actually benefited science: 1. Christianity played a significant role in the development of the experimental method in science. The Christian insistence on divine freedom undercut the view, established by Plato and Aristotle, that the structure of the cosmos is a necessary one. And if the universe is contingent on a Creator’s specific purposes, that is, if it could have been made other than it is had the Creator only so chosen, then experimental techniques as well as rational speculation must be employed in order to understand it. 2. Christianity entails humility as well as confidence in human knowledge. Confidence derives from the intelligibility and the inexhaustibility of divine wisdom. At the same time, the Christian doctrine of the Fall of Adam and Eve provides an explanation for the difficulty of human reason to achieve certainty in understanding the cosmos, with a consequent emphasis on the testing and challenging of hypotheses. 3. Christianity provided an environment conducive to scientific inquiry in the late Middle Ages, which served as a crucial foundation for the rise of early modern science. Although this thesis goes against popular images of the “Dark Ages,” actually medieval civilization was no worse for science than any other time, including our own, although no period may be held up as a golden age. While acknowledging that important natural philosophers like Ockham were excommunicated, we must still remember that Ockham attempted to base all of his thinking upon the Nicene Creed and the affirmation of divine omnipotence. The relations between science and Christianity are complex, but rarely if ever can they be accurately described as at war. And believe it or not, modern university students usually understand far less about observational astronomy than the minimum knowledge of students at medieval universities!10 Noted conservative scholar Russell Kirk argues that academic freedom, including free scientific inquiry, enjoyed strong support in the first universities, which were founded in medieval Europe. This academic freedom, he argues, was not despite but because of the influence of Christianity. The Christian worldview that dominated early universities encouraged the liberty to pursue truth. Confident in a unity of truth, Kirk writes: 10
Every medieval university student, for example, could explain the true causes of the seasons and of lunar phases. In contrast, a well-known documentary film recorded that seniors standing in line for commencement exercises at Harvard were more likely to offer the mistaken explanations that the seasons are caused by the Earth’s changing distance from the Sun, and that the phases of the Moon are caused by the Earth’s shadow upon the Moon. (Can you explain what is wrong with both of these explanations?) 28
The teacher was a servant of God wholly, and of God only. His freedom was sanctioned by an authority more than human. Now and then that freedom was violated ... yet it scarcely occurred to anyone to attempt to regulate ... the freedom of the Academic .... In medieval times, it was precisely their Christian framework that gave masters and students this high confidence. Far from repressing free discussion, this framework encouraged disputation of a heated intensity almost unknown in universities nowadays.... They were free from a stifling internal conformity, because the whole purpose of the universities was the search after an enduring truth, beside which worldly aggrandizement was as nothing. They were free because they agreed on this one thing, if on nothing else, that the fear of God is the beginning of wisdom.11 Arthur Holmes, in The Idea of a Christian University (p. 69), expands on this point for today’s university: Academic freedom is valuable only when there is a prior commitment to the truth. And commitment to the truth is full worthwhile only when the truth exists in One who transcends both the relativity of human perspectives and the fears of human concern. 4. Christianity encouraged the improvement of life on Earth through the application of science. The Fall also offered a caution against the identification of natural law with perfect being, divinity, or the moral law, which would constitute idolatry of nature. Finally, the story of the Fall was conjoined with a mandate to improve or reclaim the quality of human life as far as possible through the application of scientific knowledge. For example, when trees were no longer worshiped as embodiments of the divine, they could be harvested to improve the conditions of human life, although not indiscriminately without regard to an ethic of biblical stewardship. Study the questions and glossary on the following pages.
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Russell Kirk, Academic Freedom (Regnery, 1955), p. 18.
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Study Questions 1. How are the prominent scientists Kepler and Copernicus illustrations of Thesis #1, that no person engaging in science or any other kind of intellectual work can completely avoid the “imposition” of interpretative patterns (worldview)? 2. What is problematic with talking about “faith” and “reason” as two separate things? 3. Does everyone have faith commitments or “presuppositions”? What about agnostic cool George (perhaps a friend of yours) who says he has no religion? 4. How do Magruder and Keas define “status of divinity”—that is what kind of a claim is one making when one identifies something as “divine”?12 5. What is “divine” (what holds the status of divinity) in the opinion of one of the most brilliant physicists alive today—Stephen Hawking? 6. Define “methodological naturalism.” Is this approach to science religiously neutral? This is a commonly accepted “rule” for doing science. Defend your answer carefully in light of our definition of “religion” as assertions about what is “divine.” 7. Is a search for truth under the Lordship of Christ inconsistent with liberal arts free inquiry? 8. How might one argue that an allegedly worldview-neutral study of science is only an illusion that amounts to covert indoctrination or subtle manipulation? 9. Are we abandoning an “objective” and “unbiased” study of science by taking a Christian approach to science? How might one defend either answer to this question? 10. “Guided by no vision, bound to no distant purpose, [biological] evolution composes itself word by word to address the requirements of only one or two generations at a time.” How is this quotation from prominent Darwinian biologist Edward Wilson evidence that his approach to science is biased by particular worldview commitments? 11. Do you think most scientists are aware of the major contributions Christianity has historically made to the progress of science (we listed four contributions as the end of the reading)? 12. Study the glossary/questions (next page) as part of your preparation for class discussion of this essay.
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This definition is not really ours; it is the common legacy of western philosophy, shared by Aristotle, Aquinas, Calvin, and more recently elucidated in Roy Clouser’s excellent book The Myth of Religious Neutrality.
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Glossary Culture: The totality of human creativity & intellect in a particular place and time; shared meanings and forms of storytelling. Technology: The attempt to control natural phenomena. Compare and contrast the meaning of the terms “science” and “technology” as defined above, and give examples. Science (Natural Science): The attempt to explain natural phenomena. Usually involving some level of empirical/observational testing. Often called “Natural Philosophy.” Astronomy: Scientific study of the positions and motions of celestial bodies and phenomena. Cosmology: Scientific study of the origin, nature and physical structure of the universe: How did the universe come into existence? How large is the universe and what is it made of? What is the human place within it? Religious Belief: A heart-deep response to what a person takes to hold the status of divinity. Status of divinity: That which is considered able to exist on its own without depending on anything else for its being or character. Worldview: A worldview is a person’s overarching framework for interpreting experience. Everyone has a worldview, regardless of whether or not it is systematically constructed or consciously identified. A person’s worldview necessarily shapes the way they understand anything (e.g., ordinary everyday life, and academic disciplines of any kind, for example, theology, philosophy, and the natural sciences). Glossary Study Questions (the third and forth points might have to wait for class discussion) Technology: The attempt to _________ natural phenomena Science: The attempt to _________ natural phenomena Religion/Philosophy: The attempt to _________ natural and _______ phenomena Magic: The attempt to _________ natural and _______ phenomena Using the words in bold as defined above, draw out a concept map Draw a large circle to represent the domain of Western “culture.” Draw a second circle to represent the scope of Western natural science. Should this second circle be within the first, overlapping the first, our outside the first? (How are science and culture related?) Draw a third circle to stand for the scope of this class (see syllabus course description). Label all of your circles and continue labeling additional circles in the exercises below. Be sure that all of your circles accurately reflect the real relationships between these various subject domains. Add a fourth circle to the above diagram to represent the domain of cosmology. Add a fifth circle for technology. 31
Basic Celestial Phenomena (BCP) Unit 1: Introduction Today we have little familiarity with the most basic appearances that the stars and heavenly bodies present from day to day and season to season. Basic celestial phenomena fall among those things that become less rather than better known with the advance of civilization. If we don’t make great efforts to the contrary, city dwellers can spend their whole lives artificially isolated from the stars. The Basic Celestial Phenomena (BCP) Guide will introduce you to the heavens. To become familiar with the day and night sky we will focus on the ancient traditions of skywatching associated with Stonehenge, Babylon, Egypt, and Greece. Why study celestial phenomena through the eyes of such varied cultures? We are preparing to understand the theories that explain the phenomena while grasping different reasons that various cultures had for appreciating the heavens as the greatest show on earth. Five Levels of Skywatching The first two levels could take place in any settled community, and are evidenced from peoples and locations all over the globe. 1. Naming and Recognition of Basic Celestial Phenomena 2. Recognition of various cycles, patterns, or periodic rules. 3. Arithmetical schemes to predict future sky phenomena (with minimal need to adjust these schemes through observational correction). This amounts to quantitative control of phenomena. Ancient Babylonians did this (learn more about this in a “show” in lab). 4. Geometrical schemes to explain phenomena, even if only qualitatively. The Greeks did this beginning with Eudoxus in the 4th century B.C. 5. Realistic cosmological models capable of accurate predictions. Ptolemy certainly achieved this level of activity in the 2nd century A.D. The Basic Celestial Phenomena Guide focuses on the first three levels. Later we will pay more attention to levels 4 and 5.
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Study Questions 1. Why might a typical American today be less familiar with basic celestial phenomena (levels 1 and 2) than the average ancient Babylonian or Egyptian? 2. At which of the 5 levels would you say that the “science of astronomy” begins? Whichever answer you choose would including all lower levels of skywatching activity (e.g., choosing level 5 would include levels 1-4, whereas choosing 2 would include 1). Naming and Recognition of Basic Celestial Phenomena We now will explore the skywatching possibilities or celestial arts of Babylonian priests in their temples, of poets and sailors, of farmers and shepherds in their fields, of Arabian nomads in their desert caravans. That is, we will identify the basic celestial phenomena that require unsophisticated observing skills to name or to recognize. These may be considered only a prelude to astronomy, not the science itself.
North Star
West
earth
East
Daily Motions: The Alternation of Day and Night The Sun, Moon, planets, and stars all move westward across the sky each day, and repeat this general westward motion about a day later. All rise roughly in the east, ascend in the eastern sky until they reach their maximum South height, and then descend in the western sky until they set roughly in the west, in what is Figure 1: Imaginary sphere to called their daily or “diurnal” motion.13 The which all stars appear to be attached. stars all appear to be attached to one sphere This imaginary sphere appears to whose center is Earth’s location (see figure 1). rotate westward around Earth daily Imagine the sphere in figure 1 rotating around Earth westward. This would simulate the appearance of the movement of stars. The North Star appears virtually motionless in this imaginary simulation due to its north axis location. In real life the North Star appears virtually motionless all night.
13 Diurnal derives from Latin: "dies" = day, and "diurnalis" = daily; the latter, pronouncing the "i" as a "j," is the etymological source for "journal" and "journey" as well. "Carpe diem" meaning "seize the day," received a boost into popular culture through Robin William’s movie Dead Poets Society. Williams portrays a charismatic English professor, who in an environment of cheerless conformity, inspires his students to live extraordinary lives by "seizing the day." The disturbing component of the film shows the suicidal dead end to one boy’s attempt to "carpe diem" without the light of the Gospel.
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Z
Diurnal (Daily) Motion: Related Terms • • • •
•
Rising/Setting time: The moment when an object rises/sets relative to one’s horizon. Horizon: Where Earth blocks one’s view of the other half of the universe. In figure 2 the horizon circle, centered on O, forms the bottom of the diagram. Zenith: The point of sky directly over one’s head. Meridian: An arc going from due south to due north running through one’s zenith; the meridian divides the sky in half (making eastern and western halves). In figure 2 the meridian arc goes from S to Z to N. Meridian transit: The moment of time in a 24-hour period in which a celestial body appears to reaches its maximum height, or lies on the meridian. This occurs at roughly daily intervals when the body crosses from the eastern half of the sky into the western sky. In figure 2 the observer (O) sees a star in meridian transit.
horizon circle S
O
Figure 2: The observer (O) looks south (S) at the horizon, then looks up at a star that is one-third of the way up to the zenith (Z). The star would be at its highest position for that evening, just crossing the meridian arc that runs from due south (S) to due north (N).
Application: Navigation by Fixed Stars From a given location on Earth, a star rising above a particular reference point on the horizon on a given day will appear to rise at that same location every day. Sailors learned to guide their ships according to the rising and setting locations of fixed stars. This allowed them to determine their own position in latitude relative to their home or harbor. For example, the Pilgrims who landed in Plymouth Rock expected a relatively mild winter, comparable to that of England, for during their ocean journey they had maintained their ship’s direction on the same latitude. However, due to unanticipated effects of ocean currents, the New England winter is much harsher than that in the same latitude in England. Arabian nomads relied on the stars to navigate across trackless desert sands. The Quran affirms (6:95): “It is God who has appointed for you the stars, that by them you might be guided in the shadows of land and sea.” Azimuth: The distance in degrees of a point on the horizon measured from due north: north = 0˚, east = 90˚, south = 180˚ and west = 270˚. The azimuth-altitude coordinate system is based on the horizon circle (see figure 2). Azimuth is measured along the horizon from due north and altitude is measured above (up from) the horizon circle. In the figure 2 what are the azimuth-altitude coordinates for the star? Answer: Azimuth = 180˚ (due south). Altitude = 30˚ (1/3 of 90° which is the altitude of zenith). Read pages 2-5 of Chaisson textbook, study figures P.1, P.2, & P.3, then answer questions: 1. Compare Chaisson’s figure P.3 with my figure 3 (next page of Packet): How are circumpolar stars photographed in a way that illustrates their very definition? 2. Compare Chaisson’s figure P.2 with my figures 1, 2 & 3: What does each illustrate best? 34
N
Read Chaisson page xxiii and the first half of xxiv to learn about some important study guide features provided by the publishers of your astronomy textbook. Circumpolar: A star or constellation that never rises or sets to someone in one of the two hemispheres—northern or southern (we are in the northern hemisphere and this BCP Guide will assume this position with approximately our northern latitude throughout, unless otherwise specified). A circumpolar celestial object never dips below our horizon. Two of the most famous and easily recognizable circumpolar constellations are Ursa Minor (Little Dipper), which includes Polaris (the North Star); and Ursa Major, which contains the Big Dipper. Big Bear (Ursa Major) and the Big Dipper
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Figure 3: To find the North Star ( ), observer (O) faces north (N), then looks up 35° (along the arrow) to see the North Star ( Polaris). All the stars near Polaris that never go below the horizon are called circumpolar stars.
URSA MAJOR (Big Bear) is among the largest of the 88 officially recognized constellations. Several stars form a smaller group within this constellation, variously called the “Big Dipper” (America), “Plough” (Britain), or many other names. Any such recognized subset or segment of a constellation is known as an asterism. The Big Dipper is one of the most easily recognizable groups of stars in the sky and thus, despite its status as a mere “asterism,” is widely considered a “constellation” in its own right. The “handle” of the Big Dipper represents the “tail” of the bear even though bears don’t have long tails! A Greek myth explains that Zeus stretched out the bear’s tail and placed it in the sky. For people living north of Shawnee’s latitude of 35˚ the Big Dipper is circumpolar (never setting below the horizon) and therefore visible in northern skies year-round. For people living at Shawnee’s latitude of 35˚ there will be times when part of the Big Dipper will be obscured by the horizon, or by the haze of city lights on the horizon, or by local horizon features such as trees. You can learn, as did ancient sailors or western cowhands on the night watch, to tell the time of the night by the position of the Big Dipper. Due to the daily rotation of the Earth, the dipper appears to rotate around the North Star (Polaris) every twenty-four hours. Our planetarium show “Cowboy Astronomer” will introduce you to the star clock of our own culture. You will learn to use a your Miller Planisphere as a star clock. The Miller Planisphere Helps You Located Heavenly Objects (and Tell Time) Find the Big Dipper on your Miller Planisphere by rotating the wheel and looking near the central hole till you see URSA MAJOR printed near the white dots that trace out the Big Dipper shape (get help in lab if you can’t do this). Constellations, as traditionally recognizable star groups, are labeled in all caps on the planisphere (e.g., URSA MAJOR). Constellation subsets, known as asterisms (e.g., Big Dipper), and notable individual stars (e.g., Regulus in the constellation LEO), are labeled in lower case. Notice that the Big Dipper is located on the edge 35
of a circle that is centered on the hole (north celestial pole, or roughly Polaris) in the middle of the planisphere. This circle just touches the horizon “window frame” within which you view the stars on the planisphere. Stars within this small circle are all “circumpolar,” which means that they never go below the horizon as viewed from 30˚ north latitude (this planisphere is calibrated for 5˚ further south in latitude than Shawnee). Only part of the Big Dipper is circumpolar at the latitude for which the planisphere was calibrated. See for yourself: spin the star wheel and notice that only the part of the planisphere that is within the small circle never goes under the horizon.
What is a Planisphere?
North Pole
Think of a planisphere as a fictitious spherical model of the universe that has been squashed into a flat plane to conveniently fit into your backpack. Planisphere Creation & First Contact
E
East
West
E
East
West
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East
West
1.
Take the imaginary celestial sphere that daily carries everything else in the uni verse westward around the Earth and step on its north pole to flatten the entire universe
2.
Punch a hole where the north celestial pole is located in order to make the flat disk look like one of your old Elvis records.
4.
Stand over your celestial Elvis record and look down on your flat universe. Smile!
Flip disk Look at your planisphere with its "Miller Planisphere" label printed upside down so s o it that the "Western Horizon" is printed upright to your left and "Eastern Horizon" isis seen printed upright to your right. Now hold it over your head as you look up in the north like ern sky and the window on the planisphere this... shows the stars you see from our latitude.
West
East
Planis phere
3.
In lab we will practice using the planisphere to tell time. Follows these steps on your own: • Hold the planisphere over your head and make sure the “north” arrow is pointing north • Find a northern constellation like the Big Dipper and match its position on the planisphere • With the sky and planisphere oriented the same, read off the time that points to today’s date In the early part of the fall semester we need to re-calibrate the planisphere to take into account the conversion from normal time (displayed on the dial) to daylight savings time. For example, a planisphere setting of 9 p.m. corresponds to 10 p.m. daylight savings time (we “spring forward” and move our clocks ahead by one hour each spring to convert to daylight savings time). Accordingly, to convert from Miller Planisphere time to daylight savings time, always add one hour. Read the instructions on the back of the Miller Planisphere for an explanation of other features that are essential to accurately using this instrument.
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The Big Dipper: Your Key to the Rest of the Night Sky The Big Dipper is a useful landmark for identifying many stars, and for finding your way home. 1. Pointer Stars The Pointer Stars are the two stars forming the “side” of the bowl (or “dipper”) and which are furthest from the Big Dipper’s handle. A line drawn through the Pointer Stars point to Polaris, the North Star. Polaris (a rather faint star) on your planisphere is simply the hole around which everything turns. No matter where you are in the northern hemisphere, when you face Polaris you will be facing north, and the angle between your horizon and Polaris is equal to your latitude on Earth (see below). Thus, the Pointer Stars s can (by means of the North Star) reveal your latitude and point you north if you are lost.
2. Cassiopeia
3. Great Square
4. Arc to Arcturus
Cassiopeia is a constellation in the starry band of the Milky Way that is about as far away from Polaris as is the Big Dipper, but it is located on the opposite side of Polaris in relation to the Big Dipper. Find this on your Planisphere.
Trace a line from the Pointers of the Big Dipper to Polaris and beyond and past Cassiopeia, and you will come to a large square of four stars called the Great Square of Pegasus (flying horse).
Follow the curve of the Big Dipper’s handle away from the bowl to the fourth brightest star in the Earth’s sky, Arcturus, of the ancient constellation Boötes (pronounced “boo-ohtees”).
Cassiopeia is in the shape of a squashed and distorted “W” with the upper part of the “W” always pointed toward Polaris. The Big Dipper and Cassiopeia appear to move around Polaris, each one always retaining the same position opposite Polaris relative to the other. Cassiopeia is partly circumpolar like the Big Dipper and is visible all night and year from latitudes such as those in the northern United States.
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Find “Great Square” printed in lower case next to “PEGASUS” printed in all caps on your Miller Planisphere. At one corner of the Square of Pegasus is one of the stars of the constellation Andromeda. Near the constellation Andromeda one may see (through binoculars) the Andromeda galaxy (not marked on Planisphere). This galaxy, known as M31, is our closest neighboring galaxy, and is of similar size to our Milky Way).
Review the Big Dipper tips using your Planisphere. There will be questions on the first exam that test your working knowledge of the Planisphere. You can even use your Planisphere during the first exam!
Polaris, the Center of Diurnal Motion
A
N
Polaris 2
1
B Earth’s North Pole
of
Fix
ed
a° y ° St
ar
s
z°
O
x°
on
re
riz
he
Ho
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Earth Earth
X° is a measure of north latitude Here it is 35° (latitude of Shawnee)
C
Compare my figure with Chaisson’s figure P.2 (page 6 in textbook)
S Imagine, as in the figure above, a large sphere to which all of the regular stars are attached. The ancient Greeks called this the “sphere of fixed stars.” Suppose that this starry sphere rotates once 38
daily around an axis that runs from Polaris in the north (N) to the celestial south-pole point (S). Furthermore, imagine that Earth is in the center of this universe as shown. To draw the illustration more true to scale, we would need to greatly enlarge the size of the sphere of fixed stars so that Earth would appear to be a tiny point in proportion to the size of the starry sphere. We will use this diagram to learn something about the position of Polaris (the North Star) as the center of daily apparent stellar motion. Place yourself as an observer on Earth at the Earth’s north pole and look straight overhead along line 1 to view Polaris (N). Polaris, which is approximately at the north celestial pole, would not appear to move as the sphere of fixed stars rotates daily on its axis. If we were to greatly enlarge the size of the sphere of fixed stars to make it more true to the scale of Earth, then the observer at point O, standing at 35˚ north latitude (Shawnee), would look along line #2 to view Polaris. Line of sight #1 (viewing Polaris from Earth’s north pole) and line of sight #2 (viewing Polaris from Shawnee) would be virtually parallel, because they would converge on a single point, the star Polaris, at a huge distance out in space. Answer the study questions below assuming that the sphere of fixed stars is a million times larger than shown. Alternatively, you may wish to imagine the equivalent situation in which the size of Earth in the diagram is reduced to a tiny point. Study Questions for the Above Diagram 1. If the Earth’s axis were extended straight up northward until it reached the sphere of fixed stars, then it would touch the approximate location of the ____________ (name of star).14 2. Which point would mark a location on O’s horizon that is due north? A or C? (circle one)15 3. Point B would be O’s _________ point (technical name for the point directly overhead).16 4. Observer “O” (or anyone living north of the equator) would observe all of the fixed stars apparently moving in circles around ____________ (name of star).17 5. If the sphere of fixed stars were drawn to scale (very large) on the above diagram, then the horizon (see line A-C above) would cut the sphere of fixed stars into two:18 a. roughly equal portions (two hemispheres) b. very unequal portions (one quite large and one quite small) 6. The planetarium dome (assuming we forget the projection booth that cuts out a chunk of the dome) serves as a surface upon which celestial objects are projected and it also amounts to a representation of19 a. the half of the universe visible at any given time from a certain position on Earth b. the 1/4 portion of the universe visible at any given time from a certain position on Earth 14 15 16 17 18 19
Polaris, or the North Star A Zenith Polaris, or the North Star a (roughly equal portions) a (half of the universe)
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7. If angles “a” + “y” = 90˚ and angles “z” + “x” equal 90˚ and angles “z” and “y” are known to be equal to each other by means of a geometrical proof (that we will not prove), then we can conclude that the following two angles are also equal to each other (circle the correct pair):20 “x” and “z”................. “x” and “y”................. “x” and “a” 8. The previous question amounts to a proof for the following conclusion:21 a. A person’s north latitude is roughly equal to how far Polaris is from their zenith b. A person’s north latitude is roughly equal to the altitude of Polaris (how far Polaris is above the point due north on their horizon) 9. Observer “O” should look up ___ degrees above his northern horizon to see Polaris.22 General Study Questions to Review BCP Unit 1 1. Define diurnal motion.23 2. Describe diurnal motion in the situations below: a. In which direction do the Sun, Moon, planets, and stars all generally appear to move across the sky each day? Circle one: east/west.24 b. Where do they all generally rise roughly each 24-hour period? Circle one: east/west.25 c. Where do they generally set? Circle one: east/west.26 3. What is the azimuth of a planet at its meridian transit? ____ degrees.27 4. What is the altitude of a star at the observer’s zenith? ____ degrees.28 5. What is the altitude of Polaris at your terrestrial latitude? ____ degrees.29 6. Do any stars neither rise nor set at all from the vantage point of Shawnee, Oklahoma?30 A circumpolar star is visible at which of the following times?31 __ all night long __ every night of the year __ both all night long and every night of the year 20 21 22 23 24 25 26 27 28 29 30 31
"x" and "a" b (north latitude of observer = altitude of polaris) 35˚ Daily motion, once every 24 hours, also known as "primary motion" (how all celestial objects primarily appear to move around Earth once each day). West East West 0˚ or 180˚ (Planets can cross meridian north or south of zenith, depending on time of year and location on earth 90˚ 35˚ Yes Both all night long and every night of the year
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7. What circumpolar star enables you to determine which way is north?32__________ 8. Rising or setting locations of fixed stars would enable sailors to determine their position in which of the following ways?33 a. __ east or west in terrestrial longitude only b. __ north or south in terrestrial latitude only c. __ either in latitude or in longitude d. __ sailors should content themselves with daytime sailing 9. On the assumption of a convex or spherical Earth, what would happen to the number of circumpolar stars a resident of Italy would see if he traveled in the following ways:34 a. Northward? The number of circumpolar stars would ________ b. Southward? The number of circumpolar stars would ________ 10. How many stars (of the total stars visible during a given night at the North Pole) would be circumpolar to Santa Claus at his home?35 _____ 11. How many stars (of the total stars visible during a given night at the South Pole) would be circumpolar to a penguin?36 _____ 12. Would any of the circumpolar stars seen by Santa and the penguin in the two previous questions be the same?37 _____
32 33 34 35 36 37
Polaris North or south in terrestrial latitude only A. northward? increase B. southward? decrease All that he would see would be circumpolar. Same answer as above. None
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Wednesday September 1 BCP Unit 2: Daily and Zodiacal (Sidereal) Motion Daily Motion Helps You Find Your Way Daily motion defines the four cardinal directions. Our awareness of this can help us find our way without a compass. All celestial bodies appear to rise in the east and set in the west (or circle around Polaris without rising our setting). Here is a handy checklist for the lost. How to find the following directions: North o Find Polaris at night by means of the Big Dipper’s pointer stars East o Turn 90° (one-quarter) to the right of north as determined by above method o Roughly where the Sun rises (varies north and south of due east through the year) o Where the stars of Orion’s belt rise each night (BCP Unit 2 covers Orion) South o Turn 180° (opposite) of north as determined above West o Turn 90° (one-quarter) to the left of north as determined by above method o Roughly where the Sun sets (varies north and south of due east through the year) o Where the stars of Orion’s belt set each night Follow the Drinking Gourd Prior to the Civil War, slaves escaped from southern plantations and made their way north to the Underground Railroad by means of the Big Dipper (Drinking Gourd) and North Star. An itinerant carpenter called Peg Leg Joe traveled from farm to farm and plantation to plantation, teaching slaves a song38 that would cryptically remind them of his instructions to find their way northward. When the Sun comes back And the first quail calls39 Follow the Drinking Gourd. For the old man is a-waiting for to carry you to freedom If you follow the Drinking Gourd. The riverbank40 makes a very good road. The dead trees will show you the way. 38 For an explanation of this song, see Gloria D. Rall, "The Stars of Freedom," Sky and Telescope, February 1995, 36–38, or Gloria D. Rall, "Follow the Drinking Gourd," The Planetarian, 1994, 23: 8–12. The story is beautifully told and illustrated by Jeanette Winter in Follow the Drinking Gourd (New York: Alfred A. Knopf, 1988; a companion video is available which includes a recording of the song) 39 On the winter solstice the Sun rises in the southeast. In the months after the December solstice the Sun rises more northerly and ascends higher in the sky each day. Migratory quail winter in the south. 40 Tombigbee River, leading northward from the Gulf of Mexico toward Tennessee.
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Left foot, peg foot, traveling on,41 Follow the Drinking Gourd. The river ends between two hills Follow the Drinking Gourd. There’s another river on the other side42 Follow the Drinking Gourd. When the great big river meets the little river43 Follow the Drinking Gourd. For the old man is a-waiting for to carry you to freedom If you follow the Drinking Gourd. Daily Motion Gives You Natural Clock Options: Telling Time by the Sun and Stars With the recognition of diurnal phenomena, one can tell the time from the changing height of the Sun or, at night, of certain stars above eastern or western horizons. Aborigines and European peasants (before the development of mechanical church clocks in the Middle Ages) routinely used the Sun to determine the time of day (except on cloudy days!). Sailors, too, might learn to tell time at night by the height of certain stars. A stick in the ground that is vertical and placed so that the Sun can cast its shadow on the ground is called a gnomon. The shadow will fall on the ground in the opposite direction to the Sun, so that if the Sun rises to the southeast of the gnomon, then the gnomon’s shadow will fall to the northwest. Its length will be greatest when the Sun is closest to the horizon; i.e., at sunrise or sunset it would reach infinity. Its length will be shortest when the Sun reaches its highest altitude in the sky; i.e., when the Sun crosses the meridian, which is “local noon.” At that moment the Sun will be due south of the gnomon, and the gnomon’s shadow will point due north. Each hour a given celestial body such as the Sun (or a star) should shift its position westward by about 15˚ (360˚/24 hours = 15˚ per hour) due to daily motion. Using a sundial, this westward angular change of 15˚ per hour can be determined and found to be roughly constant. This is the essence of a sundial. Sundial: An instrument that indicates local solar time by the shadow cast by a central projecting pointer (like a gnomon, but usually very thin) on a surrounding dial that is calibrated by hours (15˚ per hour). Study Questions 1. How can one tell when a stick or pole is exactly vertical?44 41 Dead trees were used as markers with charcoal and mud drawings of a peg leg and a foot. 42 Tennessee River, which flows northward across Tennessee and Kentucky. 43 That is, at the confluence of the Tennessee River and the Ohio River (over 800 miles north of Mobile), where Underground Railroad guides would meet fugitive slaves on the northern bank and transport them to safer regions. A slave who left a farm or plantation in southern Alabama or Mississippi in the winter would arrive at the Ohio river about a year later—the best time to cross, when one could simply walk across the ice.
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2. At what time is a shadow cast by the Sun the shortest?45 3. Where is the Sun when it is highest in the sky each day?46 4. At what time is a shadow cast westward by the Sun the longest?47 5. At what time is a shadow cast eastward by the Sun the longest?48 6. You are a 2700 BC Egyptian saddled with the task of overseeing the construction of a pyramid that is to be oriented by the four cardinal directions (north, east, south, west). How could you do this (the compass has not yet been invented and you are only permitted to work in daylight).49 7. In view of the daily motions discussed above, is there anything wrong with the narrative in Charles Dickens’ Hard Times where Dickens places a dying man in the bottom of a deep vertical shaft, where the man finds solace in the light of a single star that shines down to him throughout the night?50 Fixed Stars “He also made the stars.” Genesis 1:16 “If the stars should appear one night in a thousand years, how would men believe and adore, and preserve for many generations the remembrance of the city of God which had been shown. But every night come out these envoys of beauty, and light the universe with their admonishing smile.” R. W. Emerson, Nature Some stars always retain the same spatial orientation with respect to each other; these are the fixed stars. Not all celestial bodies remain fixed in orientation from day to day or season to season. Those that do stay in the same position relative to one another are myriad in number (and we represented them earlier as the “sphere of fixed stars”; those visible bodies that change their relative positions are quite few in number. Stars are not all of the same color; some are tinged with red, blue, or yellow.
44 45 46 47 48 49
Gravity pulls a stick (held loosely) toward the center of Earth, thus establishing a vertical standard. Local noon Meridian, local noon Sunrise Sunset Use a vertical stick that will cast a shadow to determine due north (shortest shadow during the day will point due north; the 3 other cardinal directions can be established from north by adding 90˚ increments). 50 Not a likely story (only if it were Polaris viewed from North Pole).
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Study Questions Only 7 celestial bodies seem to change their relative positions against the background of other fixed stars. What are these seven “wandering” bodies, which came to be known as the “wandering stars” or “planets”? Hint, list the 5 planets that we can see without a telescope and then add the Moon and Sun to get 7 total objects.51 1. 2. 3. 4. 5. 6. 7.
________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
Note: Two wanderers (the “morning star” and “evening star”) were often recognized as being different appearances of the same body, namely, Venus. They are never seen in the sky together, and never appear very far from the Sun. We will study these appearances later. Star Magnitude and Number Heaven’s utmost deep Gives up her stars, and like a flock of sheep They pass before his eye, are number’d, and roll on.” P. B. Shelley, Prometheus Unbound (on the astronomer’s work) The brightness of stars is measured on a scale of apparent order of magnitude, expressed on a scale from 1 to 6. The fainter a star, the higher the numerical value of its magnitude number. Each magnitude value is 2.5 times brighter than the next number; for example, a star of the 5th magnitude is 2.5 times brighter than one of the 6th magnitude. Study the star magnitude key on the back of your planisphere as you make your way through the list below.
51 Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn [planet (Greek = Planetos), means "wanderer"].
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6th Magnitude Sixth magnitude stars are barely discernible to the naked eye under the best viewing conditions. There are over 1000 sixth magnitude stars. Does the Miller Planisphere indicate this magnitude of stars (see the back of it for the answer)? About 3000 stars appear to Earthlings as 6 magnitude or brighter.
5th Magnitude
3rd Magnitude
2nd Magnitude
The great Orion nebula is an example of a fifth magnitude object. Less than a thousand stars are 5th magnitude.
The 3 stars of Orion’s head are magnitude 3, and make a handy reference to evaluate observing conditions. Under 100 stars are 3rd magnitude. Use your Planisphere to find out when Orion rises above the eastern horizon at the time of the year that you are now taking this course. Will you have to be night owls or early risers to see it?
About 30 stars are 2nd magnitude, including Polaris, the North Star (1.99).
4th Magnitude A star of the fourth magnitude is (2.5 x 2.5) = 6.3 times brighter than one of the 6th magnitude. Under 300 stars are fourth magnitude.
1st Magnitude First magnitude stars are 100 times brighter than 6th magnitude stars. Less than 20 stars are 1st magnitude or brighter. For example, Betelgeuse, the reddish shoulder of Orion, has a magnitude of 0.8.
Brighter than Bright Celestial objects brighter than first magnitude are given negative numbers. Sirius, the brightest star in the sky, has a magnitude of –1.42. All visible planets except Saturn can be brighter than Sirius, the brightest being Venus, which can reach magnitude –4.4. The full Moon is –12.6. Constellations “Lift your eyes and look to the heavens: Who created all these? He who brings out the starry host one by one, and calls them each by name. Because of his great power and mighty strength, not one of them is missing.” Isaiah 40:25 The fixed stars can be named and grouped into recognizable clusters or constellations. These constellation patterns are arbitrarily imposed upon the stars in honor of particular characters or stories, not because the pattern resembles the character in form. 88 constellations are officially recognized today, and many of these are of ancient origin; others, especially in the southern hemisphere, date from more recent times. Stars within a given constellation are usually ranked according to relative brightness by the Greek alphabet so that the brightest star is alpha, the second-brightest beta, the third-brightest gamma, and so forth. Using the table below, memorize the first 5 letters of the Greek alphabet.
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The letter of the Greek alphabet that indicates a star’s brightness is conjoined with the Latin genitive form of the name of the constellation (e.g., often changing “us” to “i”). For example, the brightest star of the constellation Centaurus is α-Centauri, which happens to be the star nearest to our own Sun (though it is actually a double-star). Find Constellations on Your Planisphere: Orion and His Companions
Alpha
!
Beta
"
Gamma
#
Delta
$
Epsilon
%
Study Chaisson’s figure P.1 (page 5 of textbook). Find the stars identified by the first five letters of the Greek alphabet. These are in order of what effect as seen from Earth? Read Chaisson’s section “Celestial Coordinates” (pages 5-7) and “More Precisely P-1” (p. 10). How is right ascension / declination more precise for locating stars than constellation/brightness? The hunter Orion is one of the most easily spotted constellations, especially in winter, and is visible from every inhabited part of the globe. His belt of three bright stars in a line is quite distinctive (and lies nearly on the celestial equator). A sword hanging from his belt at first sight looks like three stars, but the middle one is ill defined (with binoculars you can tell that it is not a star, but a fuzzy region—as we are now told, a giant cloud of luminous gas, 20,000 times the diameter of our solar system, called the Great Orion Nebula). Orion’s right shoulder is Betelgeuse (pronounced roughly “beetle-juice”), a red giant that is one of the largest stars in the sky (capable of being discerned as an actual disk rather than a point of light with large telescopes; if Betelgeuse were placed at the position of our Sun, the Earth and Mars would fall well inside its surface). Orion the hunter appropriately faces the red eye (the star Aldebaran) of the adjacent bull (the constellation Taurus). Orion’s dog (the constellation Canis Major) walks at his side, containing the brightest star in the sky (Sirius). Orion’s lower right foot (Rigel) is a bright bluish-white star at a vertex of the so-called “Winter Hexagon.” The Winter Hexagon, though not a constellation, conveniently connects six bright stars forming a hexagon: Rigel, Sirius, Procyon, Pollux, Capella, Aldebaran as you can see on your planisphere and on the diagram on the next page. Each of these bright stars is part of a constellation. The Bull Taurus contains the bright cluster of six or seven naked-eye stars called the Pleiades. In Egyptian mythology, Orion was the abode of Osiris, the mythical pharaoh who invented the arts of agriculture before being slain by his animal-headed brother, Set. Osiris conquered death and, once resurrected, came to reside in Orion (his wife, Isis, dwelling near Sirius). Jewish tradition eventually identified Orion with Nimrod, the “mighty hunter before the Lord” spoken of in early Genesis. To the ancient Syrians, Arabians, and even Ptolemy, Orion was the Giant; to the Chinese Orion was (with Taurus) the White Tiger. (R. H. Allen, pp. 303ff.) Or, from Ireland, a modern tale of how St. Patrick sent him to hunt in the heavens begins thus ... “O’Ryan was a man of might Whin Ireland was a nation, But poachin’ was his heart’s delight And constant occupation....” Charles G. Halpine 47
Winter Hexagon on the Milky Way
4
CANIS MINOR 3 Procyon
Pollux Castor
GEMINI
5 Capella
Milky Way AURIGA
CANIS MAJOR
Sirius
Betelgeuse
2 ORION
TAURUS
Aldaberan 6 1
Rigel
On the planisphere and in this illustration star names are in Regular Case and constellation names in ALL CAPS
Zodiacal (Sidereal) Motion: Slower than Daily Motion In addition to the changing appearances that are repeated every day (diurnal motions), some celestial bodies (i.e., the planets, including the Moon and Sun, but not the fixed stars) change their relative positions in patterns that become apparent only when considered over longer periods of time such as a week, month, year, thousands of years, or longer. Such changes are collectively known as “zodiacal motion.” The term “zodiacal” derives from the “zodiac” constellations through which the celestial objects of interest primarily appear to move). These motions are also (more generally) call "sidereal," which means they are relative to the fixed stars.
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Distinguishing Planets from Fixed Stars If we are going to study “zodiacal motion,” then we will need to first learn how to distinguish planets from fixed stars, since only planets undergo zodiacal motion. In fact, the zodiacal motion of the planets is recognizable in reference to the stable background of the “fixed” stars. We can note several ways in which planets change their relative positions against the background of fixed stars. Variable Speeds (Speed Up and Slow Down) The Sun, Moon, and planets appear to speed up and slow down in complex ways in their motion relative to the fixed stars. Such variable speeds might appear odd, even random, to the novice astronomer (there actually is a predictable pattern to their motion, which we will study later). In short, planets do not appear to move at constant speeds, while fixed stars do appear to move at constant speeds. Variability of Rising/Setting Location In contrast to fixed stars, a given planet (including the Sun and Moon) will not always rise and set at the same location on the horizon. Sometimes a planet will rise at a more southerly location and sometimes at a more northerly location. How does the Sun’s apparent zodiacal motion provide ways to make a calendar? The Sun traces its rising and setting positions north and south along the horizon in an annual pattern that is exactly repeatable and that recurs seasonally. Thus it provides a reliable and convenient calendar, like a pendulum oscillating around the points due east or due west. This solar calendar was as significant for ancient cultures as the cycles of day to night and the lunar phases. The average American today, though ignorant of the term “zodiacal motion” knows that the Sun appears to go through a cycle that is the basis of the “year” in our calendar (postpone considering for now whether the Earth goes around the Sun or the Earth). For example, an ancient Chinese explanation of this pattern attributed the motion to the Earth, as if the Sun were rising each day at the same place but the Earth itself slowly sliding up and down along a north-south line. At Stonehenge (Britain; see illustration below of sunrises along the eastern horizon), Woodhenge (Cahokia, Illinois), or other stone circles (e.g., Medicine Wheel, Wyoming), seasonal time intervals were charted by arranging sunrise markers sighted toward the eastern horizon, running north or south of due east. Sunrises and sunsets reach their extreme northerly and southerly positions on the solstices; and occur due east and due west on the equinoxes (note that Stonehenge is at a greater northern latitude than Shawnee and thus the resulting azimuth range for Sun rises is much greater than in Shawnee).
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50° June 22
Horizon
Azimuth
90°
130°
December 22 March 21 September 23
Stonehenge Sunrises
Horizon
Study below the principal events in the Sun’s apparent cycle (Chaisson simplifies the Sept., March, June & Dec. dates by rounding them off to the 21st day; below are closer dates). 1. Equinoxes. When the Sun is at an equinox position, the following occur: a. Sun rises due east and sets due west b. Daylight and nighttime are of approximate equal length. c. Sunrise & sunset locations are shifting quickly, perhaps a solar diameter per day d. There are two kinds of equinoxes: autumnal and vernal i. Autumnal (Fall) Equinox 1. September 23, the first day of autumn 2. Sunrise/sunset locations shifting southward ii. Vernal (Spring) Equinox 1. March 21, the first day of spring 2. Sunrise/sunset locations shifting northward 2. Solstices. When the Sun is at a solstice position, the following occur: a. Sun rises at an extreme northerly or southerly limit b. Sunrise and sunset locations are shifting slowly (1/10th of a solar diameter in 4 days) c. There are two kinds of solstices: summer and winter i. Summer Solstice 1. June 22, when the Sun reaches its most northerly extreme 2. The longest daylight or first day of summer (in the northern hemisphere) ii. Winter Solstice 1. December 22, when the Sun reaches its most southerly extreme 2. The longest nighttime or first day of winter (in the northern hemisphere)
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Summer solstice sun position Equinox sun position 23.5º
North star (Polaris)
23.5º
North
35º
55º
Winter solstice sun position
South
Observer
o Sun positions from 35 north latitude
Read Chaisson’s sections “Day-to-Day Changes” and “Seasonal Changes” (pages 7-9) and use the eBook version of his textbook to click on the “physlet” illustration (solar vs. sidereal day) and other “animation” (the Earth’s seasons) for some wonderful computer simulations of Earth’s motions, which make the Sun appear to move in our sky as illustrated in my Packet. Compare his illustrations and study guide material for this part of his chapter (at the end of his chapter) with the illustrations and questions in my Packet. “Solstice” derives from Latin: “sol” means sun in Latin and the “stice” part of the English word come from a Latin word that means “stand still.” Solstice refers to the position the Sun occupies in the sky when it rises at a northerly or southerly extreme against the horizon. On the day or moment of a solstice, the location of the Sun’s rising or setting “stands still” on the horizon at its most northerly or southerly extreme before turning back, or beginning to shift each day in the reverse direction. The Sun’s Key Horizon Positions If you were living on the equator and looked out onto the eastern horizon to view sunrises throughout the year, you would be able to mark out (with stones or whatever) the three key sunrise positions marked in the diagram below.
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Equinox sunrise position
Summer Solstice sunrise position
Winter Solstice sunrise position
23.5°
23.5°
Due east
Northeast
Southeast
Sunrise Variation at 0° Latitude If you were to observe sunsets throughout the year in Shawnee, the above diagram would have to be modified to look like the one below in order to accurately describe the phenomena. Summer Solstice sunrise position
Projected angle
Projected angle
HORIZON
Winter Solstice sunrise position
Equinox sunrise position
55°
NE
HORIZON
E . 23
5°
SE . 23
5°
R TAOL USAT I ELQE CE
Sunrise Variation at 35° North Latitude Notice that the “projected angle” of extreme horizon positions for the Sun in the diagram for Shawnee sunsets is greater than the 23.5˚ angles for an equatorial viewer (see previous diagram). In other words, as a person at 35˚ north latitude (such as Shawnee’s position on Earth) looks along the eastern horizon, the Sun will appear, at its extreme annual positions, to rise further northeast (summer solstice) and further southeast (winter solstice) than for a person viewing from Earth’s equator. Why? We will discuss this in class and in lab.
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The Difficulties of Ascertaining Rising Phenomena As we continue to investigate the zodiacal motion of the Sun (its annual cycle which is the basis of our 365 1/4 day solar calendar), we need to focus our attention on the problem how to determine the points on horizon at which the Sun rises on successive mornings. The exact rising position of the Sun might be crucial for an ancient culture’s determination of the four seasons of the year (and thus religious and agricultural events as well). At first glance, one may wonder what is so complicated about such rising (or setting) phenomena so as to warrant its inclusion here. Other factors complicate this phenomenon as well, including local lighting and terrain and the reference star’s magnitude—the latter contributes to starlight refraction errors, caused by the Earth’s atmosphere, that affect the star’s apparent rising or setting position (and thus this might affect determinations of the Sun’s rising position relative to that star). In Mesopotamia (where rising and setting events were of utmost significance) sand storms could also be expected to obscure the horizon and to frustrate accurate sightings (only Babylonian eclipse records—which were not horizon phenomena—proved sufficiently reliable to later astronomers such as Ptolemy).
Apparent position Observer Horizon Earth
True position
Atmosphere
The Sun’s Zodiacal Motion & the Lengths of Seasons It was mentioned above that the Sun, like the other planets, changes its relative position from day to day against the background of fixed stars by an unequal amount. As a consequence, the lengths of seasons (the times between a solstice and equinox or vice-versa) are unequal. For the northern hemisphere, the winter half of the year (autumnal to vernal equinox) is about eight days shorter than the summer half (vernal to autumnal). That is, the Sun changes its day-to-day position against the background of fixed stars in the greatest amounts around January 2. This makes sense because a greater speed results in shorter a time for traveling a given distance. Application: Lunar Standstill & Eclipse Prediction Similarly to the annual north-south oscillation of the Sun, the Moon also traces its rising and setting positions north and south along the horizon in a repeating pattern. However, the Moon’s oscillation is not nearly so regular as the Sun’s, and recurs not annually but every 18.6 years. In 53
the case of the Moon, the northerly and southerly extremes against the horizon (28.5˚ from due east or west if you are observing from the equator, and greater as you move away from the equator) are called “lunar standstills” (analogous to the Sun’s solstice “standstill” locations). Application: Native American Directionality Many Native American tribes had a sense of directionality that is important for you to recognize as essentially different from our modern European-American cardinal directions of North, East, South, and West (remember the order of our cardinal directions by “Never Eat Soggy Worms”). Numerous Native American peoples perceived of 4 directions not in terms of North, East, South, and West, but rather the four extreme horizon positions of the Sun on the two solstices (sunrise and sunset on summer solstice which is the longest day of the year for North Americans, and sunrise and sunset on winter solstice which is the shortest day of the year for North Americans). We locate and visualize these four positions in terms of how many degrees they are away from the cardinal direction of due north. Many Native Americans, however, would consider the four extreme horizon positions of the Sun on the two solstices to be the most basic and natural sense of 4-part directionality in the universe and all other points on the horizon would be judged relative to these. Thus, we have two fundamentally different ways of conceiving of “direction” on Earth: this Native American solstice standard and our own European-American cardinal direction standard (North, East, South, and West). Which is better and for what reasons? Expand your answer to this question by working two problems. Problem #1: How would a Native American who thinks in terms of the traditional 4 solstice sunrise/sunset directions give directions to you, a Westerner, who has a compass in hand? Suppose he wants to direct you to a sacred cave 200 miles away? How could you use your compass to follow these directions? How would you find out the solstice rising and setting positions? How would the North Star and knowing the day’s date help you? Problem #2: How would you communicate about the 4 directions of North, East, South, and West to a Native American who thinks in terms of his own traditional directionality? How would you suggest that he convert any Western directions to a location into terms that could be followed by someone operating from within the Native American reference system mentioned above? Which frame of reference for directions is more easily used anywhere on the globe, especially in traveling long distances north or south? Why? Study Question Equinoxes are defined (check the correct option below)...52 __ by horizon phenomena (the Sun rising due east and setting due west) __ as dates calculated to be midpoints in time between the solstices __ both of the above Horizon Observations of Zodiacal Motion
52 By horizon phenomena (the Sun rising due east and setting due west)
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A given planet (as it undergoes zodiacal motion) changes its position from day to day in a generally consistent direction. Usually, each new day a given planet (including Sun or Moon) appears a little further eastward from the stars that were near it the day before. That is, stars that rise with a planet on one day will on the next day be visible a little before the planet rises (and located higher in the sky than the planet; to the west of the planet’s new position). After a short delay, the planet will appear to rise, following the star it rose with on the day before. The Sun's Zodiacal Motion On a given day the Sun will rise about four minutes later than a star that rose simultaneously with it on the day before. In terms of angular measurement, this four-minute delay works out to a new position about a degree farther eastward. 1˚ is about twice the angular diameter of the Sun or Moon. For reference, it’s handy to remember that the Moon and the Sun both appear about half a degree in diameter. The changing position of the Sun from one day to the next can be calculated by considering that the Sun completes a 360˚ circuit against the background of the fixed stars every year. Therefore: 360˚ ÷ 365.25 days = 0.985˚ change of position per day (about 1˚ per day) The above motion is seen against the background of fixed stars. The Moon's Zodiacal Motion The Moon rises about 53 minutes later each day, in a new position about 13.2˚ farther eastward relative to the background stars. We can calculate this 13.2° daily shift in the following manner: 360˚ = 13.2˚ change of position per day 27.3 days 27.3 days is the length of time it takes for the Moon to get lined up with the same star again (sidereal month). That is, it takes this long to make a complete 360° circle through the zodiac. Thus in one day, it only goes through 13.2˚ of that full 360° circle of the zodiac. Zodiacal Motion and Early Zodiac Mythology One consequence of the Sun’s zodiacal motion is that the Sun moves through a certain set of constellations through the year. The constellation containing the Sun at a given time would be overhead at noon, of course, invisible in the daytime sky. But one could note each morning which stars are near the Sunrise position just above the horizon before the early glow of sunrise (and from this, over the course of a year, chart out the constellations that mark out the apparent path of the Sun in its annual zodiacal motion). Consider the following ancient cultures and their traditions of marking the Sun’s annual zodiacal motion by reference to a select band of constellations. Akkadian (Assyrian/Babylonian) 55
According to R.H. Allen, the Akkadians recognized a band of constellations they called the Furrow of Heaven, ploughed by the Bull of Heaven (mentioned in the Epic of Gilgamesh). From the fourth to the second millennia BC, Taurus the Bull, one of the most ancient of constellations, was the constellation containing the Sun on the first day of spring (it not longer does today). It would make sense culturally to encode this ancient understanding of the Sun’s apparent annual path through the stars with Taurus as the beginning point of the circuit, given the importance of spring for civilizations based on agriculture. Indian and Chinese The Rig Veda of India spoke of a “twelve-spoked wheel” of heaven. In China, an independently derived “Yellow Way” began with a Rat (Aquarius), and numbered twelve constellations in a direction opposite that of the Babylonian zodiac. Greek No allusion to the zodiac is made by the early Greek poets, Homer and Hesiod. It seems not to have entered Greece until around the fifth century BC. A century later Aristotle alluded to the zodiac (literally “circle of animals”). Frames of Reference for Observing Zodiacal Motion (1) The Ecliptic and the Zodiac The Sun appears to travel through all 12 signs (constellations) of the zodiac once each year, following the same path against the background of fixed stars each time. Eventually, astronomers coined the term “ecliptic” (because eclipses can happen only here) to designate this invariable path of the Sun as it shifts from point to point roughly along the middle of the zodiac constellations. The zodiac thus can be defined as the band of 12 constellations that contain the ecliptic. The ecliptic bisects the zodiac into two rings as shown below.
Ecliptic
Zodiac (Full Width of Band)
Earth tilted 23.5° relative to the plane of the ecliptic; modern folks call this "Earth’s obliquity." We now know Earth’s obliquity varies from 22° to 25° over thousands of years; ancients didn’t know this.
Using Babylonian sexagessimal units for angular measurement (360 degrees = a full circle), Seleukid era astronomers divided the twelve zodiacal constellations equally into angular longitudinal arcs of 30 degrees (360˚ ÷ 12 = 30 degrees of arc per constellation). If the Sun 56
moved at constant speed, it would enter a new constellation about every 30 days (365 days ÷ 12 constellations = roughly 30 days per constellation), or about once a month. (2) The Ecliptic and the Celestial Equator. The circle of the Earth’s equator can be projected straight upward into the sky (onto the “sphere of fixed stars” as the Greeks conceived it) to form the celestial equator. Study the next illustration carefully to help you imagine this spatially.
Earth in Relationship to the Ecliptic Stars appear as if all attached to one great sphere
Ecliptic
X S
S
Zodiac
X
Celestial equator
Earth is still tilted 23.5° relative to the eclip tic, but this time it is drawn with Earth’s orien tation straight with respect to this paper and the ecliptic tilted (this makes it easier to visualize from an Earthling’s observational point of view, which is all that ancient people had to go by).
The ecliptic (defined by the Sun’s positions throughout a year with respect to the fixed stars) is inclined by about 23.5˚ to the celestial equator (see the illustrations above and below). The distinction between the celestial equator and the ecliptic, implicit in many archaeological structures, was explicitly articulated by the Pythagoreans in the fifth century BC, and referred to by Plato in his dialog, The Timaios. 57
The celestial equator and the circle of the ecliptic intersect at two points, the vernal and autumnal equinoxes. There are two large X marks on the diagram above to mark the equinoxes, which observationally may be identified as the two positions in which the Sun lies either due east or due west at its rising and setting for Earthlings). At the vernal equinox (March 21), the Sun crosses the celestial equator, heading northward, and appearing higher in the sky. At the autumnal equinox (September 23), the Sun descends across the celestial equator, heading southward, and appearing lower in the sky. The extreme northerly or southerly points of the ecliptic, measured from the celestial equator, are the solstices (marked above on the diagram by the two large S symbols), which the Sun occupies around June 22 and December 22. John Milton Strikes an Astronomical Chord John Milton alluded to the obliquity of the ecliptic (that it is tipped or “oblique” relative to the celestial equator) and its consequences for the seasons in Paradise Lost: “Some say, he bid his angels turn askance The poles of Earth twice ten degrees or more From the Sun’s axle; they with labour push’d Oblique the centric globe: some say, the Sun Was bid turn reins from th’ equinoctial road Like distant breadth to Taurus with the seven Atlantic Sisters, and the Spartan Twins, Up to the Tropic Crab; thence down amain By Leo, and the Virgin, and the Scales, As deep as Capricorn, to bring in change Of seasons to each clime.” The Constellations of the Zodiac The constellations of the zodiac are listed in the following table in order that the Sun moves eastwardly through them. Some boxes are blank to reduce the information you need to know. Compare Chaisson’s figure P.6 (page 8 in textbook) with the table below in my Packet: Zodiac Sign
Mythological Identity
Pisces (Pie-seez) The Two Fish Aries (Air-eez) The Ram
Appearance and Notes Sun is on the edge of this constellation on first day of spring.
Ram with Golden Fleece, could fly through the air.
Taurus (Tore-us) The Bull
Reddish eye the star Aldebaran, one corner of Winter Hexagon.
Gemini (Jem-eh-ni) The Twins
Two bright stars, Castor and Pollux, form a corner of Winter Hexagon.
Cancer (Kan-ser) Crab Leo the Lion
Prehistoric constellation. 58
Regulus is the bright point of a
backward question mark. Virgo (Vir-go) Maiden Libra (Lee-brah) Scales Scorpius (Scor-pee-us) Scorpion Sagittarius (Saj-eh-tair-ee-us) Centaur
Fishhook to Polynesians. Archer, half-man and halfhorse, shooting an arrow.
Look for teapot shape. In direction of the center of Milky Way.
Water Carrier. Babylonian constellation.
Sun is on the edge of this constellation on first day of spring.
Capricornus (Kap-rihcorn-us) Sea Goat Aquarius (Ah-kwair-ee-us) Study Questions 1. Identify which zodiac constellations are referred to in the passage from Milton quoted above. Can you identify his allusion to the Pleiades?53 2. What is the cause of changing seasons?54 a. __ Distance of the Earth from the Sun b. __ Obliquity (tilted angle) of the ecliptic with respect to the celestial equator c. __ Cooling contraction and heating expansion change the lengths of day and night 3. The Seasons in which to locate certain constellations in the evening sky. You may use your planisphere and the table above.55 4. Which zodiac constellation would cross the meridian at midnight on Christmas Eve? 5. When would Taurus be visible crossing the meridian at midnight? Precession of the Equinoxes From the fourth to the second millennia BC, Taurus contained the Sun on the first day of spring. The position of the Sun against the background of fixed stars on the first day of spring is the spring equinox. However, in the time of Hipparchos (2nd century BC), the Sun was in Aries at the spring equinox. Its position then became known as “The First Point of Aries.” Hipparchos discovered that the equinoctial point had moved westward from its earlier location in Taurus, sliding along the ecliptic, in a so-called “precession of the equinoxes.” The equinoctial points have continued to shift, by about 1˚ every 72 years, so that in roughly 26,000 years it would move all the way around the ecliptic and return to the same location. At
53 Taurus, Gemini, Cancer, Leo, Libra, Capricornus. Allusion to Pleiades: Seven Atlantic Sisters 54 Obliquity (tilted angle of 23.5˚) of the ecliptic with respect to the celestial equator. Modern answer: The axis of Earth’s rotation is tilted 23.5˚ with respect to the axis of revolution around the Sun; the tilted axis of Earth points in the same direction except for a slight shift due to "precession of equinoxes" but this is too slight to bother us in our lifetime. 55 A. Gemini B. Early December
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present the spring equinox is located about 30˚ west of the First Point of Aries, on the edge of Pisces near its border with Aquarius. Some say we have just entered the Age of Aquarius. Because astrologers still calculate from the First Point of Aries instead of the current March equinox location in Pisces, all modern horoscopes have shifted out of phase with the actual stars by one sign of the zodiac. That is, the actual zodiac of constellations now differs from the zodiac signs or houses as used by astrologers, because the zodiac of signs refers to the location of the Sun in the epoch of Hipparchos, disregarding precession. For example, if a contemporary of Hipparchos’ were born in early March, the Sun would then have been in the constellation of Pisces, and his astrological sign would have been Pisces. But someone born in early March in our time would still be given the sign Pisces by an astrologer, despite the fact that the Sun was actually in the constellation of Aquarius at the time of birth. Those who read horoscopes are one sign out of phase with the constellations! Of course correcting this error would still not astrology reasonable today. Study the two tables of zodiac sign alignments below. Read Chaisson pages 9-10a, then answer these questions about “Long-Term Changes” 1. How do we today explain the appearance of the slow 26,000-year wobble of all the stars? (Ancient astronomers explained this by saying there is a slow wobble of the sphere of fixed stars around the Earth, which is at the center of it all). 2. Every 13,000 years summer and winter would be reversed into opposite positions by the months of our calendar if we calibrated our calendars by the stars (sidereal year) rather than by the tropical year (defined just before Chaisson’s “Long-Term Changes” section). Explain why. (Our Africa Show / Precession planetarium lab helps, so don’t panic). The Zodiacal Motion of the Planets As with the Sun, the other planets move into different constellations at different times; sometimes a given planet is visible in the nighttime sky and sometimes it appears in constellations nearer the Sun in the daytime sky (and thus is usually invisible). Furthermore, when a planet returns to a given constellation it will not always be at the same month or season of the year. The planets, like the Sun, lie within a particular constellation of the zodiac at any given time. Unlike the Sun, planets can wander up to 9 degrees above or below the ecliptic (the ecliptic, by definition, marks the path of the Sun eastward through the middle of the zodiac). The zodiac may also be defined as the 18˚ band of the sky, centered on the ecliptic, through which the planets wander. The traditional 12 signs of the zodiac (12 constellations named after animals and human dignitaries) do not all exactly fit within the more technical modern sense of zodiac, which refers to the precise 18˚ band of the sky that is centered on the ecliptic. In contrast to the planets, the fixed stars themselves change from season to season in a more regular manner: those fixed stars overhead at midnight in midwinter will be overhead at midday in midsummer (invisible except during total solar eclipses). A fixed star returns to the same position in the sky at a given time of day after exactly one year.
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Study Questions 1. One fine day in early summer, the Sun rises with a star of Orion’s belt. Exactly two months later... (answer each of the following questions based on this; your planisphere can help)56 a. Which will be higher in the morning sky? b. How much time will elapse between the rising of one and the rising of the other? c. How far apart will they be in angular degrees?57 d. How would you answer the above three questions for exactly six months later?58 2. How might you determine which constellation contains the Sun at a given time of year?59 3. When will fixed stars that are overhead at midnight in mid-autumn be visible overhead at midday?60 4. How is it that the Sun and the Moon can appear to have the same angular diameter, if the Sun is truly larger than the Moon?61 Sidereal (Zodiacal) Period Since the direction of a planet’s motion is roughly consistent, eventually it will return to about the same location at the same time of year with respect to the fixed stars (in the zodiac). The time it takes to do so is called the planet’s “sidereal” (or “zodiacal”) period. Remember that the term “sidereal” literally means “related to the stars.” The term “zodiacal period” is even more specific for this kind of period of planetary motion because it refers to the zodiac constellations through which planets move. Planet Sun62 Moon Mercury63 Venus Mars
Sidereal Period about 365 1/4 days about 27 1/3 days about 1 year about 1 year about 687 days
56 a. Orion b. Assume two 30-day months, giving 60 days, thus about 60˚ difference in angle at about 4 minutes per day comes to 240 minutes (4 hours). 57 60˚ 58 6 months time difference would produce a 180˚ difference between the Sun and Orion. At 4 minutes each degree, this is 720 minutes, or 12 hours. 59 Obviously, you can’t see which stars are right by the Sun, because the Sun’s light obliterates the light from the stars. However, you could take notice of which stars rise just before the Sun and map them out; do this periodically through the year until the end where you started. You could essentially map out all 12 constellations of the zodiac (or some other similar map of stars along the ecliptic). 60 Six months later (mid-spring). 61 The sun is much larger than the Moon. 62 Remember that this year is about 20 minutes longer than the seasonal year. 63 Venus and Mercury are "inner" or "inferior" planets. The other 3 planets visible without a telescope are Mars, Jupiter, and Saturn. These are "outer" or "superior" planets. The division between inner/outer can also be designated by the asteroid belt that lies between Mars and Jupiter, making Mars the last of the inner planets, rather than the first of the outer planets (we will not use this convention because the asteroid belt was discovered long after the historical focus of this course on 17th century and premodern astronomy).
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Jupiter Saturn
about 12 years about 30 years
Changes in Brightness Planets tend to be brighter than fixed stars. They don’t twinkle, as do the fixed stars. Because of their brightness, planets are among the first “stars” to appear in evening twilight and the last to disappear in the morning sky. The brightness of a planet changes over time; in contrast, fixed stars shine with a generally constant magnitude. Changes in Direction and Speed As some planets grow brighter they concurrently change positions from day to day against the background of fixed stars in a direction opposite or “retrograde” to the ordinary direction described above. That is, a planet begins to rise ahead of the fixed stars that rose with it on the day before (instead of rising slightly later as is usually the case). Another way to describe this reversed direction is to say that a retrograding planet appears further westward each day (instead of slightly eastward as usual) against the background of fixed stars, once the daily motions have been subtracted (disregarded). Furthermore, the distance between successive daily positions of planets changes as well (that is, they move with changing speeds at this time). Study Question: What are five ways planets differ from fixed stars?64
64 Five ways could include: planets don’t twinkle (stars do), planets don’t rise (or set) in the same place each night (stars do, at least perceptibly so for amateur astronomers in your lifetime), planets don’t remain fixed in relationship to other stars (stars do, at least perceptibly so for amateur astronomers in your lifetime), planets are very noticeable brighter and then less bright in a periodic way (stars, at least the vast majority, in your lifetime, remain virtually constant in brightness), planets appear to speed up and slow down (stars appear to go around Earth at a constant rate, about once every 24 hours).
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Monday Sept. 6, Labor Day (do lab this week) Lab 2: Place in Space (Planetarium) Place in Space: Lab Report • Name: _________________ Introduction to Your Place in Space: Coordinate Systems for Identifying Location 1. Shawnee’s longitude: -97° = distance from equator or Greenwich England? _____________ (Hint: longitude is distance in degrees along the equator, not away from the equator) 2. Shawnee’s latitude: ____° = distance from equator or Greenwich England? ______________ Horizon Circle Defined by Your Position on Earth 3. Where is horizon circle on planisphere? ________________ On the dome? ______________ 4. Azimuths of 4 cardinal directions: N ________, E _________, S _________, W _________ 5. What is the relationship between our north latitude and Polaris’ altitude? ________________ Celestial Equator Defined by Earth’s Equator: Guide to Daily Motion 6. Where is celestial equator on planisphere? _______________ On the globe? _____________ 7. What is the relationship between earth’s equator & the celestial equator? ________________ 8. Does the celestial equator always intersect the horizon at due east and due west? _________ 9. What is the altitude of the celestial equator on the meridian as seen from Shawnee? _______° 10. Celestial equator altitude _____° + _____° more degrees up = ______° total altitude of zenith 11. Polaris altitude _____° + _____° more degrees up = ______° total altitude of zenith 12. Right Ascension is measured along the equator in these units: ___________ & ___________ 13. Declination is measured above (+) or below (-) the equator in ______________ (units) Ecliptic: Circle Defined by Sun’s Position as seen from Earth: it marks plane of solar system Instructor acts out solar system and galaxy orientation in the room, then see it in the night sky! 14. Cygnus (swan) flies down the Milky Way (plane of our ______________) toward Sagittarius (teapot), which marks the direction of the galaxy’s _______. Is our solar system in the same plane as our galaxy? _____ 15. Use flashlight on the dome to model Sun’s apparent daily motion at key dates of this table: Key Dates rising azimuth noon (meridian) altitude setting azimuth June solstice December solstice Spring/fall equinox 16. Sun appears to move east or west along celestial equator? _____. Daily or annually? _______ 17. Sun appears to move east or west along ecliptic? _____. Daily or annually? ______________ 18. Is the Sun ever directly overhead (at zenith) as seen from Shawnee? ______ 19. What did you learn in grammar school as the astronomical meaning of 23.5°? ____________ 20. How can we figure this from the table above? _____________________________________ Celestial Globe Activity: Simulate longest and shortest days for Shawnee (assume Earth at rest) Hold globe so Shawnee is on top (hold globe so north pole star is 35° above due north) 64
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Wednesday September 8 BCP Unit 3: Synodic Patterns All heavenly bodies are visible in the nighttime sky for a period of weeks or months, then disappear into the daytime sky for a period of days or weeks before becoming visible again. That is, they follow a recurring pattern relative to the Sun, which is called a synodic pattern. It makes no sense to talk about the synodic pattern of the Sun, because the term “synodic” entails the idea that the motion of the body under study is judged relative to the Sun. Synodic period: the time required for a body to return to a given alignment with the Sun.
Synodic Patterns: Outer Planets In the diagram below, you are facing south, looking up into the sky. The loop path traced by an outer planet occurs against the background of the fixed stars over a period of multiple months. Daily motion from east to west is not shown. Outer planets generally appear to drift eastward relative to the fixed stars, but not as rapidly as the Sun. Sometimes the outer planets appear to stop their usual eastward drift and move westward in retrograde motion relative to the fixed stars.
Synodic Phenomena: Outer Planets First Appearance
Last Appearance
South
?
West
East First Stationary
-Retrograde-
Point
Second Stationary Point
Opposition Synodic Period of Outer Planets (A) First Visibility (Heliacal Rising) At its heliacal rising, the planet appears momentarily on the eastern horizon just ahead of the Sun; i.e., it rises in the morning sky “with the Sun” (which is the meaning of “heliacal”), just before sunrise, at which time it lapses into invisibility again.
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(B) Western Quadrature Because the Sun appears to drift more rapidly eastward than the outer planets (relative to fixed stars), on successive mornings an outer planet will typically rise a few minutes earlier and be visible for a longer period before sunrise. Over the next several months it will rise at an earlier time each morning, and reach a higher position in the eastern sky before the light of dawn veils the nighttime sky. Eventually it will rise in the east around midnight, and cross the meridian at sunrise. On this date an earthly observer would measure the Sun-Earth-Planet angle to be 90˚; this is called its “western quadrature.” Compare this first quarter (which is west relative to the Sun) of the synodic cycle of outer planets with the first quarter of the Moon (which is east relative to the Sun). Why are these opposite (west and east)? Answer: Outer planets appear to drift eastward slower than then sun and the Moon always appears to drift eastward faster than the Sun (both eastward drifts are relative to the fixed stars). (C) Opposition At opposition, an outer planet transits the meridian at midnight. To cross overhead at midnight, the planet must rise opposite the Sun, i.e., be rising in the eastern sky just as the Sun sets in the west. An earthly observer would measure the Sun-Earth-Planet angle to be 180˚. The planet now appears at its brightest and is in the middle of its retrograde motion. That is, with reference to the above diagram, opposition comes a week or so after the First Station, and precedes the Second Station by a week or so as well. (D) Eastern Quadrature Over the next several months the outer planet will rise in the east at an earlier time in the evening, and will cross the meridian before midnight at ever-earlier times. Eventually it will transit the meridian at sunset. An earthly observer would measure the Sun-Earth-Planet angle to be 90˚ at that time, which is called its “eastern quadrature.” At that time the planet lies east of the Sun by 90˚. Finally, as it approaches the date of its “heliacal setting,” it will appear closer to the western horizon at the time when sunset reveals the starry sky, the planet being visible for shorter and shorter periods in the early evening. (E) Last Visibility (Heliacal Setting) At its heliacal setting, the outer planet appears momentarily on the western horizon just behind the Sun (i.e., in the evening just after sunset). For weeks it has been appearing lower and lower in the western sky at sunset, and now it makes its last brief appearance before its first invisibility.
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(F) Invisibility The outer planet now lies close enough to the Sun that it is above the horizon only in daytime. This period of invisibility lasts several weeks, during which the following occur... • Sun and the planet move closer together; • The planet achieves “conjunction” (its closest position to the Sun); and • The Sun and the planet then begin to move farther apart, eventually so much as to make the planet reappear in the morning sky, beginning a new synodic cycle. Planet Mars Jupiter Saturn
Average length of retrograde motion 65–85 days 120 days 140 days
Enters retrograde motion every 780 days 399 days 378 days
Synodic Patterns: Inner Planets Mercury and Venus follow a different synodic pattern than the one described above for outer planets. Mercury and Venus are always located in the same region of the sky as the Sun, unlike the other planets which can be found at any angle up to directly opposite (180˚) the Sun. We will now investigate the stages of the synodic period through which Venus and Mercury go. (A) First Visibility (Heliacal Rising) The heliacal rising of Mercury of Venus refers to when either of them rises just before the Sun (just west of the Sun). At its heliacal rising Venus has the shape of a slim crescent, although under most conditions this appearance can only be detected with a telescope. Venus shines brighter when in its crescent phase than when it is full because at this time its angular diameter happens to be much greater (due to Venus actually being closer to earth). (B) Maximum Western Elongation As the Morning Star, Venus continues to rise earlier each morning before sunrise (to the west of the Sun), until it achieves its maximum western elongation. Elongation means the angular distance from the Sun. The elongation of Mercury and Venus is the angular distance of either planet from the Sun. When an inner planet is as far from the Sun as it ever gets, it is in maximum elongation: 47˚ for Venus and 28˚ for Mercury. Because Mercury and Venus are never far from the Sun, they cannot transit the meridian at midnight. For the same reason, Mercury and Venus never reach opposition, as do the outer planets. (C) Invisibility When Venus or Mercury moves closer to the Sun it is eventually lost in the glare of a daytime zone of invisibility. 68
(D) Maximum Eastern Elongation As Venus emerges from invisibility on the far side of the Sun, it becomes an Evening star. At its first appearance, it sets heliacally (with the Sunset). Then it falls more and more behind (east of) the Sun at sunset, eventually reaching a maximum elongation to the east from the Sun, appearing higher in the western sky at sunset. (E) Last Visibility (Heliacal Setting) Before disappearing into the zone of invisibility as it moves closer to the Sun, Venus will set heliacally for a second time (along with the Sun at sunset). (F) Invisibility A second period of invisibility follows as Venus moves in front of the Sun, before rising heliacally to begin the next synodic cycle. Like the outer planets, Venus and Mercury do reverse their apparent direction of motion. However, instead of speaking of the direction reversal of Venus and Mercury as simply retrograde in the sense described for the outer planets, visualize their synodic pattern as an oscillation, like a pendulum swinging back and forth around the Sun: Synodic Stage: Inner Planet Appearance Western elongation Morning Star Invisibility None Eastern elongation Evening Star Invisibility None Modern Planetary Tables of Synodic Patterns Planet Mercury Venus Mars Jupiter Saturn Moon
Synodic Periods 115 days 584 days 780 days 399 days 378 days 29.5 days
Study Questions 1. Define synodic period.65
65 Synodic period is the time required for a body to return to a given alignment with the Sun
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2. Number the following in the chronological sequence as they occur for Mars, Jupiter, or Saturn (outer planets), beginning with heliacal rising:66 a. __ heliacal rising b. __ heliacal setting c. __ western quadrature d. __ eastern quadrature e. __ opposition f. __ conjunction g. __ invisibility 3. Match each term with its corresponding angular measurement (the angular distance between a celestial body and the Sun as viewed from Earth):67 a. Maximum elongation of Venus ___ 180˚ b. Quadrature ___ 90˚ c. Opposition ___ 0˚ d. Conjunction ___ 47˚ 4. At its maximum eastern elongation, Venus appears as the:68 a. __ Morning star b. __ Evening star 5. Match each stage of the synodic period as discussed for outer planets (left column below) to a corresponding stage of the lunar cycle (right column below):69 a. Heliacal rising __ 1. New Moon (invisible) b. Opposition __ 2. Full Moon c. Heliacal setting __ 3. Waning crescent before New Moon d. Conjunction __ 4. Waxing crescent after the New Moon 6. In what sense does one’s location on Earth have a “synodic period” of one day?70
Synodic Patterns: Moon The lunar cycle, in which the Moon passes through successive phases from New Moon to New Moon, is analogous to the synodic period of the outer planets. That is, the phases result from the relative position of the Moon and Sun. The Moon exhibits phases because it is not intrinsically illuminated, but shines only by reflecting the light of the Sun. Ancient astronomers assumed this. Half of the Moon is always illuminated by the Sun (except during a lunar eclipse), though the illuminated half is not always turned toward the Earth. The synodic period of the Moon (or
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a1, b5, c2, d4, e3, f7, g6. a47˚, 90˚, c180˚, d0˚ Evening star, because it would rise after the Sun and thus not be visible until after the Sun set. a4, b2, c3, d1 Earth rotates on its axis once daily (sun appears to go around Earth once daily), thus an observer on Earth would get realigned with the Sun in the same way (e.g., sunrise) once every 24 hours, thus a "synodic" period of 24 hours.
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lunar month) ranges from 29 to 30 days; the actual value, known to ancient Babylonian astronomers, is 29.53059 days. Study the Lunar Synodic Cycle Table Day 0 1–3 7 10–12 14-15 18–20 22 25–27 29-30
Phase New Moon Waxing Crescent First Quarter Waxing Gibbous Full Moon Waning Gibbous Third Quarter Waning Crescent New Moon
Synodic Cycle Conjunction
Location and Description In line with the Sun. Moon-Earth-Sun angle = 0˚. Lost in daytime glare. Low in east after sunrise.
Eastern quadrature: Rises in east about 6 hours after sunrise. 90˚ east of Sun Behind (east) of Sun Ever lower in east at sunset. Opposition
Moon-Earth-Sun angle = 180˚. Rises in east at sunset.
Ahead (west) of Sun Rises after sunset, appearing later each night. Western quadrature: Rises in east about 6 hours after sunset. 90˚ west of Sun Ever lower in east at sunrise. Conjunction
Invisible; illuminated side is facing away from Earth.
Read Chaisson pages 18-19, then answer these questions about “Lunar Phases” 1. What did you learn from running the “Phases of the Moon” physlet from Chaisson’s eBook? 2. Compare Chaisson’s figure 1.1 with the above Packet table. What do you learn? Examine the following two diagrams and compare them with the table above and Chaisson.
Moon ( first quarter ) S slightly under 90° E
W
(a) 71
SUN
S
Moon
180° apart
(full)
E
W
SUN
(b) Full moon is also called second quarter. Draw your own illustration of a 3rd quarter Moon.
The Moon’s Sidereal (Zodiacal) Period Since the Moon appears to move eastward about 12.19˚ per day with respect to the Sun, and since the Sun appears to move eastward about 1˚ per day with respect to the stars, the Moon will appear to move eastward with respect to the stars about 13.19˚ per day. The Moon’s sidereal period (sidereal month), or the time it takes for the Moon to complete one 360˚ lap with respect to the stars, will therefore be 360˚ ÷ 13.19˚ = 27.3 days, which is about 2.3 days shorter than the Moon’s synodic period (synodic month of 29.5 days). The Moon’s Synodic Period and the Problem of the Solar Calendar The 29.5-day synodic month (time from New Moon to New Moon) constituted the chief timereckoning cycle of nomadic peoples. In fact, it is still about the number of days that we ordinarily call “a month.” The solar year lasts about 365 1/4 days and, since it corresponds to agriculturally important seasons, was adopted by most settled communities. A problem arose: How could one devise a calendar that would keep lunar months from getting out of phase with solar years? A “year” of 12 lunar months would quickly fall out of phase with the seasons unless adjustments were made to maintain a desired association between a particular month of the year and a given season (e.g., harvest time). The problem turns on accurately determining the lengths of the synodic month and the year, and finding a common multiple. The problem is that there is no exact common multiple and so one must settle for a more or less satisfying approximation.
Eclipses Read Chaisson pages 19b-22a and revisit his diagrams as you read this part of the Packet. Eclipses may occur when the Sun, Moon, and Earth line up with either the Moon or the Earth in the middle. If they line up exactly, then one body (whichever is in the middle) will eclipse (cast a shadow upon) another. 72
Answer these questions about the relationships of Earth, Moon, and Sun in eclipses: 1. In which Moon phases are the Sun, Moon & Earth lined up on a straight line (any order)?71 2. Which body is eclipsed in a lunar eclipse?72 3. Which body is eclipsed in a solar eclipse?73 4. Which (S, M or E) is in the middle during a lunar eclipse? ______. Solar eclipse? _______74 5. Why does an eclipse not happen every time there is a Full or New Moon?75 The Anatomy of a Lunar Eclipse 1. The Moon is obscured by Earth’s shadow. Earth’s shadow cone, when cast upon the Moon, is three times the Moon’s diameter. 2. The angle Sun–Earth–Moon is 180˚ (opposition of Moon and Sun as viewed from Earth) 3. Occurs only at Full Moon, but does not occur at every Full Moon The Anatomy of a Solar Eclipse 1. The Sun is obscured by the Moon’s disk as viewed from at least for some locations on Earth 2. Conjunction of Moon and Sun, or New Moon, but does not occur at every New Moon 3. Usually visible from smaller percentage of Earth’s surface than is the case with lunar eclipses Kinds of Solar Eclipses (due to varying Sun-Moon-Earth distances) 1. Annular Eclipse: The lunar disk is too small to cover the solar disk, but the centers of the two disks meet at least approximately. What causes this? More than half the time the Moon is far enough from Earth (relative to the changing Sun-Earth distance) that it appears smaller than the Sun. During this period of greater relative Moon-Earth distance, the Moon (if lined up with the Sun) fails to totally eclipse (cover) the Sun. 2. Total Eclipse: The lunar disk is just large enough to cover the solar disk, and the centers of the two disks meet at least approximately. What causes this same apparent size of Sun and Moon, which makes possible a total solar eclipse? The relative Sun-Earth distance and 71 New moon and full moon (but eclipses don’t occur every new and full moon because usually the Moon is a little above or below the plane that includes the Sun and earth). 72 Moon 73 Sun 74 Earth; Moon 75 Eclipses don’t occur every new and full moon because usually the Moon is a little above or below the ecliptic (up to about 5˚), that is above or below the plane that includes the Sun and earth, the plane of the "solar system".
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relative Moon-Earth distance just about exactly compensate for the real size difference between Sun and Moon, making both appear about the same size when viewed from Earth. 3. Partial Eclipse: either above eclipse when disk centers are not lined up with the observer. Draconitic Period of the Moon: The Key to Eclipses The draconitic period (month) of the Moon, although difficult to understand, is vital to understanding if one hopes to make sense of eclipses. The motions of the Moon are said to have given even Newton a headache, and they are much more complicated than will be described here. Various perturbations, or deviations from the simpler patterns, are caused by the gravitational attraction of the Sun and are the reason why only average values are given in modern tables for many parameters for the Moon (including speed and distance from the Earth). Cut out the figure on the next page using the instructions on the pages that follow.
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12 11 10
9
8
8°
5° 7
6 75
5
4
3
2
1
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Draconitic vs. Sidereal (Zodiacal) Period of the Moon Instructions for Constructing “Draconitic vs. Sidereal Figure” Cut out the figure on the previous page so that it forms a strip of paper that is about 7 inches long and about 2 inches wide with the figure on it. Leave some extra paper on the right end of the strip (the end that is labeled 8˚); trim off any extra paper that may be on the end of the strip that ends with segment #12. Form a loop with your paper strip with the figure on the inside surface of the loop. Staple or paste the backside of the left end of the strip to the front side of the right end of the strip so that segment #12 of the figure is just touching segment #1. “Draconitic vs. Sidereal Figure”: Activities and Questions 1. Observe the two circles formed on the inside surface of the paper loop. One circle is formed by the originally straight dotted line that runs down the center of the paper strip. What does this dotted-line circle represent? __________. 2. The second circle, which is formed by the originally snake-shaped line on the paper strip, forms a distorted/broken circle upon close examination. This second circle is tilted with respect to the first circle by an angle that is supposed to be about 5˚ (to represent what we want it to in the realm of astronomy). What does the second circle represent? __________. 3. What do the 12 segments of the figure represent? _____________________. 4. An Earthling would be observing this loop of paper from a point roughly in the center of the interior space within the loop. Can you imagine your eyeball looking out at the loop from the interior space within the loop? 5. The Moon moves along its circular path at about 13˚ per day, while the Sun moves along the ecliptic at about 1˚ per day. The circular path of the Moon is inclined by 5˚ to the ecliptic path of the Sun. The two points at which the Moon’s path intersects the ecliptic are called the ascending and descending nodes, which are analogous to the March and September equinox points where the ecliptic similarly intersects the celestial equator. Find these nodes now. 6. For a solar or lunar eclipse to occur, the Moon must enter its New or Full phase while it occupies one of its nodes, otherwise it will lie slightly above or below the line between the Sun and the Earth. Can you visualize why this is the case using your model? 7. The Moon’s draconitic period is the time it takes for it to cross the ecliptic in the upward direction twice (or downward direction twice). The Moon’s sidereal period is the time it takes to go through the one complete 360° of all 12 signs of the zodiac. Which of the two periods (months) must be greater? ______________________ Hint: Draconitic period = 27.2 days. Sidereal period = ______days. 77
Predicting Eclipses is Not Easy! In “The Greatest” astronomical work, i.e., “Almagest,” the Greek astronomer Ptolemy (ca. 150 AD) relied on eclipse records dating from the reign of the Assyrian ruler, Nabû-nasir (Nabonassar), 747–735 BC. Because the darkening of the Sun or Moon constitutes one of the most spectacular of celestial phenomena, so the anticipation and prediction of eclipses must have been one of the most spectacular successes of ancient astrologers. Anthony Aveni comments: “The fear engendered by the departure from the regularity of nature epitomized in the eclipse was as real then as is our present fear of nuclear war.” Prediction of eclipses was also one of their most difficult tasks, given that the Moon’s motions are so complicated. Study Questions 1. Do the Moon’s phases result from the Earth blocking the light of the Sun?76 2. What percentage of the Moon do we see?77 3. The same side of the Moon always faces Earth. Answer the questions below after contemplating this poetry: “O Moon! When I look at thy beautiful face, Careening along through the boundaries of space The thought has quite frequently come to my mind If ever I’ll gaze on thy glorious behind.” Ronald Ross a. If you lived in ancient times, how might you have explained this phenomenon of only one side of the Moon always pointed toward Earth?78 b. Can you provide an explanation, or does it seem a coincidence to you now, that the period for the revolution of the Moon about the Earth should equal the time for one rotation around its axis?79
76 No, but this is a common misconception according to surveys. 77 At most at any given moment, only 50% (we can only see half of a sphere at any time, viewed from on perspective). However, this half of the Moon (hemisphere) that is potentially visible from Earth at given times is not always completely illuminated by light from the Sun (any phase other than full moon). 78 Ancient Greeks would probably attribute this appearance to the Moon being embedded within (attached to) a large celestial sphere that rotates on its axis with Earth as its center, carrying the Moon around with it. In this conceptual context, ancients would likely conceive of the Moon as not rotating on its axis. 79 Viewed from outside the rotating-revolving system, the Moon’s orientation changes as it revolves around Earth. It’s orientation changes in such a way that only one face of the Moon always faces Earth, which must be the result of its period of rotation being equal to its period of revolution (using modern definitions). In Ferris wheel terms, this would result in a person being turned upsidedown at times (which we intuitively want to call "no rotation" but such is not the case using modern scientific definitions in which the Ferris wheel car is indeed rotating on it axis as viewed from the birds-eye view looking on the whole system).
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4. In the Rime of the Ancient Mariner, Samuel Taylor Coleridge wrote of...”The horned [crescent] Moon with one bright star within the nether tip.” What is wrong with this poetic description?80 5. How much of the Moon is illuminated by the Sun at all times?81 6. When the Moon is Full, where is it located (answer the three parts to this question below each with a separate answer). Hint, how far apart in degrees is the Sun from the Moon (as viewed from Earth) in each of these situations:82 a. ...at sunset? b. ...at midnight? c. ...at sunrise? 7. Henry W. Longfellow wrote that: In broad daylight, and at noon, Yesterday I saw the Moon...” Is this poetic account possible? If so, could the Moon have been in its Full phase?83 8. Draw and label three circles Sun, Earth and Moon so that their alignment corresponds to that occurring at a solar eclipse. Show how the appropriate body is eclipsed.84 9. During a solar eclipse, in which phase is the Moon?85 10. Draw and label three circles Sun, Earth and Moon so that their alignment corresponds to that occurring at a lunar eclipse. Show how the appropriate body is eclipsed.86 11. During a lunar eclipse, in which phase is the Moon?87 12. Why does an eclipse not occur at every Full Moon or New Moon?88
80 There is no way to see a star within the bowl of a crescent moon because the un-illuminated part of the Moon stands in the way between the Earth observer and any stars that might be otherwise visible in the background. Trivia: do you know of a modern American firm that has a commercial trademark with such a misconceived lunar non-observation? 81 Always half (a hemisphere), but we don’t always see all of this half. When we see half of this half, then we are seeing 1/4th of the total spherical surface of the Moon, which appears to us as a "half moon" (first or third quarter). 82 In all three situations, the Moon and Sun are 180˚ apart (opposition; full moon). Thus, the answers are: a. Moon is just rising in the east, b.Moon is crossing the meridian, c. Moon is just setting in the west. 83 In broad daylight, yes, you can see the Moon (e.g., half way up from the horizon toward the meridian in half phase when the Sun is 90˚ away and half way up from the other horizon). In broad daylight, and in full phase, no, because in full phase, just as the Sun rises, the Moon sets and just as the Sun sets, the Moon rises), 84 You can do this on your own, just keep straight that full moon makes possible a lunar eclipse and new moon a solar eclipse. 85 New Moon. 86 You can do this... problem. 87 Full Moon. 88 Because the tilt of the Moon’s orbit is 5˚ relative to the plane of the Sun-Earth-solar system, placing the Moon usually a little above or below the ecliptic, where the Sun appears to be throughout the different times of the year. Only rarely does the Moon happen to cross the ecliptic at the moment of either a full Moon (producing a lunar eclipse) or a new Moon (producing a solar eclipse).
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Further Reading •
Allen, Richard Hinckley. Star Names: Their Lore and Meaning. 1899; reprint. New York: Dover, 1963. Source for many of the epigrams in this BCP Guide.
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Aveni, Anthony F. Skywatchers of Ancient Mexico. Austin: University of Texas Press, 1980. Good introduction to archaeoastronomy, particularly Mayan. Includes an excellent overview of observational phenomena, “Astronomy with the Naked Eye” (chapter six).
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Crowe, Michael J. Theories of the World from Antiquity to the Copernican Revolution. New York: Dover, 1990. The present Basic Celestial Phenomena Guide originally served as a companion and introduction to this text (we no longer use it as a text in US 311). See the first chapter for an introductory orientation to the celestial motions. The appendix includes an excellent discussion of Stonehenge.
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Knox, Richard. Experiments in Astronomy for Amateurs. New York: St. Martin’s Press, 1976. Includes instructions for constructing and using sundials, a quadrant, an astrolabe, etc.
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Krupp, Edwin C. Echoes of the Ancient Skies: The Astronomy of Lost Civilizations. New York: Harper and Row, 1983.
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Menzel, Donald H. and Jay M. Pasachoff. A Field Guide to the Stars and Planets. Peterson Field Guide Series. Houghton Mifflin, latest version. Highly recommended: This guide, plus Chet Raymo’s book and a few nights each month outdoors, are all you need to become familiar with the night sky.
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Neugebauer, Otto. The Exact Sciences in Antiquity. 2d ed. Providence: Brown University Press, 1957. The best and most reliable introductory survey of Mesopotamian and Egyptian mathematics and astronomy. Highly recommended.
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Raymo, Chet. 365 Starry Nights: An Introduction to Astronomy for Every Night of the Year. New Jersey: Prentice–Hall, 1982. One of the easiest ways to become familiar with celestial motions, to recognize the constellations (and learn their lore) is to read through this book in a year. If you do, you’ll discover that you don’t need a telescope to enjoy the starry sky.
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Sky and Telescope. The leading journal for amateur astronomers. Each issue includes a star map for the month, with accompanying descriptions and explanations of celestial events.
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Monday September 13 Lab 3: Babylonian Show & The Planets (Planetarium) Planets: Lab Report • Name: _________________ Stars Over Ancient Babylon 1. What class of Babylonian people kept records of celestial events over 20 centuries? _______ 2. Babylonian numbers used ________values (like decimals) and were ___-based, not 10-based 3. What math did 7th-1st century Babylonians use for accurate prediction? geometry / arithmetic 4. Early Greek astronomy was geometrical & qualitative (not based on precise _____________) 5. Babylonian science (like Newton's gravity) found mathematical reasons not physical ______ 6. Planets slowly wander through the _____________constellations (Babylonians named all 12) 7. What kind of religion motivated Babylonian astronomy? _____________________________ 8. Conclusion: Evidential support (regardless of personal motivation) is the key to good science (How does this conclusion impinge on the argument of Darwinists today who proclaim that design theorists have substantial religious motivation and thus design theory isn't scientific?) Inner Planets 9. What is the bounded elongation for each inner planet? Mercury: _______° Venus: _______° 10. Are Mercury and Venus ever visible at midnight? ____ Why? ________________________ 11. How many conjunctions with the Sun per synodic period? Mercury _______ Venus ______ 12. Why is a planet invisible during a conjunction with the Sun? __________________________ Outer Planets: list those visible to the naked-eye: ___________, ____________, ___________ 13. Direct motion is eastward or westward against the background of fixed stars? ____________ 14. Retrograde motion is eastward or westward against the background of fixed stars? ________ 15. Outer planets spend most of their time in which motion, direct or retrograde? ____________ 16. Define opposition ____________________________________________________________ 17. Are the outer planets ever visible at midnight? _______ 18. An outer planet in the middle of retrograde motion is at conjunction or opposition? ________ 19. When does an outer planet appear brightest (outdoors, not in planetarium)? ______________ Moon: The Four Quarters of the Lunar Football Game 20. New moon means the Moon is _____° away from the Sun as measured along the ecliptic 21. At the end of first quarter the Moon is _____° away from the Sun (east or west? ________) 22. At the end of second quarter the Moon is _____° away from the Sun; also called _____ moon 23. At the end of third quarter the Moon is _____° east of the Sun; also called _____ moon 24. At the end of forth quarter the Moon is _____° away from the Sun; also called _____ moon 25. The moon drifts eastward _____° along the ecliptic daily; the Sun only about _____° 26. The moon drifts eastward _____° faster than the Sun each day 27. Compare the drift eastward (relative to the fixed stars) of the Sun, outer planets, Moon: Which is fastest? _____________ Slowest? _____________ Medium speed? ____________ 28. First quarter moon phase is “eastern quadrature” & first quarter for outer planets is “western quadrature.” Why? ___________________________________________________________ 82
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Cosmic Dimensions: Past and Present In Romans 1, Paul argued that the power and majesty of God are self-evident from the things God has made. A corollary principle is that “Humans are utterly small compared to the vastness of the cosmos.” Has this insight only recently dawned on humanity through the power of modern science? Or have humans known this since ancient times? You will find answers to these questions in this reading. Together with the other reading due today, we will address the topic of the size of the universe and its implications for human significance. Notes about the Table of Data Below • Measurements before the Aristarchos row represent modern (current) data • Some of the data is presented by means of a familiar scale model: Earth as 12-inch globe (you then compare the relative size of other objects as estimated at historic moments) • Study this table with the assistance of the questions that follow Distances and Diameters of the Sun, Earth, and Moon Units and Scientists
DISTANCE DISTANCE DIAMETER DIAMETER DIAMETER Sun–Earth Earth–Moon Sun Earth Moon Kilometers 149,600,000 384,400 1,390,000 12,755 3476 Miles 93,000,000 239,000 864,000 7926 2161 Earth Diameters 11,733 D 30 D 109 D 1D 0.27 D 12” Diameter Globe 2.2 miles 30 feet 109 feet 12” model 3.3 inches Figures in this row and 389 x x above are modern Aristarchos, 280 BC 18 to 20 x x 6.6 feet 12” model 4 inches Ptolemy, 150 AD 5.5 feet 12” model 3.5 inches Tycho Brahe, 1600 5.2 feet 12” model 3.4 inches William Whiston, 1715 96.3 feet 12” model 3.3 inches Study Questions for Reflection on the Table Above 1. If Earth were a 12” diameter model (a standard school globe), then what would all of the above estimates (even back to Aristarchos) render as the Moon’s relative size on the same scale (take the average of the data above)? Answer: the Moon would be about the size of a… a. Golf ball b. Softball c. Basketball 2. What object is 93 million miles from Earth (current estimate)? _____ 3. What object is about 8 thousand miles wide in diameter (current estimate)? _____
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4. If “D” stands for the diameter of Earth, then how many Earth diameters would it take to form a continuous chain from the Earth to the Moon (current estimate)? _____ 5. If “x” stands for the Earth-Moon distance, then according to Aristarchos how many times further from Earth is the Sun compared to the Moon’s distance from Earth?” _____ 6. Pre-18th century estimates of the Sun’s diameter compare to modern estimates in one of the following ways (circle the correct answer): a. Early estimates are about the same as the current one. b. Early estimates of the Sun’s diameter (about 5.7 feet using the average of the 3 figures on the scale model above) are about 19 times smaller than the current estimate (about 109 feet using the same scale model for Earth at 12 inches in diameter). [Note: 5.7 times 19 is about 109, in case you don’t have a calculator handy] 7. If a person thinks that a given object is many times smaller than it actually is, then it would stand to reason that this person would also think that this same object is many times (circle answer)... a. closer than it actually is b. further away than it actually is 8. Does your answer to the previous question roughly agree with the following observation? If we take, 20x, the upper limit of Aristarchos’ estimate of the Sun’s distance from us, then about how many times smaller is it compared to the current one of 389x (rounded up to 400x)? That is, how many times smaller is 20 than 400? Answer: _____. If your answer is 20, you are right. So, if Aristarchos mistook the Sun to be 19 or 20 times closer to us than it actually is, then does it make sense that he and other pre-modern people thought the Sun was almost that many times smaller than it actually is? 9. Have the actual numbers representing the scale of the accessible part of our universe gone up in value as one compares early and current estimates?
Classic Texts on the Size of the Universe Antiquity (Old Testament) Job 38.31–33 Can you bind the beautiful Pleiades? Can you loose the cords of Orion? Can you bring forth the constellations in their seasons or lead out the Bear with its cubs? Do you know the laws of the heavens? Psalm 8.3–4 When I consider your heavens, the work of your fingers, the Moon and the stars, which you have set in place,
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What is man that you are mindful of him, the son of man that you care for him? Psalm 103.11 For as high as the heavens are above the Earth, so great is his love for those who fear him. Isaiah 40.25–26 To whom will you compare me? Or who is my equal? says the Holy One. Lift your eyes and look to the heavens; Who created all these? He who brings out the starry host one by one, and calls them each by name. Because of his great power and mighty strength, not one of them is missing. Isaiah 55.9 As the heavens are higher than the Earth, so are my ways higher than your ways and my thoughts than your thoughts. 1 Kings 8.27 (Solomon’s dedication of the Temple) But will God really dwell on Earth? The heavens, even the highest heaven, cannot contain you. How much less this temple I have built! Isaiah 45.18 For this is what the Lord says—he who created the heavens, he is God; he who fashioned and made the Earth, he founded it; he did not create it to be empty, but formed it to be inhabited—he says, ‘I am the Lord, and there is no other.’ Nehemiah 9.6 Blessed be your glorious name, and may it be exalted above all blessing and praise. You alone are the Lord. You made the heavens, even the highest heavens, and all their starry host, the Earth and all that is on it, the seas and all that is in them. You give life to everything, and the multitudes of heaven worship you. You are the Lord God, who chose Abram and brought him out of Ur. Late Antiquity Pliny the Elder, 23–79 AD, Natural History, II.173ff. Pliny considers the extent of the habitable surface of the land, subtracting impassable oceans. Then he advises, “Calculate moreover the dimensions of all those rivers and vast swamps, add also the lakes and pools, and next the ridges too that rise into the heaven and are precipitous even to the eye, next the forests and steep glens, and the deserts and areas for a thousand reasons left deserted; subtract all these portions from the Earth or rather from this pin-prick [very small object], as the majority of thinkers have taught, in the world—for in the whole universe the Earth is nothing else: and this is the substance of our glory, this is its habitation, here it is that we fill 86
our positions of power and covet wealth, and throw mankind into an uproar, and launch even civil wars and slaughter one another to make the land more spacious! And to pass over the collective insanities of the nations, this is the land in which we expel the tenants next to us and add a spade-full of turf to our own estate by stealing from our neighbor’s—to the end that he who has marked out his acres most widely and banished his neighbors beyond all record may rejoice in owning—how small a fraction of the Earth’s surface? Or, when he has stretched his boundaries to the full measure of his avarice, may still retain—what portion, pray, of his estate when he is dead?” [That is, why fuss so much over acquiring much land when the habitable land is so insignificant when compared to the Earth’s surface as a whole, or the universe at large?] Ptolemy, Book I, Almagest (ca. 150 AD) “Moreover, the Earth has, to the senses, the ratio of a point to the distance of the sphere of the so-called fixed stars.” [That is, it as if the Earth were as small as a point compared to the huge distance that separates us from the fixed stars] Middle Ages Distance to Closest Star A typical medieval estimate of the distance to the closest star: 20,000 Earth radii. [This is not much by modern standards, but it is still very large for the cultural context of the medieval period] Goutier of Metz, Image du Monde (ca. 1245). If a man could travel upward at a rate of “forty mile and yet som del mo” a day, he still would not have reached the Stellatum (“the highest heven that ye alday seeth”) in 8000 years. [That is, the universe is so large that it is difficult to express it in words that are meaningful to humans] Study Questions 1. What is the general cultural sense that emerges from this stream of premodern texts about the size of the universe? Circle the best answer below: a. “Earth is utterly small compared to the vastness of the universe” b. “Earth occupies a large portion of the total space of our small universe” 2. Did premodern estimates of the size of the universe’s local parts, small as they were compared to current figures, have the cultural affect of people believing that the universe is a small place with quite limited room?
The Cosmic Calculations of Aristarchos of Samos (280 BC) Aristarchos of Samos (ca. 310 - ca. 230 BC) has been known since antiquity for having suggested that Earth both rotates on its axis daily and revolves about the Sun annually. Those who mention this reputation, most notably Archimedes who was a near contemporary, did not comment much on this idea because it was considered physically absurd in light of Aristotle’s 87
physics. What Archimedes found significant in Aristarchos were his calculations of the size of our immediate part of the universe. It was on this basis that Aristarchos was respected and most remembered. Aristarchos on the Relative Distances between the Earth, Moon, and Sun Units and Scientists Miles Earth Diameters 12” Diameter Globe Figures in this row and above are current Aristarchos, 280 BC
DISTANCE Sun–Earth 93,000,000 11,733 D 2.2 miles 389 x
DISTANCE Earth– Moon 239,000 30 D 30 feet x
18 to 20 x
x
How did Aristarchos determine the distance to the Sun in terms of the Earth-Moon distance? The key to his method is the determination of the angle between the Moon and Sun (as viewed from Earth) at the time of half Moon (first or third quarter phase). This angle is not easily measured (Galileo eventually went blind because of his habit of gazing at the Sun). Many of Aristarchos’ conclusions about the scale of the cosmos rested on a figure for this angle that turned out to be significantly off from the current estimate of 89.83˚. For the sake of his calculations of the Sun’s distance, Aristarchos took this angle to be 87˚. We not only have technical measurement difficulties to consider in explaining Aristarchos’ error, but more substantially, Aristarchos probably had other priorities in mind when he used the 87˚ value in his calculations. He was more likely interested in demonstrating his mathematical problem- solving techniques than in getting accurately measuring celestial distances. Let’s investigate the triangle proposed by Aristarchos—one with three points defined by the relative positions of Moon (M), Earth (E), and Sun (S). Label correctly in the diagram below the angle Aristarchos said was 87˚ (angle M-E-S). Note that the 3° angle M-S-E is already labeled for you.
M E
3°
Study Questions 1. What are the measurements in degrees of the three angles of this triangle? ___, ___, ___ 2. Which angle can be directly measured by an Earth-bound observer? EMS, MSE, or MES? 3. Which angle can be deduced from the way in which a spherical Moon would reflect the Sun’s light at the moment of half Moon? 4. Take out a ruler and do the necessary measurements and calculations on the triangle above to answer this question. How many times longer is the Sun-Earth line relative to the Moon88
S
Earth line (divide the Sun-Earth line by the Moon-Earth line)? Answer: The Sun-Earth line is ____ times longer. 5. Is your answer to the previous question between 18 and 20 times. This is the range of answer reported by Aristarchos. This range was appropriate given his rough approximation of the 87˚. If you got an answer of about 19, then you have just reached a rough idea of the power of geometry to determine distances in space that are inaccessible to direct measurement. One of our labs in this course expands your geometrical skills even further in such applications. More Study Questions: These target the primary source of Aristarchos below 1. Do estimates of the relative distances (or sizes) of the Sun, Moon, and Earth depend on whether the Sun or the Earth is taken as the center of the solar system? _____ 2. Which is more reliable, Aristarchos’ method or his actual results? _________ Aristarchos’ method for calculating the distance to the Sun depended upon certain astronomical principles that were well accepted by his time. Try to spell out the astronomical principles in use here, based upon pure mental reflection as well as based upon a close reading of Aristarchos’ own text below. What follows is an English translation of the part of Aristarchos’ text in which he determined the sizes and distances of the Sun and Moon. Aristarchos of Samos, On the Sizes and Distances of the Sun and Moon, Hypotheses and Proposition 7. Translation of TL Heath (Oxford, 1913).89 Hypotheses: 1. That the Moon receives its light from the Sun. 2. That the Earth is in the relation of a point and center to the sphere in which the Moon moves. 3. That, when the Moon appears to us halved, the great circle which divides the dark and the bright portions of the Moon is in the direction of our eye. 4. That, when the Moon appears to us halved, its distance from the Sun is then less than a quadrant by one-thirtieth of quadrant.90 5. That the breadth of the [Earth’s] shadow is [that] of two moons.91 6. That the Moon subtends [encompasses] one-fifteenth part of sign of the zodiac.92
89 M. Cohen and I.E. Drabkin, A Source Book in Greek Science (New York: McGraw-Hill, 1948), p. 217. 90 One quadrant is 90˚;1/30th of a quadrant is 3˚; Finally, 90 - 3 = 87 degrees. Thus, angle MES is 87 degrees. 91 I.e., in a lunar eclipse the diameter of the Earth’s shadow through which the Moon must pass is twice the diameter of the Moon. 92 I.e., the apparent angular diameter of the Moon (and Sun) is 2 degrees (i.e., 1/15 of 30 degrees). Archimedes credits Aristarchos with a value of 1/2 degree (which is much closer to the modern value).
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We are now in a position to prove the following propositions: 1. The distance of the Sun from the Earth is greater than eighteen times, but less then twenty times, the distance of the Moon (from the Earth); this follows from the hypothesis about the halved Moon. End of excerpt from Aristarchos of Samos, On the Sizes and Distances of the Sun and Moon About a generation later, Eratosthenes of Alexandria, calculated the size of Earth in absolute units. He used a common unit of distance at that time: stadia. We can express his work in an approximate equivalent in kilometers or miles. Read Chaisson, “Discovery P-1: Sizing up Planet Earth,” page 14. Compare it with below.
Eratosthenes of Alexandria: Sizing up Planet Earth Eratosthenes knew that deep wells in Syene Egypt, upstream on the Nile from Alexandria, reflect an image of the Sun off their water at high noon on the day of summer solstice. Compare Chaisson’s diagram on page 14 with the one below.
If s/p, then a=7.2° angle "a" s
p Use your protractor to draw a tri angle that represents the one formed by the following three lines in Era tosthenes’ work: 1. the portion of the gnomon that sticks out of the ground, 2. the shadow of the gnomon stick upon the ground, 3. the line from the tip of the shadow to the top of the gnomon. You can do this by drawing a triangle with the follow ing angles: 90, 82.8, and 7.2 degrees (this could give you a right triangle with the following lengths— if you want it to comfortably fit on a standard piece of paper: 3 cm, 27 cm, and 27.1 cm).
23.5°
How many degrees? 90
Imagine with Eratosthenes two virtually parallel rays of sunlight: one striking water in Syene (in a deep well), the other impacting Earth at the ancient city of Alexandria, a large and thriving city downstream on the Nile at a more northerly latitude. This second light ray, imaginarily extended through Earth’s interior, would not pass through the center of the Earth as we perceived in the case of the first light ray, but back up on Earth’s surface, such a ray of light would cast a shadow in the presence of a vertical object such as the gnomon that Eratosthenes used. Why, at high noon on the day of summer solstice, would the first ray of light not cast a shadow on the ground in the presence of a vertical object, while the second ray, hitting Alexandria, would cast a shadow? The illustration above clearly shows a vertical pole, a gnomon perhaps stuck in the delta sand along the Nile at Alexandria. A shadow of certain length would be cast by a pole, P, of certain height at high noon on the day of summer solstice in Alexandria, the same day of the year when vertical sticks facing off the Sun at Syene have nothing shadowy to show in wake of their heavenward reach. Question: Why would it be crucial for Eratosthenes to perform the observations at Alexandria on the same day of year (though not necessarily the same year) as the observation of the Sun at high noon when seen from Syene)? Answer: This would insure that the two rays of light were virtually parallel, allowing an ancient mathematician like Eratosthenes to transfer his calculation of the angle “a” (see diagram above) to the unknown angle created by the vertical stick imaginarily extended to Earth’s center and our original ray of light from the Egyptian well overhead at Syene. This unknown angle would amount, when added to Syene’s northern 23.5° latitude, to the latitude of Alexandria. The well-traveled due north-south route between Alexandria and Syene, along the proud Nile, provided Eratosthenes a critical figure for his work, rough as the figure was (calculated perhaps by the average camel ride per day). Working from the top down, he could deduce the angle “a” by the trigonometric properties of triangles (based on the length of lines that were directly measurable on such a triangle). Given that the two rays of light were practically parallel (the Sun is far enough away from Earth, even on ancient calculations, to insure this as a practical result), Beta concluded that angle “a” equals the unknown latitude difference between Syene and Alexandria, which came to 7.2 degrees. Thus, Eratosthenes calculated the distance from Alexandria to Syene to make up 1/50th of Earth’s circumference (360˚ * 1/50 = 7.2˚). Verify the size of the gnomon shadow relative to the gnomon itself (between 1/8th and 1/9th) by actually measuring with a ruler the lengths of the sides of the triangle formed by the angles 90, 82.8, and 7.2 degrees. Is the shortest side of this triangle roughly between 1/8th and 1/9th the size of the next longest side? Because Eratosthenes reasoned that the known distance from Alexandria to Syene amounted to 1/ 50th of Earth’s total circumference, he simply extended this calculation to conclude that the size of Earth’s circumference is 23,100 miles (he expressed the answer in stadia). Eratosthenes estimate was short of the actual figure, which comes closer to 24,900 miles. Although his data was off a bit, his geometric reasoning was flawless. 91
Chaisson: Pages 0-1, 10-16 (read study guide in Packet first) A Main US 311 Theme: Evidence from Science & History Challenge Chaisson’s Viewpoint Eric Chaisson, the lead author of your textbook, directs a science education institute at Tufts University. Tufts is 15 minutes from Harvard and possesses a similar Ivy League ethos. In 1999 I was invited to speak to Chaisson’s science education institute about the use of history of science in science education (my specialty). Although Chaisson is a nice guy and on the leading edge of astronomy education (in many areas), we shall critique parts of his textbook in light of new findings from astronomy and the study of astronomy history. The companion text for this course, The Privileged Planet, forms the centerpiece of our critique of Chaisson. “Of all the scientific insights achieved to date, one stands our boldly: Earth is neither central nor special. We inhabit no unique place in the universe.” Eric Chaisson and Steve McMillan
The first paragraph in Chaisson (page 0) contains a series of claims, half of which are wrong. The Privileged Planet will document by means of new evidence from astronomy how these claims about Earth not being “special” are wrong. The real basis for Chaisson’s opinion that Earth is unremarkable and mediocre is not so much science, but rather his faith that nature is all there is (naturalism) and that thus we (and our planet) are the product of unguided natural causes. On page 16 (introduction to “The Copernican Revolution”) Chaisson wraps his pseudo-scientific worldview of naturalism in a false storyline traditionally imposed on the history of science. We know this storyline is false because professional historians of science (regardless of their personal worldview) have thoroughly discredited it. This false storyline about astronomy history makes it look like Copernicus, Kepler, Galileo, and Newton were arguing that humans are no longer special given that we are not in the geometric center of the universe. In fact, these leading scientists of the Scientific Revolution considered humans and Earth to be very special and they argued that their work as scientists helped to support this conclusion. In short, biased by his faith in naturalism, Chaisson distorts some critical matters of fact about astronomy and astronomy history. We shall set the record straight in US 311 by allowing you to have full exposure to all the relevant evidence, both scientific and historical. In the end, you must discern for yourself where the evidence actually leads. 92
Read Chaisson: Pages 0-1, and 16 Chaisson provides a helpful introduction to the relative sizes of things, the main point of which is to show us just how small humans are compared to the vastness of the cosmos. He seems to suggest that nobody knew this until the advent of modern astronomy. This is not correct, as we demonstrated in the previous Packet reading, “Cosmic Dimensions: Past & Present.” Read Chaisson: Pages 10-15 By studying pages 10-15 you are finally finishing all of Chaisson’s Prologue Chapter. Answer all the practice questions at the end of the chapter and make use of additional study guide material in the Chaisson eBook. All of this material will help prepare you for exam 1 and some of it will help prepare for a later lab on the distances of celestial objects. Last Reminder: Always use Packet study guides (the 1st Danielson study guide is found below) and any built-in study guides in Chaisson: questions at end of chapter, eBook, text website, etc.
Danielson: Pascal, Chesterton: Pages 195-197, 347-349 The eternal silence of these infinite spaces: Blaise Pascal A meditative mathematician peers anxiously into the twin abysses of the infinitesimal and the infinite. Q1: Besides being a leading scientist, Pascal constructed many arguments for the intellectual coherence of the Christian faith (thus, he was also a Christian apologist). Explain this sample of his apologetic work: “In short, it is the greatest sensible mark of the almighty power of God that imagination loses itself in that thought.” What is the “thought” that points so strongly to God’s omnipotence?
Q2: Pascal remarks that humans are in the “middle of things” (p. 197). What are the two humanly unknowable extremities between which we are centrally located?
Q3: “The eternal silence of these infinite spaces frightens me.” How did Pascal intend to convey here a feeling that would drive humans toward, rather than away from, trust in the God of the Bible?
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Cosmos without peer and without price: G. K. Chesterton A writer of detective stories cherishes the universe as a great might-not-have-been. Q1: Chesterton, writing in 1908, dismantles a pervasive assumption of modern materialism. What is this “contemptible notion” that is often packaged as an obvious result of objective science?
Q2: “… it is … the only thing there is. Why, then, should one worry particularly to call it large? There is nothing to compare it with. It would be just as sensible to call it small.” What is the “it” throughout most of this clever chain of reasoning? _________________ Is Chesterton affirming that “it” is “the only thing there is,” or showing the inconsistency of others who simultaneously say “it’s the only thing there is” and “it’s so big that humans aren’t special”? If Chesterton were writing today, how might he lampoon the increasingly common materialist strategy to believe in an infinity of “its” (universes) in response to the proliferating scientific evidence that many physical features of our universe have to be “just right” in order to for “it” (or any other “it”) to support life.
Q3: How does Chesterton cherish the universe as a great might-not-have-been by allusion to Robinson Crusoe?
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Wednesday September 15 Privileged Planet: Introduction & Ch. 1: Wonderful Eclipses Quiz/exam questions over this book come exclusively from this study guide and class discussion! About The Privileged Planet Authors Guillermo Gonzalez is an Assistant Research Professor of Astronomy at Iowa State University. Jay Richards is Vice President of Discovery Institute. Details at http://privilegedplanet.com. About The Author of this Study Guide (quoting The Privileged Planet, p. 417) “… Mike Keas gave us excellent advice on the manuscript, especially on our historical section.” Main Thesis of the Book Earth is optimized for both habitability (life support) and scientific discovery (measurability). Angry rejection of such a thesis would seem the normal response of a member of the SETI Institute, dedicated as it is to the proposition that life is common in the universe due to the almighty power of Darwinian evolution. Surprise! Read what one SETI Institute guy says below. Review of The Privileged Planet by the World’s Leading Scientific Journal Nature June 24, 2004. Review by Douglas A. Vakoch (SETI Institute). His only criticisms were that the criteria for measurability appear subjective, and that we don’t yet have enough data to determine how rare earth is: “So far, Earth is the only planet we know that has the privilege of bearing life that searches for signs of other intelligence – whether in the form of other technological beings transmitting evidence of their existence or through patterns indicating underlying design. It may be some time, however, before we can accurately judge whether our blue dot is – as planets go – commonplace, unique or somewhere in between.”
Introduction Preview this study guide to know what to look for in your reading, then read the text of this part of The Privileged Planet, then answer the questions below. What event on Christmas Eve, 1968, attracted the largest single TV audience in history? A majority of scientists think that our Earthly existence is accidental and purposeless. The Privileged Planet challenges this view on scientific grounds. What matters most to the practice of science is not where scientists get their initial ideas (e.g., intuition, the Bible, or a dream), but rather how well those ideas are tested against publicly accessible evidence. A scientist may begin assuming the importance or unimportance of our cosmic position and possession of biological life (or intelligence), just so long as those initial assumptions are open to being accountable to evidence. The Privileged Planet’s main thesis: the conditions that allow for __________________ on earth also make it strangely well suited for ____________ and ____________ the universe. 95
Technical version of this thesis: ________________ correlates with habitability. Identify three views (among prominent scientists since the mid-20th century) of how common or uncommon life is in the cosmos (answer in the #1-#2-#3 outline below). View #1: Drake-Sagan “Billions and Billions” Hypothesis Life, even intelligent life, is common / uncommon (circle one). The late Carl Sagan (author of the novel Contact, upon which the motion picture by the same name was based) was fond of extolling the “billions and billions” of stars in the cosmos; we will use this as a convenient device for remembering this most common 20th-century view. Frank Drake is the early SETI researcher who is especially remembered for his mathematical formula that attempts to calculate the number of advanced civilizations capable of communicating with radio signals in the Milky Way Galaxy. What is the so-called Copernican Principle? Define naturalism by completing Carl Sagan’s liturgy: nature is “all that _____, or ever _______, or ever _________.” If naturalism is true, the Copernican Principle seems to naturally follow. SETI = Search for __________________ Intelligence. Drake & Sagan were big SETI advocates. View #2: Rare Earth Hypothesis Simple life is common / uncommon, but complex life is common / uncommon (circle correct) The name of this viewpoint comes from Peter Ward and Donald Brownlee in their book Rare Earth (2000). This view has taken its contemporary form within the new discipline of astrobiology, which is the study of the conditions necessary for life. In what limited regard does the Rare Earth view (#2) challenge the Copernican Principle (CP)? Answer: it challenges the CP in regard to simple / complex life (circle one)? Does the “Rare Earth” view keep faith with the broader naturalistic worldview that supports the Copernican Principle? Explain. View #3: Privileged Planet Hypothesis (thesis of the present book) Part A, Habitability Thesis: Life, both complex and “simple,” is common / uncommon (circle one). This thesis, although not new, has taken on an unprecedented degree of scientific rigor in its latest form within the new discipline of astrobiology (Guillermo Gonzalez has co-authored several ground-breaking technical articles with Rare Earth authors Ward and Brownlee). Insights from “origin-of-life” experts such as Dean Kenyon (who infers intelligent design as the best explanation for the origin of life on Earth) distinguish this thesis from the Rare Earth Hypothesis.
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Views #2 and #3 both recognize the precise fine-tuning (or “just right” arrangement of natural laws and events) that is required for the possibility of life’s existence. Part B, Habitability-Measurability Correlation Thesis: The conditions that allow for intelligent life on earth also make it strangely well suited for measuring (analyzing) the universe. Measurability [definition]: “those features of the universe as a whole, and especially to our particular ____________ in both in space and time which allow us to detect, observe, discover, and determine such features as the size, age, history, laws, and other properties of the physical universe.” Measurability is quite high, and it takes intelligent agents like us to recognize this. Does the Privileged Planet Hypothesis keep faith with the broader naturalistic worldview that underwrites the Copernican Principle? Explain (compare with the Rare Earth Hypothesis).
“All design involves conflicting objectives and hence compromise, and the best designs will always be those that come up with the best compromise.” How does this insight, called constrained optimization, guide the Privileged Planet thesis? How does laptop computer design illustrate constrained optimization?
How this book-- The Privileged Planet--fits into this course. Most science courses assume the measurability of the cosmos without comment. This course, with the help of The Privileged Planet, will focus attention on the amazing degree of measurability (and broader intelligibility) that makes science possible. We will also investigate the cultural factors (often Judeo-Christian ones) that historically gave rise to the human desire to measure and understand the world.
Privileged Planet: Ch. 1: Wonderful Eclipses Kinds of Solar Eclipses •
Total Eclipse (figure 1.1A): The fully shaded umbra of the Moon’s shadow reaches Earth. This is called a total eclipse for those located on Earth where the umbra touches, because the Moon totally covers the Sun.
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•
Annular Eclipse (figure 1.1B): The semi-shaded penumbra of the Moon’s shadow reaches Earth, while the dark umbra falls short. The Moon fails to totally cover the Sun for any observer on Earth.
Figure 1.1 More Detail on Total Solar Eclipses (figure 1.1A) 1. 2. 3. 4.
Moon’s disk is large enough to cover the bright solar disk (Sun’s photosphere) Centers of the two disks at least approximately meet Umbra touches Earth’s surface There are two kinds of total eclipses: super & perfect a. Super eclipse: Moon’s disk appears ________ than the solar disk and thus more than covers it. b. Perfect eclipse: Moon’s disk is just large enough to cover the bright solar disk. What causes a perfect solar eclipse? The relative Earth-Moon and Earth-Sun distances just about exactly compensate for the real size difference between Moon and Sun, making both appear the same size as viewed from Earth. What can one see during the 7.5 minutes (or less) of a perfect solar eclipse? See Plate 3 in the book (all color plates are in middle of book). See especially the top photograph for an excellent look at a perfect eclipse. Observe two things: (1) pink ________________ around the edge of the Moon, which looks like a thin jagged crown with protruding pink flames; this is an irregular layer of gases on the 98
Sun within which sunspots, flares, and prominences (protruding pink flames) occur. (2) silvery-white _____________, which is the Sun’s outer atmosphere, and extends out several times the Sun’s diameter. More Detail on Solar Eclipses that are Not Total (figure 1.1B) 1. Annular Eclipse (figure 1.1B): The Moon’s disk is too ____________ to cover the bright solar disk (photosphere of the Sun), but the centers of the two disks at least approximately meet. Explanation: More than half the time nowadays the Moon is far enough from Earth (relative to the changing Earth-Sun distance) that it appears a bit smaller than the Sun. During such periods, the Moon (if lined up with the Sun) fails to totally eclipse (cover) the bright solar disk. Under these conditions, the Sun’s bright light prohibits observations of the following scientifically interesting effects: (1) pink chromosphere and (2) silvery-white corona. These two solar phenomena are otherwise visible during a total solar eclipse (especially during a perfect total solar eclipse as described above). 2. Partial Eclipse: A solar eclipse in which an observer is located in the penumbera. One may experience either a total or annular eclipse as a “partial eclipse” if one is situated in the penumbera. Earth-Moon-Sun Configuration is Well Suited for Earth’s Habitability and Measurability Gonzalez discovered the habitability-measurability correlation after first seeing it in the EarthMoon-Sun configuration that makes possible complex life and science-friendly solar eclipses. Four planet-moon-sun features required for the support of complex life on a planet: #1. “A moon large enough to just cover the Sun also _______ the rotation of its host ________.” This keeps planet’s tilt within a narrow range that is important for sustaining complex life. #2. What celestial body is the main cause of ocean tides? Sun / Moon (circle one). In the absence of this body, ocean currents would be insufficient to regulate global climate. OBJECTION: “As long as they are the right relative sizes and distances apart, a perfect total eclipse could happen with a larger or smaller moon or sun.” So, there is nothing special about our perfect total eclipses. ANSWER: This objection evaporates in light of new evidence (e.g., points 3 & 4 below) that few of the eclipse-friendly planet-moon-sun arrangements also provide these two correlated benefits: • Able to support complex life on the host planet (habitability) • Able to support highly useful scientific measurements (measurability) #3. A star similar to the Sun’s mass is required for complex life. A less __________ sun requires that a planet orbit closer to keep liquid ________ on its surface. The band around a star wherein a terrestrial planet must orbit to maintain liquid water on its surface is called the __________________ habitable zone. But, if the planet orbits too close, you 99
get rapid __________-locking (one hemisphere of planet always faces its sun). What’s bad about this? _________________________________________________________________________ ______________________________________________________________________________ What difference between our Moon’s tidal-lock and this hypothetical planetary tidal-lock stands out? Hint: Why is one side of our Moon not perpetually dark? ___________________________ ______________________________________________________________________________ #4. If a planet is much bigger or smaller than ours, then complex life is impossible there. Why? Because the host planet needs to be about Earth’s size to maintain the following features that are critical for the support of complex life: A. Plate tectonic movement B. Maintenance of some __________ above the oceans C. Retention of an ___________________ Planet-moon-sun features that support life also support science-friendly perfect solar eclipses #1. The planet-moon-sun features that favor perfect over super total solar eclipses are not only critical for the support of complex life, but they also increase scientific measurability. Explain how super total solar eclipses are less science-friendly than perfect total solar eclipses. When did/will Earth have only super eclipses? Past / future (circle one) by 2.5 billion years? Why? #2. A comparative study of moons in our solar system reveals something important about our Earth-Moon-Sun configuration: Earth is unusually well set up to be a platform from which to make scientifically useful measurements during solar eclipses. Summarize the evidence for this conclusion with the aid of the bullet points below: •
•
Figure 1.4 (page 11) shows that only two moons in our Solar System (ours and one of Saturn’s) appear the same angular size as the Sun when viewed from their host planet. o By angular size of the Sun we mean the angle between two lines of sight: To one edge of the Sun and To the opposite edge of the Sun o Even these two wonderful moons vary in their distance from their host planet and so these moons sometimes appear smaller than the Sun (left of “1” on the graph) and sometimes larger than the Sun (right of “1”) Explain why the farther a planet is from the Sun, the briefer are its eclipses (and why this retards scientific measurements during eclipses). o So who has more science-friendly eclipses on this account: folks on Earth or hypothetical people on Saturn? o How does the potato-shaped of Prometheus make matters worse for scientific measurements taken from the surface of Saturn during a total eclipse?
Research Aided by Perfect Solar Eclipses Led to Three Monumental Scientific Discoveries #1. Perfect solar eclipses helped scientists discover the chemical (elemental) makeup of stars
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In 1811 Joseph Franhaufer first described the dark gaps that intersperse the smooth continuum of the solar light spectrum, called Franhaufer lines or _________________ lines. Atoms and molecules both emit and absorb light at characteristic points on the spectrum, called _______________ and absorption lines. By learning to read this bar-code-like information, scientists were able to discover the elemental makeup of ______. This major advance in science was made possible by pointing a spectroscope at prominences (plumes of gas that surge out from the photosphere into the ___________) during the few minutes of totality during a perfect solar eclipse. These discoveries helped confirm the proposal of Jesuit priest Angelo Secchi and John Herschel in 1864 that the Sun is a ball of hot ______. Only because we understand how absorption lines form in the Sun’s atmosphere can we interpret the spectra of distant _________, and thereby determine their chemical makeup, all without leaving our tiny planet. Such knowledge is the linchpin for modern astrophysics and cosmology. #2. Total solar eclipses provided scientists the earliest and one of the most influential “confirming tests” of _______________ Relativity (one of most important laws of nature)
Figure 1.7: The Moon is not shown eclipsing the Sun in the top drawing, but this was the case, and necessarily so in order to enable these early 20th century scientists to see the stars on either side of the Sun during daylight hours. The bottom drawing shows that the angle measured between star 1 and 2 (at nighttime) would be less months later with the Sun out of the that part of the sky. The difference in angle between the stars results from the bending of starlight as illustrated in the top drawing.
#3. Total solar eclipses gave scientists the best way of measuring the slowdown of Earth’s _____ •
What causes the slowing of Earth’s rotation?
•
A total solar eclipse is only visible as such by those in its _______ (dark shadow’s) track
•
The slowing of Earth’s rotation (before it was discovered) translated into errors in prediction of where the umbra would sweep across Earth’s surface for a total eclipse
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•
By examining ancient accounts of total solar eclipses at known dates and places, scientists discovered the phenomenon of Earth’s slowing rotation and then used this new knowledge as a key to historical placement of other human events
Bizarre Conclusion “There’s a final, even more bizarre twist. Due to Moon-induced tides, the Moon is gradually _____________ from the Earth, at 3.82 centimeters per year. In ten million years, the Moon will seem noticeably _________. At the same time, the Sun’s apparent girth has been swelling by six centimeters per year for ages, as is normal in stellar evolution. These two processes, working together, should end total solar eclipses in about _______ million years, a mere _______ percent of the age of the Earth. This relatively small window of opportunity also happens to coincide with the existence of ________________ life. Put another way, the most habitable place in the Solar System yields the best view of solar eclipses just when ________________ can best appreciate them.”
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Monday September 20 Lab 4: Africa Show, Precession, Exam Review (Planetarium) Keep these notes to study for exam. I will return your lab reports 1-3 so you can study those too. Precession: North Pole Drift (Face North in Planetarium) 1. Will Polaris always be the North Star ... in your lifetime? ______ ... in history?________ 2. What was the North Star when the Great Pyramid of Khufu was built? ________________ 3. What will be Polaris 2000 years from now (what part of Cepheus)? ____________________ 4. The period of precession is _____________ years (rounded to nearest thousand) Precession: Equatorial Slip (Face South in Planetarium) 5. What happens to the right ascension of Orion during precession? It gets _______________ 6. How does the celestial equator appear to slide along the ecliptic (tricky because the dates on the ecliptic are continually relabeled to make spring equinox March 21)? __________________________________________________________________________ 7. Imagine a star exactly at the location of the September (fall) equinox. a. Where will that star be located at the next September equinox? __________ (what fraction of a full circle along the ecliptic) b. At a September equinox 1000 years later? __________ (fraction of a circle) c. At a September equinox 2000 years later? __________ (fraction of a circle) 8. In which direction does an equinox precede the stars it was associated with before? (This is the meaning of “precession of the equinoxes.”) eastward / westward 9. Does the angle between the ecliptic and celestial equator remain at 23.5 degrees, or does it change with precession? __________________ 10. Why is your horoscope hopelessly out of date? ____________________________________ ___________________________________________________________________________ 11. Historical Question: Given that Hipparchos of Nicaea discovered precession around 150 B.C. using Babylonian records, what do you think he was looking for in the Babylonian records that allowed him to make the discovery? ___________________________________________________________________________ ___________________________________________________________________________ Review for Exam 1 • Understanding basic celestial phenomena in terms of 3 models: planisphere, globe, dome • Practice locating objects on the planisphere with right ascension and declination coordinates • Distinguish between apparent primary and secondary motion: DEMO on DOME: o Which circle is a guide to primary motion? ____________________ o Which circle is a guide to secondary motion? _____________________ o Other motions of stars aren’t apparent in our short life span.
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Chronology Memorize this Chronology for the Course You need to know the dates below for exam 1: •
Ancient World (Antiquity) = before 529 AD93
•
Medieval (Middle Ages) = 529–1400 AD
You need to know the dates below for exam 2 and the final exam: • • •
Renaissance = 1400–1500 (1400’s or 15th century) Reformation = after 1517 (Martin Luther posted his 95 Theses; 16th century) Scientific Revolution = 1543–1687 (or 17th century) • •
1543 = Copernicus’ book, On the Revolutions of the Heavenly Spheres 1687 = Newton’s book, Mathematical Principles of Natural Philosophy
•
Enlightenment = 1700-1800 (or 18th century)
•
Modern = since 1800 (or 19th and 20th centuries)
•
Postmodern = recently (cultural trend rooted in the claim* that there is no absolute truth) *What is inconsistent with this claim? “I absolutely know for sure that there is no absolute truth”
93 The sixth century AD may be taken as the end of antiquity and the beginning of the middle ages. The year 529 AD is chosen arbitrarily. However, it has some symbolic value representing both the end of ancient learning and the beginning of medieval culture in that during 529 AD Justinian closed the Academy at Athens, and Saint Benedict founded his monastery at Monte Casino in Italy.
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Ancient Greek Astronomy In courses from western history to philosophy, students survey many well-known cultural achievements of the ancient Greeks. Few of these achievements rival the creation of a geometrical astronomy. Babylonian astronomy reached impressive heights centuries earlier, but in contrast the Greek approach emphasized geometric models rather than predictive calculations based upon arithmetic and observations. One wonders why the Greeks were willing to take a giant step backwards in accurate prediction in order to pursue their preferred geometric methodology. But choice of methodology is a valid but contentious point of disagreement in science. There were two main ways of doing science at this time: (1) Quantitatively accurate control of observed phenomena through arithmetic (Babylonian), and (2) Geometrical method with only a rough qualitative proof of concept without any real predictive capacity for the positions of the planets (early Greek). Plato and his student Eudoxos apparently initiated the early Greek theoretical tradition of geometrical astronomy.94 Plato (428 - 348 B.C.) appears to have challenged others to explain the apparently non-uniform motions of the heavenly bodies (e.g., planets speed up, slow down, and change directions periodically) in terms of combinations of a few perfect circular uniform motions. The Western tradition of astronomy was established as an eventual cross-cultural fusion of these two scientific traditions in the Hellenistic and Roman periods. This fusion largely began with the work of Hipparchos (150 BC) and was accomplished by the work of Ptolemy (150 AD). From the Babylonian tradition Hipparchos and Ptolemy appropriated various numerical parameters for celestial motions; records of observations going back at least as early as 750 BC; and even the ideal of quantitatively accurate prediction. From the early Greek tradition represented by Eudoxos and Plato, they appropriated the attempt to explain planetary motion in terms of these main components: Main Components of Astronomy in the Western Tradition • Circular motions • Uniform motion (constant speed) • Combinations of circular motions, as needed for each planet’s observed movements There were 7 celestial objects, all called “planets” (literally, “wanderers”) by the ancient Greeks, whose motion required explanation in terms of the 3 components listed above: the Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn. The regular fixed stars were conceived of as all attached to a single sphere with its pole and equator amounting to extensions of the Earth’s pole and equator.
94 Simplicius, a commentator on Plato who lived in late antiquity, credited Plato with having initiated the Western tradition of astronomy, saying that Plato had challenged people to find out "the uniform and ordered motions by the assumption of which the apparent movements of the planets can be accounted for." (Simplicius, as quoted in Crowe, Theories of the World, 22).
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Study Question From a Christian perspective, how would you critique the methodological values and explanatory aims of astronomy according to these contrasting traditions below? 1. The Babylonians explained the motions of the heavens with a non-physical model (the gods and goddesses). With this religious motivation they created the first sophisticated quantitative science. Is this a violation of methodological naturalism (the rule that is routinely imposed on science today that one can only resort to unguided natural processes for causes of natural events)? What does this tell you about the Babylonian science of astronomy, and what does this tell you about the modern rule of methodological naturalism? Was Babylonian astronomy fruitful even though it did not follow methodological naturalism?
2. The Greeks explained the motions of the heavens using geometrical models (often with the idea that the physical spheres were divine beings). In order to attribute their geometrical conception of beauty to the spheres, they were willing to abandon precise quantitative predictions. Was making the spheres less personal a move toward methodological naturalism? Or away from anthropomorphism? Does it make sense as a positive move away from polytheism? Or does it make better sense as a negative move away from a personal divine?
Eudoxos of Knidos, ca. 400 - ca. 347 B.C. Although we have none of Eudoxos’ writings today, other authors whose work has survived give us a good idea of what Eudoxos wrote. Eudoxos’ Model of the Sun Eudoxos, known as an associate of Plato’s celebrated Academy in Athens, proposed a geometrical explanation of the Sun’s motion that was essentially the same kind of model as we used in the planetarium labs. We had you use large plastic spheres representing the sphere of fixed stars, with the Earth motionless in the center of the universe and with the yearly path of the Sun inclined 23.5˚ relative to the Earth’s equator (and the celestial equator).
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Stars appear as if all attached to one great sphere
Ecliptic
S
Zodiac
23.5°
X S
X
Celestial equator
Ecliptic Earth
is still tilted 23.5° relative to the
The drawings below repeat, in simplified form, the features illustrated in the above diagram. Earth, sits motionless in the center of a spherical universe and the Sun, S, moves around the Earth once per year eastward (the Sun’s secondary motion) along the ecliptic which is tilted at 23 1/2 degrees. Of course, the Sun primarily appears to move around the Earth westward once daily. This primary solar motion would be simulated in the model below (as in the model you used in lab) by moving the whole spherical universe, carrying the Sun with it, once around the Earth westward in the short span of a day.
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S E
Eudoxos conceived of a model to explain the Sun’s apparent motion that consisted of a set of concentric spheres (spheres having the same center). Although he used 3 spheres in his model for the Sun’s motion, we are only sure about the role of 2 of out of his 3 spheres (shown below).
North
E
East
S
South .
The two spheres in this model each have Earth, E, as their center. Each sphere is drawn with its equator traced out. The equator of the outermost sphere is oriented due east and west, while the 109
equator of the 2nd smaller sphere is tilted 23.5° off of this due east-west orientation. The Sun, S, is placed on the equator of the 2nd sphere. To simulate the apparent path of the Sun in the course of a day, in this case the shortest day of the year for North Americans like us, the diagram above has a bold circular path traced out for inspection. Notice that the Sun would appear to rise south of due east and set south of due west, which fits our actual observations (and our simulation in the planetarium). Notice also that to simulate the longest day of the year (about 6 months later), we would need to trace out a bold path for the Sun using Eudoxos model reproduced below.
North
S E
East
South Eudoxos’ model for the Sun further specified the following. The outermost sphere turns around the Earth once (the complete 360 degrees) per day westward, like the sphere of fixed stars (this explains the Sun’s primary motion). The 2nd sphere (secondary motion) turns in the opposite direction, from west to east, at a very slow rate, about a degree per day, so that on each successive day, the Sun would appear to rise about a degree further behind (further east from) a rising star observed on a previous day. In the course of a year, then, the 2nd sphere would realign the Sun with a given star that moves exactly like the motion of the outermost sphere in Eudoxos’ model shown above. Notice, again, that Eudoxos’ model for the Sun’s motion puts the 2nd sphere, upon whose equator the Sun is attached, at a 23.5˚ angle relative to the 1st sphere. This means that the Sun would not only appear, on successive mornings, about a degree further eastward relative to a given fixed star (due to the 2nd sphere’s slow motion back eastward), but also the Sun would appear to rise sometimes north of due east and sometimes south of due east, and every position in-between over the course of a year.
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Thus, with just 2 concentric spheres, with the Sun enjoying the combined motion of both spheres, we can mathematically simulate the most obvious observed motions of the Sun. This constitutes a very early scientific model (explanatory, but not predictive as in Babylonian astronomy ) of celestial phenomena. An even older Greek scientific explanation lies in the background of Eudoxos’ work, namely the conception of a spherical universe with the stars located on an outer sphere that rotates westward once daily (sphere of fixed stars). Eudoxos’ Model of the Moon Eudoxos’ Moon model is identical to his solar theory in terms of the orientation of the first two spheres. An additional, third, sphere is critical in the model of the Moon. This innermost sphere is tilted about 5˚ relative to the 2nd sphere in order to make it tilted about 28.5˚ relative to the 1st or outermost sphere. The first two spheres put the Moon moving along the same basic path as the Sun (though at a different rate). The 3rd sphere, combined with the first 2 spheres, result in the motion of the Moon, M attached to the equator of the 3rd sphere (this equator is drawn in bold below), such that it appears to generally move along the ecliptic (Sun’s apparent path against the background of fixed stars), but sometime 5˚ above and sometimes 5˚ below the ecliptic (and every position in-between). Indeed, this is what patient observers roughly see. Thus, Eudoxos’ model roughly produces that actually observed motions of the Moon over the course of successive months and years.
23.5°+ 5 °= 28.5 °
North
M E
Eudoxos’ Moon Model East
Eudoxos’ Planetary Models Eudoxos’ planetary models each employed 4 spheres, as illustrated below. S1, referring to sphere #1, is, again, the outermost sphere of the model that undergoes a daily westward spin like that of the sphere of fixed stars. S2, sphere #2, moves from eastward. S3 and S4 (label them yourselves
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in the diagram below) stand for the 3rd and 4th spheres, with the planet, P, attached to the innermost sphere (4th). The 3rd and 4th spheres, considered together, but in isolation from S1 and S2, will produce a combined motion such that the planet, P, will appear to move in a figure-eight path. When this figure-eight (resulting from S3 & S4 combined) is considered in conjunction with the motion of S2, the resulting composite motion approximates the usual eastward drift of the planets relative to the background of fixed stars (which is roughly equivalent to S1) with a periodic westward “doubling back” motion (retrograde motion) of each planet. Thus, Eudoxos’ 4-concentric spheres, properly adjusted for speed and tilt, could approximate each planet’s motion (Mercury, Venus, Mars, Jupiter, and Saturn). On the other hand, these approximations were only qualitative, not predictive. Eudoxos must have known his models could not account for some kinds of observations, even in theory. For example, all retrograde motions generated by this kind of model are symmetrical loops, whereas the observed retrograde motions of the planets are anything but symmetrical. And the models of Eudoxos were of no use in explaining the changing brightness of stars during retrograde motion.
S1: E-W
S2
: W -E
E P
Heraclides of Pontos (ca. 388 - ca. 315 B.C.) Heraclides proposed a rotating Earth, but his ideas did not initiate a tradition with any notable continuity. Very few astronomers took this approach seriously until Copernicus. Besides, doesn’t commonsense and ordinary observation tell us that Earth is at rest? 112
Apollonius of Perga (ca. 240 - ca. 190 B.C.) and the Epicycle-Deferent System Apollonius seems to have invented the epicycle-deferent system, which superseded much of 3Eudoxos’ approach to astronomy. We still have perfectly uniform circular motion, but lost forever is the notion that all of these circles have one common center. Label the epicycledeferent diagram below (label epicycle and deferent) based on this description. Apollonius’ Epicycle-Deferent System Deferent: Main circular motion that accounts for a planet wandering eastward through the stars Epicycle: A secondary circular motion that rides on top of the deferent (center of the epicycle is on the deferent) and to which a planet is attached. The epicycle explains retrograde motion.
Epicycle-deferent system Planet located on this circle ___________ (label this circle here)
Earth
___________ (label this circle here)
The epicycle-deferent system enabled astronomers to account for a certain kind of appearance in the planets that escaped explanation from Eudoxos’ concentric (same-centered) spheres. Earlier you learned that planets undergo a certain sort of change, the most extreme case of which (for outer planets) occurs at the moment of opposition. What appearance had skywatchers noticed that is most pronounced in the opposition of the 3 outer planets that were known in premodern times? How could the epicycle-deferent system make sense of this phenomenon, while Eudoxos’ concentric sphere models were deemed powerless in this regard? Answer: the changing brightness of planets (outer planets brightest at point of opposition; analogous to “full Moon”). The epicycle-deferent system also allowed astronomers to explain retrograde motion in a more powerful manner. Complete the exercise below to see how the planet, as it moves through positions 1-5 on the epicycle-deferent, appears to stop, back up in retrograde motion, and resume its usual eastward drift relative to the background of fixed stars. The diagram amounts to 5 snapshots of time with the epicycle turning one-quarter turn between each snapshot, while the deferent also carries the epicycle along. Can you see how the planet’s motion, when considered against the backdrop of the fixed stars, will appear to stop, back up, and then regain its customary eastward motion.
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East
Background of ixed f stars 1 West 5
2
4
Planet at 1 position 1
3 Complete the other lines of sight to stars
Earth
Eccentric device Greek astronomers some time after Apollonius invented the eccentric device to work in conjunction with the epicycle-deferent system.
Epicycle-deferent system with eccentric Planet located on this circle
Earth
Earth is off-centered (placed eccentrically)
By placing Earth off centered (eccentric position), astronomers sought to better account for the apparent change in speed of planets at various times. When viewed from such an eccentric point, motion along the deferent (even without the epicycle) would appear non-uniform: speeding up when a point on the deferent is near Earth and particularly slowing down when a deferent point is on the opposite side of the center of the deferent circle as the eccentrically positioned Earth. Indeed, planets (including the Sun and Moon) do appear to speed up and slow down in various complicated ways and the eccentric mathematical device went a long way in making sense of such phenomena. Notice the retention, in both the epicycle-deferent system and the eccentric device, of the traditional premises of Greek astronomy since Plato: explain apparently irregular planetary motion in terms of combinations of perfect circles moving a constant rates. By placing
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Earth off-centered, astronomers were also able to explain the unequal length of the four seasons of the year. Hipparchos of Nicaea produced this solar theory. Hipparchos of Nicaea (ca. 190 - ca. 120 B.C.) Hipparchos began to fuse the earlier Greek attempt to construct geometrical models with the Babylonian aim of quantitative prediction. In doing so, Hipparchos took advantage of Babylonian observations, and various Babylonian numerical parameters for planetary motions including the lengths of the seasons and of the year. He incorporated these into models that were inspired by the qualitative deferent-epicycle systems of Apollonios. A simple deferent-epicycle model can be equivalent to an eccentric system. In the case of the Sun, Hipparchos opted for the eccentric approach. Hipparchos put Earth just off center within the circular path of the Sun (or, more true to Greek cosmological tradition, he shifted the position of the Sun’s circle since Earth traditionally is at the center of the cosmos by necessity). This theory beautifully explained the different lengths of the four seasons.
June Solstice
Hipparchos’ Solar Theory ecliptic as an eccentric circle
AE
92.5 days 88 1/8 days
94.5 days 90 1/8 days
December Solstice
VE (Winter and summer are reversed in the southern hemisphere)
Winter half=178.25 Summer half=187
“Where is the one who has been born king of the Jews? We saw his star in the east and have come to worship him” (Matt. 2:2). “...The star they had seen in the east went ahead of them until it stopped over the place where the child was” (Matt. 2:9). Whether God arranged for this “star” supernaturally or naturally, the Magi were Seleukid astronomers in the Babylonian tradition who responded to the call to worship the Christ child. 115
Our next astronomer was born after Christ, in the wake of the Resurrection, had already left our ordinary space-time continuum.
Ptolemaic Astronomy Claudius Ptolemy of Alexandria (ca. 100 - ca. 130 A.D.) worked in association with the great library and museum at Alexandria, Egypt, a leading center of Greek culture in the Hellenistic period. His most celebrated work, Almagest, is remembered by this Arabic word that means “the greatest.” Its original Greek title meant “mathematical synthesis.” Indeed, his book is considered the greatest mathematical synthesis of astronomy prior to Copernicus. His treatment of the Sun was virtually identical to Hipparchos’ solar theory, but his approach to the other planets introduced new levels of sophistication. Although we will not take the time to investigate his complicated Moon model, his outer and inner planetary theories are within our patient grasp. Before taking these two classes of planets separately, note the most novel addition that Ptolemy made to the mathematical devices used by astronomers to “save the phenomena” (explain the appearances): the equant. The Equant Device What is an equant? Study the diagram below. An equant is defined as that off-centered point within a circle from which a point on the circle appears to move through equal angles in equal times. We illustrate this below by choosing 4 planetary positions that connect with lines of sight through the equant point that cross and form two equal angles. From geometry we know that two straight lines, when crossed, form opposing angles that are equal. Thus the angle from P1 to P2 is equal to that swept out from P3 to P4. We know that the time for the planet to move from P1 to P2 is equal to the time needed for the planet to move from P3 to P4 given that the planet sweeps out equal angles in equal times (as viewed from the equant, not the circle’s center). If you were looking down on this planetary system, as you are now looking down on the diagram, would you see planet, P, moving uniformly or nonuniformly on the circle? Would it speed up and slow down (nonuniform motion), or would it move at a constant rate (uniform motion)? Try to answer this question on your own and then come to class to compare your answers with others. Ptolemy and subsequent astronomers used this mathematical device to better save the appearances of planets speeding up and slowing down as viewed from Earth. Study Questions 1. Besides the aesthetic problem of non-uniform motion with respect to the center entailed by the equant, is there a physical objection to the equant as well? Hint: Is the equant system consistent with the rotation of a solid sphere? Could one make a mechanical model of an equant system using solid materials? Why not? 2. In opting for greater observational accuracy than he could obtain using purely epicyclic/eccentric systems, Ptolemy abandoned a strict interpretation of uniform circular motion and a physically plausible explanatory model. Discuss how this choice reflects a compromise between the explanatory aims of the two ancient astronomical traditions (Babylonian and early Greek). 116
P4 P3 earth center equant
Equal Angles
P1 P2 Ptolemy’s Planetary Models Beside the equant, the parameters that Ptolemy had to work with in explaining planetary motion included: size, speed, and motion direction of the deferent and epicycle circles (even multiple epicycles per planet), an Earth placed eccentrically, and more. He cleverly employed such devices to best “save the phenomena” (account for the appearances in the sky), while retaining to a large degree, the Platonic rules of perfectly uniform circular motion (the equant pushed these rules to their limit, and perhaps over the edge). Outer Planets Ptolemy’s explanation of the outer planets (Mars, Jupiter, and Saturn) required that he rig up models for each of these planets that always pointed the radius of the epicycle in the same direction as a parallel line going from Earth to Sun (indicated below by the dotted arrows). This feature saved the appearances associated with the synodic cycles of each of the outer planets. Each of these planets appear their brightest at the point of opposition, midway through their retrograde (backward loop). With each outer planet model rigged as just mentioned, examine the illustration below and discern where the Sun would be located when P is closest (brightest) relative to Earth.)
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same direction as dashed arrow below P toward sun
Epicycle Radius
earth
Epicycle
center equant
Deferent
If we animate this model (see next diagram) and label 5 critical points at 5 snapshots in time (as we did earlier when first introducing the epicycle-deferent system of Apollonius) then we will clearly reveal why Ptolemy had to specify that the epicycle radius had to always point in the direction of the Sun (as artificial as this might sound otherwise). Complete lines of sight #4- #5 below and then superimpose this illustration on the one above to see how the epicycle radius would have to be choreographed in sync with the distant Sun to get the model to produce our actual observations of the Sun’s position relative to the outer planets (the synodic cycle of each of the outer planets). At what point would the planet be at opposition to the Sun—180˚ away from the Sun—in the diagram below (circle the correct answer: 1, 2, 3, 4, or 5)?
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East
Background of ixed f stars 1 West 5
2
4
Planet at 1 position 1
3 Complete the other lines of sight to stars
Earth
Inner Planets Study the Ptolemaic strategy for explaining inner planets using the diagram below. Why did Ptolemy have to rig each of his inner planet models so that the center of the epicycle is always lined up with the Sun in the background? What observations of Mercury and Venus does this account for? How do you think Ptolemy had to adjust the epicycle size to get one model for Mercury and another for Venus?
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epicycle center toward sun
P
earth center equant
Ptolemy’s Almagest and its Place in History Ptolemy’s book, Almagest, in which we find all of the above astronomical theories, might be considered the most famous book of science of all time. More people have talked about this book of science more than any other, with the exception of Euclid’s Elements of Geometry. It is a book that synthesizes the best of ancient Babylonian and Greek traditions of astronomy and developed mathematical astronomy to an advanced state. Ptolemy argues in the first chapter of Book I of his Almagest that only mathematics can provide sure and unshakable knowledge because its methods of proof are indisputable. Book I then lays out six postulates: 1. 2. 3. 4. 5. 6.
The heavens move spherically around Earth Earth is spherical (he gives observational evidence that we use in our Flat Earth Lab) Earth is at the center of the universe Earth is the size of a point (virtually nothing) compared to the size of the universe Earth is motionless There are two kinds of motion in the heavens a. Daily motion (primary motion) shared by the fixed stars and planets alike b. Special motion (secondary motion) of each planet in addition to daily motion 120
Later Ptolemy notes that opinions vary as to order of the planets. Although there was consensus in ancient Greek astronomy that the Moon comes first and the Stars come last, Ptolemy dismissed the problem of the order (and distances) of the other planets as insoluble (at least in this book; he picks up this topic in another book). Ptolemy was deeply concerned with what had become know as “saving the phenomena”... to offer a mathematical system for each planet that agrees with observations, even if that meant departing a bit from the geometrical ideals of astronomy that had guided its Greek development since Plato and Eudoxos. He then turns in his book to the accumulated data of astronomy available to him (through the great library of Alexandria, Egypt, and through various contemporaneous cuneiform sources which only recently have begun to be studied). His mission is to “save the phenomena,” that is, explain the data recorded by the Babylonians and others. Ptolemy reviews some tables of the motions of the 5 wandering stars that had been computed from Hipparchos’ observations and corrected with recent observations. He then launches in with a review of previous theoretical devices such as the epicycle-deferent system with Earth eccentric in the deferent, and then he adds his new device, the equant, as mentioned above. Ptolemy’s system of astronomy was capable of making fairly accurate predictions of where planets would be in future, despite our obvious hindsight observation that he incorrectly took Earth to be motionless in the center of the universe. Mathematically, the heliocentric hypothesis of Copernicus (and of less known ancient figures) can be made equivalent to a geocentric (Earth in the center), geostatic (Earth at rest) picture of the cosmos. Ptolemy’s theory of astronomy was so successful that it could be updated today to still yield accurate predictions. Just such updating is performed by the engineers who design mechanical star projectors that accurately project, from an observer-centered perspective, the motions of heavenly bodies in a planetarium.
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Danielson: Ptolemy and Proclus: Pages 68-77 The peculiar nature of the universe: Claudius Ptolemy The most influential astronomy textbook of all time smashes some enduring clichés about geocentrism. P. 69-71a is optional. Required reading begins again on p. 71b (regarding Earth’s size) Q1: “The earth has, to the senses, the ratio of a point to the distance of the sphere of the so-called fixed stars”? What does Ptolemy mean by this (draw a picture below) and what evidence does he offer in its support?
Q2: Most premodern Western scholars viewed Ptolemy’s arguments for an immobile Earth as irrefutable, based upon common sense, ordinary observations, and consistent with Aristotle’s cosmology. Why did the moving Earth hypothesis appear so ridiculous?
The weaknesses of the hypotheses: Proclus A late ancient follower of Ptolemy asks us to apply “a critical mind” to the Ptolemaic model. Q1: What summary of Plato’s approach to astronomy does Proclus provide? (p. 75)
Q2: What is the meaning of this enduring question about the methodology and conclusions of astronomy? “Are they only conceptual notions or do they have a substantial existence in the spheres with which they are connected?” (p. 76).
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Wednesday September 22 Presocratic Science Aims Understand how the Presocratics formulated approaches to science that are still with us Critique the Presocratics in light of our analysis of “aspects of reality” (the “rose” exercise) Show that the Presocratics did not replaced religion with science as is often claimed The Presocratics... Initiated the idea of “nature” as an entity capable of being studied theoretically as well as empirically (careful observation), with focus on the problem of “change” in nature Proposed mathematics as a means of studying nature Established the importance of debate over foundational ideas such as these alternatives: monism vs. pluralism materialism vs. idealism plenism vs. atomism chance or necessity vs. design finite vs. infinite cosmos look for other opposites The “Rose” Analysis of Aspects of Reality Reflect back on the rose exercise by which we generated this table that lists “aspects of reality.” Reality Table #2: Aspects of Reality Person Giving/Receiving a Rose Rose in Itself “Thank you” (response of numinous awe) “With all my love” “This is your rose” “How beautiful!” “How much does it cost?” “I’ll communicate love with a rose.” “My love is like a red, red rose....” “I grew it in my own rose garden.” “It differs from other plants because of its fragrance and prickly stem...” “Mmmm” (nose); “Ouch!” (finger) Growing Synthesizing oxygen Matter, individuality Bends in the wind Location Number of petals
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Aspect of Reality Worshipful, meaningful Ethical Juridical Aesthetic Economic Social Linguistic Historical-cultural Logical, analytical Sensory Biotic Compositional Physical Kinematic Spatial Quantitative
In order to best understand and critique the Presocratic achievement, we should outline a Christian view of reality that builds off of our findings in the rose exercise.
Christian Principles by which to Evaluate the Presocratics 1. Pancreationism. God is the creator of all reality. He is the only one responsible for the origin and continued existence of everything, regardless of whether he accomplishes this through primary causation (miracle) or secondary causation (natural law). He alone is uncreated; all else is created and created by him. God is therefore the creator of every “aspect of reality.” 2. Aspectual Irreducibility. No aspect of reality can carry the weight of existence of all the other aspects. Each aspect is equally and individually dependent upon God alone for its existence and thus cannot be “reduced” to another allegedly more “basic” aspect. There is, however, a weak sense in which those aspects lower on the list are more “basic” than higher aspects. Experience shows us that properties belonging to lower aspects are necessary but not sufficient conditions for properties belonging to higher aspects. For example, all ordinary objects with which we are familiar must exhibit quantitative, spatial, and physical properties; but not all of these objects are “alive” like plants (biotic aspect) or have the ability to perceive and feel like animals (sensory aspect). Although all living things must have physical properties, not all physical things are alive. Furthermore, the properties of life (biotic aspect) are more than just an extension of physical properties (physical aspect). The properties of life owe their existence to God alone, not to some other aspect of creation. This is to say that they are radically dependent upon God, rather than reducible to one another. The Presocratics lacked this perspective and ended up “reducing” all aspects of reality to one or more single aspects of reality. Thus they worshipped the most fundamental “aspect” as “god.” Reductionist theories of reality have been enormously influential in the history of science and are essentially idolatrous from a Christian standpoint. They are idolatrous in that they replace the creator with substitutes from within the created realm. For example, philosophical naturalism is one of the most influential theories of reality among non-Christian Western scientists today, and it often amounts to making an idol out of matter/energy. Philosophical naturalists believe that even ethics can be reduced to matter/energy, by claiming that ethical principles are merely the product of a multi-billion year unintelligent and blind natural process. This is a reductionist conclusion of 20th-century idolatry. From a Christian standpoint ethical principles are no more or less real than matter/energy. Both depend upon God directly for their existence. We employ this principle of irreducibility to critique ancient Greek scientist-philosophers, because it helps us identify the particular ways in which they invented new kinds of idolatries that departed to one extent or another from traditional Greek mythology, but yet were equally religious and idolatrous. 3. Religious Non-neutrality. Every theory in every discipline of knowledge assumes certain prior religious belief. The alleged religious neutrality of integrating perspectives of theoretical knowledge (e.g., physics, biology, psychology, etc.) is only apparent. Here’s why: A religious belief is an assertion of what holds the status of divinity. Something is given that status of divinity if it is considered able to exist on its own without depending on anything for its being.
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Aristotle himself articulated this definition of “the status of divinity:” Therefore about that which can exist independently and is changeless, there is a science.... And if there is such a kind of thing in the world, here surely must be the divine, and this must be the first and most dominant principle [i.e., all else depends on it] (Metaphysics 1064a34). Anyone with theoretical knowledge of any kind necessarily presupposes some kind of religious belief, even if that person perceives herself to be religiously neutral. 4. God as the Universal Lawgiver. God alone is the one who ordained the laws that govern each aspect of reality. Pagan theories of reality ascribe this lawgiver role to various parts of creation. The pagan philosophy of objectivism (e.g., scientific positivism) views the source of order (laws) to be the objects of creation themselves, while the pagan philosophy of subjectivism (e.g., postmodernism, which is popular on university campuses today) views the source of order (laws, the meaning of texts, etc.) to be the knowing human subjects themselves. A Christian theory of reality can avoid both horns of the objectivism/subjectivism dilemma, for God alone is the universal lawgiver to creation and thus both objects and (human) subjects are governed by the same God-imposed framework of law and meaning. Glossary Aspect of reality A particular category of properties and patterns (laws) of reality Religious belief An assertion of what holds the status of divinity Status of divinity Nondependent; totally self-sufficient (able to exist on its own without depending on anything else for its being or character) Theory A set of closely related hypotheses that fruitfully explains something Theory of reality The core of a person’s worldview, consisting of ultimate commitments about what is real, what we can know, and how we can know Worldview A person’s overarching framework for interpreting experience. Everyone has a worldview, regardless of whether or not it is systematically constructed or consciously identified.
The Character of Presocratic Science What was the basic character of Presocratic science and to what extent did it distinguish itself from traditionally religious Greek explanations of the world? In our pursuit of answers to these questions, we will use the following terms: Divine That which is not dependent upon anything (i.e., self-sufficient) Polytheistic Many gods and goddesses believed to exist Anthropomorphic Gods and goddesses have human traits Physis The Greek word that came to mean “nature” (“nature” as a whole) Natural Philosophy The study of physis; equivalent to “physics”
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The Meaning of “Nature” (Greek: Physis) Aristotle made physis a technical term to refer to what changes according to an internal principle. The growth of a tree is natural change governed by the internal principle of the tree seed from which the tree came. To sculpt a dead tree into a statue would not be natural change, but art (techne), where the principle of change is external (the craftsman) rather than internal (the seed). Those philosophers who study physis, that is changes occurring according to an internal principle, Aristotle called physiologoi, or “physicists” (= “natural philosophers”). Most of our knowledge of the origins of the abstract Greek idea of nature (physis) depends upon Aristotle’s account found in his books Physics and Metaphysics, and thus is liable to many of the dangers of anachronism commonly associated with retrospective explanations for a present state of affairs. Yet it was Aristotle’s regular practice when raising any question first to survey the opinions and arguments of others who had considered the given topic. This was his means of ensuring the comprehensiveness and thoroughness of his account. Following primarily Aristotle, we summarize below the ideas about nature of the Presocratic philosophers (scientists).
The Presocratic “Scientists” (Natural Philosophers) Thales of Miletus According to Aristotle, Thales was the originator of the “line of thinking” that led to physics. Thales’ contributions to science included cryptic aphorisms, which may be variously “decoded” into propositions of pertinence to physics. Here are the prominent phrases:
“All things are full of gods.” This can be taken as implying a principle of movement (or animism) within nature. It shows a preoccupation with the problem of change and the existence of a universal entity called nature that persists through change in the way that gods are immortal. Perhaps this is an attempt to rationalize and reform anthropomorphic religious ideas and can be taken as a kind of “conservation of nature” principle.
“All things are water.” Aristotle displayed some bewilderment about what Thales might have meant by this. It is more important here to examine how Thales’ predecessors interpreted him than how he understood himself. It appears that he thought “water” is the element out of which all things are made.
“Nature” (physis in Greek). From Aristotle’s point of view, what mattered was that “nature” had been conceived in a universal, abstract way, and identified as one substance, persisting through every change. We may characterize Thales’ position as one of “materialistic monism,” because it made the world dependent on a single divinized material principle— water.
Anaximander of Miletus and Anaximenes of Miletus Ancient science is usually a story of a handful of individuals, either isolated or connected by a tenuous relation, often communicating across a century or more in their writings rather than 127
working together in a sustained collective enterprise or institution (as we know today). Yet Thales was followed by two successors in the same century in the same city of Miletus, both of who advocated a variation of materialistic monism: the idea that everything can be reduced to being dependent on a single material principle. Anaximenes and Anaximander each affirmed a monistic conception of nature—that everything is one—but they rejected water as the ultimate principle.
Anaximander suggested apeiron (a boundless, indefinite, material principle) Anaximenes suggested air (a definite material principle)
The arguments for apeiron were carried out on a high intellectual plane—as indeed must be the case for any assertion that everything is actually the same. If water were the principle of all things, then everything would be wet. Thus the ultimate element must be something as-yetundifferentiated, which could give rise to both wet-dry, hot-cold, and other opposite qualities in equal amounts and simultaneously. This is much like the creation of a pair of anti-particles from a fluctuation in an energy field in 20th-century physics. While it may appear that the proposal of air represented a backward step after the highly abstract apeiron, air could be supported by empirical analogies from sense experience involving condensation and rarefaction. All three Milesian monists (Thales, Anaximenes, and Anaximander), then, identified nature as the matter that persists through change, and conceived of it as a single universal substance. Heraclitus of Ephesus Another early natural philosopher that Aristotle numbered among the physicists was Heraclitus of Ephesus. He continued the focus on matter and changes in matter. He was a monist (all is one) like the above three Milesians, but rejected water, apeiron, and air as candidates for the “one” nature upon which all else depends. He emphasized the reality of change, as well as the character of matter. For him all things are changing, and nature is always in a state of flux. This is the import of his phrase: “you can’t step into the same river twice, for new water is ever flowing around you.” Matter cycles. The question is not of matter only, but also of the changes through which matter persists. The question “What is the underlying nature or matter?” is not sufficient by itself to explain the nature of things. A pond and a river are both made of water, but the latter one stresses change in location of water. Thus he stressed in his science that “All things are in a state of flux,” a tension of opposites. Despite the fact that appearances may remain much the same, matter perpetually changes. Consistent with this emphasis on change, Heraclitus rejected the three earlier candidates for the one ultimate substance, and nominated fire instead—fire exemplifying wonderfully what is always changing yet remaining much the same. Therefore the all is one, and the one is fire. Fire included both flame (displays fire to vision) and heat (displays fire to touch). Fire is the principle of all things; a flickering flame is always changing but its appearance never changes, thus, it is a model of the nature of the universe. 128
Leucippus of Miletus and Democritus of Abdera: the Greek atomists The Roman poet Lucretius’ work, On the Nature of Things, which was rediscovered in the 1400’s, is the only source of information about Greek atomists except for hostile quotations in ancient sources. Democritus of Abdera said that everything he knew he learned from his teacher, Leucippus (yet no works of either survive). Democritus and Leucippus clearly rejected the monistic view of nature. For them nature consisted of two realities:
Indivisible atoms varying in shape, size, and orientation The void (empty space).
Changes in nature resulted from the chance or random motion of atoms in the void, aggregating or splitting apart to comprise the objects of sense. Qualities other than those of the atoms (such as taste) resulted wholly from the primary features of atoms (e.g., sharp taste resulted from sharply angled atoms). While this view is not monistic, it does give an account of matter and its changes, though the idea of a void (empty space) was to prove very problematic (and ended up being rejected more than accepted throughout the history of physics). The atomists rescued the idea of change by denying the plenum (the idea of continuous matter filling up all space) altogether, and asserted two of the most controversial of concepts in the history of science: the significance of chance, and the existence of the void. According to the atomists, the universe consists of many small, imperceptible, separate pieces too tiny to see, each of which is an indivisible miniature plenum particle. Since they are indivisible, being plenums, they are called atoms (tome = to divide; with “a” prefix, means “cannot divide”). Since they are separate there must be empty space, a void, between them (or else everything is a plenum). Only atoms and the void are real (thus this is “dualism” [2 natures] rather than “monism” [1 nature]). The infinite number of atoms differ in size and shape but not in substance. Differences we observe in nature are due to differences in the shape or arrangements of atoms; for example, small and angular shaped atoms produce an acid taste while sweetness is caused by large round atoms. The void permits movement of atoms and allows for change. Coming-to-be or passing away results from the separation of atoms as they move through the void to combine into new arrangements. Thus the atomists created a possible response to the challenge of Parmenides, who denied the reality of motion on the grounds of an absolute material monism and plenum. Atomism was consistently rejected by ancient philosophers because of its insistence on the possibility of a void. For how can nothing (the void) exist? Or the question “How can ‘what is’ consist in part of ‘what is not’?” seemed unanswerable by the atomists. In addition, from antiquity through the 16th century, until the work of Christian natural philosophers such as Pierre Gassendi and Robert Boyle, atomism was strongly associated with a denial of teleology (intelligent design) and an atheistic insistence that all things occur by chance. For both reasons, the atomists represented one possible answer that became the “road not traveled.”
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Study Question Of what significance is it that the atomists’ attempted to justify their atomic theory in part by claiming that it eliminated the need to fear the gods? In other words, if birth and death are the result of chance rather than the will of the gods, humans need not fear the torments of an afterlife. Is this anti-religious motive itself evidence of science “replacing” religion, or of science and religion in a complex but intimate interaction? Pythagoras of Kroton and the Pythagoreans The concerns of physics—i.e., matter, and changes in matter—could be turned in another direction. Although Aristotle did not call them physicists, the Pythagoreans advocated a “substance” underlying the natural appearances, though not a material substance. The primary claim of the Pythagoreans was that “all things are number.” Contemplation of number and the relations of numbers, for them, held the key to the understanding of nature and its changes.
Ten was considered a perfect number, partly because it was the sum of 1 + 2 + 3 + 4.
Yet there were only nine bodies: the Earth, Moon, Sun, Venus, Mercury, Mars, Jupiter, Saturn, and the sphere of fixed stars. How could this be in a universe that was composed of beautiful harmonies (i.e., there must be a 10th body in the universe)?
The solution was to put the Earth in motion, along with a Counter-Earth, about a central fire, thus yielding ten bodies and a perfect cosmos.
The Pythagoreans abandoned a monistic view of nature by focusing on the elements of number or by emphasizing various dualisms within number (e.g., Great-Small).
Study Question Of what significance is it that the Presocratics were a religious order who worshiped Number as divine, offered prayers and performed rituals, and regarded the working out of geometrical proofs as an ascetic activity of religious contemplation? Is this evidence of science “replacing” religion, or of their continued coexistence and interaction? Parmenides of Elea Parmenides of Elea lived in the early fifth century BC. He claimed that he had experienced a prophetic revelation from the gods that gave him the insight that reason rather than sense experience could apprehend nature truly. His scientific vision included the following:
The void (empty space) cannot exist for how can that which is, consist of what is not?
And if the cosmos is a plenum, then how could change occur, there being no void in which it could move?
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Parmenides took the monistic position to its ultimate conclusion, arguing that if all is one, an indivisible plenum, then change of any kind is impossible (despite illusions of change). Aristotle said Parmenides and Zeno were not physicists because they denied change altogether (and they said our senses totally deceive us). Study Question Of what significance is it that Parmenides claims divine revelation for the knowledge that he has received? Is this evidence of science “replacing” religion, or of their continued coexistence and interaction? Anaxagoras of Klazomenai Anaxagoras’ ideas can be summarized as:
Nature consists of an infinity of elements (radical pluralism): “everything is in everything.” In everything there is a portion of everything.
Anaxagoras’ view easily explained away the question of how change occurs (in the face of the challenge posed by Parmenides), but at the expense of an infinity of elements (not an easy idea to accept).
Everything occurs as a result of logos, or mind, rather than by chance (in contrast to the atomists).
Empedocles of Akragas Another philosopher whose work was written in verse, and who answered Parmenides’ denial of change, was Empedocles of Akragas. Empedocles was a physician who went about claiming to do miracles of healing. Although he even went so far as to proclaim himself a god, he denied that the cosmos was the work of any god. In contrast to Anaxagoras he advocated an origin of animals from the chance association of body parts in a primordial sea. Empedocles picked up on the “elements” of the Milesians and Heraclitus. Here we have a “limited pluralism” view of nature (as opposed to monism, dualism, or radical pluralism). His approach to science entailed the following: •
His view is materialistic, but not monistic, with nature comprised not of one but of four “root” principles (elements): air, water, earth, and fire (Aristotle himself adopted this view).
•
Change could occur (in argument against Parmenides’ challenges to the idea of change) by exchange of place, as in the mixing of a painter’s pigments. No void was required for change to be able to occur, as with the case with the atomists.
•
“Strife and Love” are the driving forces of orderly change (repulsion and attraction).
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The Influence of Presocratic Science The Presocratic natural philosophers established a tradition of debate that became enormously successful in the development of natural philosophy (science). Think about how they contributed to the development of science by studying the tables at the end of this essay. Study Questions 1. In what ways did the Presocratics show the importance of intellectual debate over foundational scientific ideas, rather than merely empirical work that assumes some set of these ideas?
2. Which Presocratics emphasized mathematics as a means of studying nature? 3. Although we ought to admire the Presocratic frameworks within which scientific theories have been developed (table below), how might the Judeo-Christian tradition be seen, even by scholars with no commitment to Christianity, as a later resource for cultural development that provided science with other vital resources (see examples below)?
monism vs. pluralism chance or necessity versus design
materialism vs. idealism finite vs. infinite cosmos
plenism vs. atomism Can you see others?
For Further Thought: Judeo-Christian Contributions to Science (going beyond ancient science) 1. The Judeo-Christian tradition helped scholars see beyond the dualism of “chance and necessity.” A third option of “choice” or “intelligent acts” became a matter of serious attention since medieval times. How are intentional choices (e.g., typing a paper) a different kind of intelligent cause in the universe from either chance or necessity?
2. The Presocratics had no alternative to the idea of the “Eternity of the World”, the notion that the universe always has existed in one form or another. What alternative did Judeo-Christian theology provide for Western culture?
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Evaluation of Presocratic Science A Christian critique of the Presocratics would begin by commending their monistic inclinations as a valuable reform movement in the context of polytheistic, anthropomorphic Greek religion. However, the One (ultimate cause of all) that these Greek reformers envisioned was perhaps actually more idolatrous than the traditional Greek gods, because the One could be discussed abstractly, with no fear of direct personal contact with the divine such as gripped the simple Greek who knew that Zeus might hit him with a thunderbolt or feared that Poseidon might overwhelm him at sea at any moment. This point edges into a fundamental criticism of the entire Presocratic enterprise: “nature” was to them an abstraction, in every case a severely contracted (over-simplified) entity from a theistic perspective, with one or a few created aspects of reality either elevated to self-existent status (thus acting as creator instead of creature), with the remaining aspects of creation vitiated (explained away) by reduction to the few ultimate principles. Theistic scientists today have every reason to continue to oppose reductionistic scientific theories that depend on similar kinds of idolatrous presuppositions. Every ancient scientist, from Thales to Aristotle, failed to conceive of a source of order transcending the cosmos, a Creator who imposes his laws upon creatures that he made from nothing, by the sheer exercise of his divine will. It was this biblical perspective that helped fuel some of the most creative Western scientific approaches, including the experimental method. Review the Presocratics by studying the tables below. Matter and Changes in Matter: A Summary of Presocratic Views Physiologoi (Physicist) Thales of Miletus Anaximandrus of Miletus Anaximenes of Miletus Heraclitus of Ephesus Leucippus and Democritus
Answer (to “what is nature?”) Water Apeiron (the “Boundless”) Air Fire Atoms + Void (Empty Space)
Character of Answer Materialistic monism. Materialistic monism. Materialistic monism. Monism. Motion (change) is key. Pluralism and Anti-Plenism. Chance. Pythagoras and the Pythagoreans Number Idealism and Monism Parmenides of Elea No change despite illusion of it. Extreme Monism. and Zeno of Elea Eternity of the world. Extreme Rationalism. Our senses totally deceive us Plenism. Necessitarianism. Anaxagoras of Klazomenai All in All (infinite # elements) Radical Pluralism. Teleology. Empedocles of Akrago 4 “Roots” (Aristotle’s 4 elements) Moderate Pluralism. Chance. Aspects of Reality Divinized by the Presocratics Physiologoi Milesians Heraclitus of Ephesus Pythagoras and the Pythagoreans Parmenides and Zeno of Elea
Character Materialistic monism Monism Ideal monism Rationalism. Plenism. 133
Aspects of Reality Idolatrized Physical Kinematic or Physical Quantitative and Spatial Logical
Danielson: Hebrew and Greek Worldviews: Pages 1-30 We have seen but few of his works: Torah, Sacred Poetry, Apocrypha, New Testament Western cosmology arises, textually, from two different traditions, the Greek and the Hebrew. It is the latter, the “biblical” tradition, that gives us a world which is spoken into being (like a book) and which points to its Creator. Q1: Identify items below as primarily Greek or Hebrew: Circle Greek (G) or Hebrew (H) Q1A: Cosmos described with organic (agricultural) or architectural metaphors: G / H Q1B: Cosmos described as it appears to ordinary human observers: G / H Q1C: Cosmos described in abstract theoretical terms: G / H Q1D: Cosmos described as a covenant (lawful and relational agreement): G / H Q1E: Humans described as made in God’s image and given a stewardship role: G / H Q1F: Humans described as a miniature cosmos & a necessary part of the whole: G / H Q2: Premodern Babylonian and Greek astronomy considered the number of stars in the universe to be a matter... A. susceptible to human calculation B. beyond human calculation Q3: The Old Testament considers the number of stars in the universe to be a matter... A. susceptible to human calculation B. beyond human calculation? Q4: What human significance/insignificance paradox emerges in the Old Testament and in later Hebrew writings (Apocrypha)? Q5: How does John (chapter 1) identify Jesus? In what terms? How does this relate to Genesis?
Q6: Upon whom does everything (the cosmos and all reality) depend according to the Bible?
Twice into the same river? Heraclitus and Parmenides Two of the first philosophers of nature embody an enduring antithesis: the cosmology of change versus the cosmology of permanence. Q1: Upon what does everything depend according to Heraclitus? Is it something characterized by A. strife (change) B. permanence (no change)
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Q2: Diogenes Laertius, a later ancient Greek writer, referred to the answer to the above question as “the element.” What element? Q3: Diogenes Laertius goes on to say that the single Heraclitan element from which all things originate is: A. personal (like the traditional Greco-Roman gods and goddesses) B. impersonal (abstract) Q4: Characterize the kind of explanations Laertius says Heraclitus offered for various celestial phenomena: A. personal (like the traditional Greco-Roman gods and goddesses) B. impersonal (abstract) Q5: Parmenides’ worldview is difficult to understand from his own writing. How does Arthur Koestler explain Parmenides’ thought in contrast to that of Heraclitus?
Q6: According to Koestler how did Aristotle synthesize the worldviews of Heraclitus and Parmenides?
Skip pages 16-17.
The things of the universe are not sliced off with a hatchet: Empedocles & Anaxagoras Empedocles uncovers the roots of all physical things and tells how Strife entangles them, but Anaxagoras declares that Mind rules the cosmos. Q1: Carl Sagan (1934-1996) was fond of declaring that the cosmos is “all that is or ever was, or ever will be.” What is the equivalent quotation expressing the philosophy of naturalism in Empedocles?
Notice how “love and strife” (Presocratic terms applied to the elements) sound more human-like than “attraction and repulsion” (modern terms applied to material things). Q2: The closing line of the Anaxagoras selection draws attention to religious nature of this new natural philosophy. How does this “god” compare to the God of the Bible?
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Q3: Anaxagoras treats “mind” as a special case in the world of things. How? Does Anaxagoras go as far as the Bible to declare that the ultimate mind is the cause of all things, both material and mental?
Atoms and empty space: Leucippus, Democritus, Epicurus, Lucretius The Atomists forge two ideas breathtaking in their simplicity and influence: indivisible units (atoms) and places where nothing is (space). Q1: What did Leucippus identify as the two elements (the two basic entities out of which all else arises)? Hint: he did not identify different kinds of atoms as modern scientists do, and he used the term “full” to refer to the chunks of matter that he called “atoms.”
Q2: What is more basic in Democritus’ worldview: atoms and empty space, or the four elements previously suggested by other Presocratics: earth, water, air and fire?
Q3: Lucretius’ poetry sought to forge an alliance among the following: radical democratic politics, naturalistic philosophy, and atomism. Write out one line or phrase from his poetry for each of these: Radical democratic politics: Naturalistic philosophy: Atomism:
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Monday September 27 No Required Lab: Try to Finish Extra Credit Skywatch This optional lab is found near the end of the Packet. I encourage you to finish it before the weather turns cold. This lab is due on the Monday just before Thanksgiving.
Plato and Aristotle: Two Worldviews that Shaped Science Aims How Plato and Aristotle assimilated, critiqued, and extended the work of the Presocratics Recognize Platonic and Aristotelian influence in the later scientists and literary figures How Raphael’s “School of Athens” painting (below) depicts Plato’s & Aristotle’s views Two Views of Reality and Their Impact on Science Plato and Aristotle each had a distinctive view of reality that greatly influenced the development of science. Each of them had a different answer to the question: What does the world “really” consist of? All science assumes some answer to this question. Plato’s view of reality: Reality is... Not what appears to us in our normal sense experience Instead, reality resides in the eternal realm of unchanging ideas (he called them “Forms”) Physical things are crude imitations of the eternal Forms (like design templates) E.g., no human is a perfect specimen of humanity Plato’s method for doing science: Science is primarily... Mental effort to grasp eternal unchanging ideas (observations are largely useless) Observations only connect with a crude imitation (material world) of reality (Forms) Beautiful ideas are very likely to be true ideas Mathematics is the best example of beautiful, and thus true, ideas. For example: Precise statements about ideas, e.g., definitions of line, plane, and sphere Aristotle’s view of reality: Reality is... What appears to us in our normal sense experience (the material world) Our ideas are abstractions from the material world These ideas are not transcendent truths (as Plato thought), but inseparable from matter Aristotle’s method for doing science: Science is primarily... Engaging in sense experience Observational, common-sense methods (including common educated opinion) Non-mathematical, qualitative, holistic approach to acquiring knowledge 137
Plato, Aristotle, and the Scientific Revolution Alfred North Whitehead famously declared that western history has been one long series of footnotes to Plato. Clearly, Aristotle was of at least equal significance, so much so that the Scientific Revolution of 16th and 17th centuries can, in part, be viewed as the merging of Platonism and Aristotelianism. It was much more than this, of course, for one must never discount the significant contributions of biblical theology, Stoicism, or Archimedean mathematics, to name just a few other important strands. Indeed, there are severe problems with any single characterization of the Scientific Revolution. However, on a superficial level one may say that Isaac Newton’s 1687 book The Mathematical Principles of Natural Philosophy shows signs of the influence of both Platonism and Aristotelianism. Notice the two components: mathematical (Platonism) and natural philosophy (Aristotelianism). Aristotle’s View of Nature and Motion Aristotle provides us with an impressive summary of ancient knowledge about nature. His writings included a book called the Physics, which focused on the study of physis--nature as an abstract entity capable of being studied as a whole. Physics, according to Aristotle, is study of matter and changes in matter, using a qualitative, not quantitative approach. Today, after the efforts of Kepler, Galileo and Newton to create a mathematical physics, we use a quantitative (mathematical) approach in physics. Nature, according to Aristotle, is that which has within itself a principle of motion (change) and stasis (reaching maturity). Recall the Presocratic preoccupation with the problem of change as you study how Aristotle attempted to solve the problem of “change” in his idea of “nature.” The Greek word for “nature” is phy . “Nature” in a Christian worldview among scholars/scientists since the Middle Ages generally refers to the way God has chosen to cause the universe to exist, with certain regularities that we label natural laws. “Of things that exist, some exist by nature, some from other causes,” wrote Aristotle in his book called Physics. Here are things that are “natural” or have “natures” according to Aristotle:
The four elements: earth, fire, air, and water The three kinds of souls o Vegetative soul: basic property life (grow, reproduce by internal principle) o Animal soul: basic life + self-mobility o Rational soul: all of former, plus the ability to think, create culture, etc. The cosmos as a whole moves by means of its “world soul” (the prime mover)
“Natural changes,” for Aristotle, each consist of motion toward a goal, or final cause (adulthood in the case of humans). For example, a child has a rational soul, but this potentiality for rationality must be actualized over time. When a natural thing reaches its goal, it comes to rest and it ceases to change. For example, a rock falls until it hits Earth, its natural resting place. This goal is the “natural state” or “natural place” of that thing.
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Each of the four elements (earth, water, air and fire) has an inherent tendency to move toward a certain part of the universe and then to stay at rest there. These tendencies are the principles of change and rest in elements. The natural motion of an object composed mostly of earth element is down toward the center of the universe. The natural motion of an object rich in the element air is to go upward away from the cosmic center. Violent (unnatural) motion occurs when something external to an object comes into contact with the object and pushes it in a manner contrary to the way in which the object would have moved if left alone. The difference between natural motion and violent motion is that the former has internal causation and the latter has external causation. Aristotle’s Cosmology Cosmology today may be defined as the study of the origin and physical structure of the cosmos. Before the influence of Christianity, however, Western cosmology generally lacked a concern with origins, because of the influence of the Greek idea of an eternal universe with no history. For Aristotle, cosmology was the study of the one, necessary and eternal structure of the cosmos. Aristotle argued that the cosmos consisted of two distinct regions: superlunar and sublunar.
Superlunar Region of the Cosmos: The Moon and Higher
Fixed Stars Saturn Jupiter Mars
Sun Venus Mercury Moon
4 Sublunar elements:
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pin air k chr om osp her e Fig
water
earth
The superlunar (or supralunar) region of the cosmos, according to Aristotle, consists of everything from the Moon on up higher. In the superlunar region there is no change except change in place in circular paths. The superlunar region is not like the sublunar region in which bodies undergo generation (come to be) and corruption (fall apart). No real substantial change occurs in the “heavens” (superlunar region). Order of Objects in the Superlunar Region (see above diagram) The Moon’s orbit around Earth defines the beginning of the superlunar region of the universe. Above the Moon, in order as one goes upward are: Mercury; Venus; Sun, Mars, Jupiter; Saturn; Sphere of Fixed Stars; and the Prime Mover (the ultimate source of motion for all objects; not shown in the above diagram). Each of the above celestial objects (except the Prime Mover) is attached to a crystalline-like sphere made of a “5th element” called ether. It is the “5th”element in the sense of being totally “other” than one of the 4 elements thought to exist below the Moon. It was considered frictionless, transparent, but physically real. The sublunar region of the universe, for Aristotle, consists of everything below the Moon’s orbit around the Earth. There are 4 elements that exist in the sublunar region out of which all material things are composed. These 4 elements are defined in terms of their weight or levity.
Fire: absolutely light; it moves to the highest part of the sublunar region, below the Moon’s orbit Air: relatively light; it moves upward, but not as much as the fire element Water: relatively heavy; it moves downward, but not as much as the earth element Earth: absolutely heavy; it moves as close as possible to the universe’s center
Study Question
What is the only kind of natural motion that takes place in the superlunar realm?
Answer to Study Question
Aristotle would say that the superlunar realm, due to its perfection, admits only “natural” motion. “Violent” motion can only occur in the sublunar realm, which is imperfect and characterized by generation (coming to be) and corruption (passing out of existence). The only sort of natural “change in place” (motion) that can occur in the superlunar realm is perfect circular motion, which really amounts to no overall change since “going in circles” gets you nowhere unique. Thus, the heavens experience only natural motion, not violent motion. Furthermore, the heavens undergo only one type of natural motion, namely circular motion.
The problem of explaining violent motion within Aristotelian physics Aristotle considered violent motion to require constant and direct contact between the external source of motion and the object being moved. This assumed requirement presented Aristotle and his followers with a complicated conceptual problem to solve, for the continued external cause of 140
violent motion is not easy to conceive in many instances of violent motion. In the case of pushing a pencil gently across a table, there is a clear constant and direct contact between the hand moving the pencil and the pencil being moved. As soon as the hand ceases to exert its gentle horizontal force, the pencil also ceases its violent motion across the top of the table. In the case of a football or similar “projectile” motion, one is left with the conceptual problem of how to explain the continued “violent” motion of the projectile (football or whatever) after the projectile has left the hand of the person who flung the object into its unnatural horizontal motion through the air. Here is a summary of ancient Greek views:
The antiperistasis view, rejected by Aristotle, but advocated by some of his followers, amounted to the claim that the air that is parted by the leading edge of a projectile comes around the back of the projectile and pushes it yet further along.
The longitudinal wave view, apparently favored by Aristotle himself, has us conceive of waves of air that successively push the projectile along horizontally.
Both views appear to be problematic within Aristotle’s own system of physics because both attribute the continued cause of projectile motion to air. This is a problem because Aristotle also thought of the medium of air as a source of friction that resisted projectile motion. How could air both serve as the cause of continued projectile motion as well as the cause of resistance to projectile motion? Aristotle and his followers failed to find a convincing solution to this problem. Christian and Islamic natural philosophers, working centuries later, identified this contradiction and proposed creative solutions to it. Whether motion can take place through empty space (void) Aristotle considered the existence of empty space (a void) to be impossible for various reasons internal to his system of physics. One of the arguments in favor of the impossibility of the void had to do with the thought experiment of a projectile moving through empty space and then through various media of various degrees of resistance. Aristotle’s general physical principles, which he formulated in the context of such thought experiments, may be summarized as follows:
The greater the force exerted on a projectile, the greater its speed
The greater the resistance to a projectile due to the medium it moves through, the less the speed
The following mathematical expression is a modern attempt at summarizing these features of Aristotle’s physics (Aristotle and his followers did not express physics quantitatively using mathematical symbols): V α F/R (velocity is proportional to the force divided by resistance)
Example 1: Push a beach ball through air (little resistance, thus great speed)
Example 2: Push a beach ball through a hill of sand (much resistance, thus little speed) 141
Aristotle reasoned that if there is no external force, then there is no projectile motion, but if there is no resistance (as would be the case in motion in a void), then you would get an infinite speed, which is impossible. Thus a void is impossible in nature because infinite speed is impossible. For most of the history of science, Aristotle’s arguments against the void (including the one from projectile motion) were preferred over the atomists’ arguments for the void through which atoms supposedly moved. Aristotle’s Conception of Space According to Aristotle, wherever there is space, there is also matter. Aristotle argued that this is the case because a void or empty space is impossible. So space and matter are not separate concepts, but coextensive attributes of reality. Space has the inherent properties of “up” and “down.” Up means “away from” the center of the universe and down means “toward” the center of the universe. Study Questions 1. Aristotle defined “up” and “down” in reference to one unique point in the universe. What point in space is that? 2. Label (on the diagram a few pages earlier) the following “directions in space” as defined by Aristotle: “Up” (away from center of universe), “Down” (toward center of universe), “Around the Center” (the only other basic direction in the spherical universe) 3. In which region of the universe would it be “natural” for things to move “around the center,” rather than “up” or “down”? 4. Is the spherical shape and central location of Earth a necessary or incidental feature of Aristotle’s cosmology? In other words, given Aristotle’s worldview and physical principles, could the Earth have been shaped or located other than we find it now? Answers to Study Questions 1. The center of the universe is the single point of reference in terms of which “up” and “down” have meaning. This is a single and absolute frame of reference, as opposed to our modern notion of “up” and “down” being relative to numerous gravitational centers in the cosmos. 2. Check your answer with another class member. 3. Only in the superlunar region does “natural” motion consist of “circular” motion. In the sublunar region motion is naturally either “up” or “down”. Sideways motion in the sublunar region is “violent” motion, such as in the case of a projectile (football) moving across a football field.
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4. Earth’s shape and location are necessary features of Aristotle’s cosmos. It just couldn’t be otherwise, given Aristotle’s presuppositions. Why? Review the section above on Aristotle’s conception of space in which there are “natural” places for each of the 5 elements. The natural place for each of the 4 sublunar elements is illustrated in the diagram above by the central shaded core and the 3 other shaded concentric rings—the core being the natural place for “Earth” element and the other 3, as one moves outward, for water, air, and fire. The 5th element naturally exists and moves in perfect circular paths in its “natural place” in the superlunar region (the Moon and everything beyond it). Thus, the notion of “natural place”, a derivative of Aristotle’s notion of “space,” necessitates that “Earth” accumulates as best it can, near the center of the universe, thus forming a roughly spherical object “Earth” with much water on its surface. Greek Thought vs. Christian Alternatives Christian thinkers helped liberate the Western mind from the restrictive notion of natural “necessity” by means of the doctrine of “creation” in which God freely chose to create the universe in whatever fashion he wanted. This emphasis on the absolute power and freedom of God in his creative commands to bring the universe into existence undermined the logical necessity that forced Aristotle into saying things such as the Earth must be in the center of the universe. Another way of expressing the creative Christian notion of the cause of the universe’s existence is to say that the universe is “contingent”. The cosmos is “contingent” in that it “could have been otherwise” or it is “not necessary” in any one form as Aristotle conceived. The universe “could have been otherwise” in that its actual form is only one form among a potentially infinite number of forms that God could have conceived in his creative command (“let there be...”) that called this particular universe to be. According to the typical features of ancient Greek worldviews (such as that of Aristotle), Nature, Knowledge, and History all result from “chance and necessary” rather than “contingent” intent or choice. In other words, nature can only be one way and our knowledge of nature can only occur one way and the course of human and natural history is fixed in an eternal cycle of change that really goes nowhere unique at all, just in endless circles. What “is”, simply “is” and cannot be otherwise. We are all caught in a self- contained, self-explaining universe that is just a brute “given”. In light of this comparison of Greek and Christian worldviews, we notice that “science” or the “attempt to explain natural phenomena” would be pursued quite differently within the context of these two worldviews. For an ancient Greek, knowledge of nature is necessarily demonstrative (not “tentative” or “open-ended” as in a Christian framework) and history is necessary in the way it unfolds (not “open-ended” as in the Christian view, in which acts of God and choices of humans have real consequences that change the course of history in unique ways at key points in time... think for example of the incarnation of Christ as the ultimate example of a singular unique event that resulted from the free choice of God and that altered the course of history beyond human imagination... or think of the big bang theory with its “ultimate singularity”—the moment of the big bang when time, space, and matter all had a beginning, a view that would have been impossible in a pagan Greek frame of mind). By the way, if you think that the “big bang” theory is inherently atheistic (rather than Christian-friendly), think again. For example, Hugh Ross in 143
his book The Creator and Cosmos argues that it is one of the best arguments for the existence of God available from modern science. Study Questions 1. How did Aristotle and Plato differ in their response to the question “What is real?” 2. Of what value were sensory perceptions in obtaining knowledge of reality for Plato? 3. How did Aristotle and Plato differ in epistemology; that is, with respect to the question: “How do we know?” 4. How did Aristotle define “nature”? How, in his definition, did he focus on the “problem of change” that the Presocratics identified as the central problem of natural philosophy? 5. Summarize the principal features of Aristotle’s cosmology. Look at the markings that you made on the large cosmological diagram that was repeated several times in the text above. 6. Explain the difficulty that projectile (violent) motion posed within Aristotle’s physics. 7. Why is a spherical, motionless Earth in the center of the universe a necessary scientific conclusion within the framework of Aristotle’s physics and cosmology?
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Danielson: Plato and Aristotle: Pages 31-42 The moving image of eternity: Plato The voice of Timaeus tells a story of how the physical cosmos began. Q1: Find a few phrases (look especially for repeating ones) that express Plato’s view that the creator (the Demiurge) had to submissively look to eternal Forms (ideas or design templates) beyond himself to utilize in the materialization process that produced the physical world that we inhabit--and that thus this world is an imperfect copy of the eternal Forms. Most repeated phrase: Other phrases: Q2: How does this Platonic creator differ from the God of the Bible in the following respects? Power Freedom Divinity (totally self-sufficient; that upon which all else depends)
The potency of place: Aristotle Aristotle’s writings on physics and the heavens establish concepts that undergirded much of humankind’s understanding of the world for almost two millennia Q1: What two sources of Aristotle’s authority does Danielson mention in his commentary? A. B. Q2: What does Danielson summarize Aristotle’s teaching in this reading by the “potency of place”?
Q3: About what did Aristotle comment when he wrote: “For that without which nothing else can exist, while it can exist without the others, must needs be first; for place does not pass out of existence when the things in it are annihilated”?
Q4: Does Aristotle think that the world could be radically other than it is, but that it just happened to turn out this way? Explain why or why not.
Q5: What is the old cliché about the alleged connection between geocentrism and anthropocentrism that Danielson identifies and then offers Aristotle’s own words to refute? Where does Aristotle say the place of honor is in the universe: center or circumference? Why? 145
Q6: What observational arguments does Aristotle offer for the conclusion that Earth is small compared to the vast size of the universe?
Danielson: Cicero: Pages 50-57 No erratic or pointless movement: Cicero In a dialogue, Cicero lays out a smorgasbord of Roman cosmologies: Epicurean, Academic, Stoic. Q1: Cicero uses the character of Velleius to represent the Epicurean worldview. How does Velleius poke fun at Plato’s academic god (the Demiurge) and the Stoic pantheistic god (all nature is possessed by a universal mind that organized its own chaotic body into the world we now see)?
Q2: How does Velleius, an Epicurean, imagine the world coming to take its present form and how does he justify his position from what he believes to be the infinite size of the universe?
Q3: Cicero uses the character of Belabus to represent the Stoic worldview. How does Belabus argue that the universe is possessed by a universal mind—the deity whose body is all there is (pantheism)? How is this a pagan version of the argument from intelligent design in the universe? How does the fact that intelligent design arguments have sometimes been used by pagans bear upon today’s vigorous refurbishment of intelligent design arguments by prominent scientists? How should we think about arguments from design today that are made by people holding various worldviews, both theistic and non-theistic?
Q3: What did the Greeks think was so beautiful about a sphere (or circle in just two dimensions)?
Q4: What does this mean? “…the uniform movement and regular positions of the stars could not have been preserved in any other shape.” (p, 53). Most in the Western tradition (till modern times) have taken this to be the inescapable conclusion of logic and observation. How do we explain this differently today (we will answer this last question in class)?
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P. 54-55 optional. You may be able to visualize the movements of the other celestial bodies from this archaic language. Q5: Why did Stoic design theorists look to the heavens more than Earth to see evidence for intelligent design? What assumptions about the nature of intelligence are behind this preference?
Q6: How did ancient Stoics proclaim human importance despite the cosmologically inferior location of Earth in the center (bottom) of the universe?
Danielson: Boethius, Maimonides, Dante, Oresme, Cusanus: Pages 80b-96 [Skip Martianus Capella, p. 78-80a]
The Love that rules the universe: Boethius Q1: This part of Boethius’ poem hinges on the covenant God declares to creation—to faithfully maintain it in a consistent manner (a persistent theme in Psalms). How does “Love” fit into this poem? How about humans?
We consider time a thing created: Moses Maimonides The greatest Jewish teacher of the Middle Ages articulates a non-naive monotheistic doctrine of creation and takes a critical view of geocentrism. Q1: Following Maimonides’ argument, give an example of each: Astronomical knowledge established beyond reasonable doubt: Doubtful astronomical knowledge:
In his case for the beginning of time (something well established within Big Bang cosmology today on quite different evidential grounds), Maimonides refers to time as an “accident.” In medieval philosophy “accident” does not refer to a chance event. Rather, an “accident” is something that is known to exist in dependence upon a “substance”--some other part or aspect of the created world. 147
Q2: According to Maimonides, upon what does time most directly depend within the created world?
Q3: To what degree and in what manner does Maimonides accept the teachings of Aristotle and Ptolemy?
Skip pages p. 86-88.
From this point hang the heavens: Dante Alighieri Q1: Dante’s Divine Comedy builds a moral analogy upon medieval (Aristotelian) cosmology. Where is hell located in this picture of the world, and why?
Q2: Dante, following the Bible, shudders at the reality of hell’s extreme discomfort. But why does Dante replace the biblical metaphor of hell as a sweltering hot place with hell as an icy cold place?
Optional reading: p. 91. Upon reaching the Empyrean (the place of God’s throne beyond the universe), Dante’s imagery is difficult to follow. Everything--”heaven and nature all”--is dependent upon God.
Easily imagined by anyone with good powers of understanding: Nicole Oresme A medieval churchman, astronomer, and minister of finance considers the “economical” (simple) idea that Earth rather than the rest of the universe rotates every twenty-four hours. Oresme’s thought experiment was, in part, motivated by the Christian theological idea that God is free to make the universe many different ways--not just the way Aristotle claimed the cosmos existed. The first step, historically, in considering alternatives to Aristotle was to examine the intellectual coherence of other ways the physical world could exist besides the one endorsed by Aristotle. Oresme offered no proof that Earth actually rotates daily on its axis (neither could Copernicus or Galileo), but at least he argued that one could imagine either viewpoint (mobile or immobile Earth) as true without crossing over into physically absurd claims. Galileo made use of much the same reasoning, but took it a few steps further.
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P. 93: Here Oresme begins with the traditional case of the immobile Earth viewpoint. Don’t be fooled by its claim to being the only reasonable state of affairs. Oresme eagerly undermines this initial account of Earth’s immobility with a counter argument that hinges on the relativity of motion. Q1: What is the main point of the thought experiment about ships A and B on p. 93b?
Q2: “Similarly, if the earth made a daily rotation and the heavens did not, then it would seem to us that the earth was at rest and that the heavens moved.” (p. 94). How does Oresme support this conclusion?
Q3: In the end, we read: “Therefore I conclude we could make no observation that would establish that the heavens make a daily rotation and that the earth does not.” How does Oresme reason his way up to this final assertion?
A single cosmos with the action and reaction of star upon star: Nicholas Cusanus A cardinal envisages both an infinite universe that has no center and an earth that moves. Q1: How does Nicholas Cusanus express “relativity” under the absolute cosmic lordship of Christ in the following aspects of created reality? This medieval cardinal sounds modern (p. 97). Change in place (rest vs. motion) Location or “place” in the cosmos (center vs. circumference) Q2: How does this treatise on relativity support a “moving Earth” hypothesis? (p. 97a).
Page 97 shows Nicholas toying with the hints of a system of geometry that has proved critical for 20th-century cosmology. Non-Euclidean geometry (and the work of Einstein and others) now sets us up to think of space as curved in the presence of massive objects--the universe itself being 149
curved in on itself by the total mass of the cosmos (thus every point in the cosmos is in the center as Nicholas theorized on Christian theological grounds). Q3: On what basis does Nicholas assert the existence of extraterrestrial life? (p. 98). Q4: On what basis does Nicholas declare a cosmos unified by one consistent set of laws? (p. 99). Optional: p. 100. Q5: Based on this last paragraph, why did Nicholas entitle his book On Learned Ignorance? Hint: how does “paradox” figure into his book as a whole? What are three prominent ways in which the Christian worldview contributed to the development of science through the Middle Ages and Scientific Revolution? 1. The ancient Greek notion of a dichotomous universe--the heavenly (superlunar) and earthly (sublunar)--with two separate sets of natural laws, was superseded (by small steps through the medieval and early modern periods) with the idea of a universe “unified” under one “covenant of creation,” or one system of physical laws, in a way that owed much to the positive influence of Christian theology. Christianity provided science with the fruitful idea of a single Creator who created “many creatures in one creation,” or “universe” in which we would expect to find an orderly system of cause and effect throughout the cosmos as a manifestation of the Creator’s consistent sovereign oversight (detected by humans as “natural law”). 2. Early in the Western tradition (from at least the time of Aristotle), scholars commonly assumed the “heavens” (celestial realm) to be changeless. Observations of real change on earth were translated into a belief in real change in the celestial realm, but only after the ancient pagan Greek notion of a dichotomous universe came under sufficient criticism to begin to unify the heavens and Earth into one cosmos--a cosmos increasingly viewed by many Western scientists as a creation of God undergoing change under God’s consistent sovereign guidance. Hebrews 1:10-12 (quoting Psalm 102:25-27) refers to earth and the heavens as undergoing a process of aging and decay (downhill change)--metaphorically expressed as “they will wear out like a garment.” As this biblical view of a changing cosmos gradually displaced the idolatrous Greek notion of a changeless divine heaven, astronomers in the Western tradition became more likely to interpret such a phenomenon as a supernova as a new star rather than a change in the sublunar conditions of visibility 3. The experimental method of science owes much of its inspiration to the Christian doctrine of contingency in which the creator freely chose to create the universe with one set of consistent laws that is a subset of a potentially infinite number of different sets of laws (other possible universes). Often drawing from this doctrine of contingency (in a “voluntarist” Christian theological tradition), scientists forged the notion that one cannot simply deduce the one “necessary” universe (an ancient Greek idea) by just thinking about how the universe “must 150
be,” but rather one should generate a variety of hypotheses about how the universe might be constructed and test them to see which way God freely chose to create. We will explore how these three contributions of the Christian worldview were expanded in the Scientific Revolution.
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Read in preparation for viewing the Flat Earth film For the full script of this show, see http://hsci.cas.ou.edu/exhibits/ (search for “Shape of the Earth”; the Babylonian and Copernicus shows are also online at this website). “The Myth of the Flat Earth” by Jeffrey Burton Russell for the American Scientific Affiliation Conference, August 4, 1997 at Westmont College. These comments by Dr. Russell are based on his scholarship in his high acclaimed book, Inventing the Flat Earth: Columbus and Modern Historians (New York: Praeger, 1991). ---------------------------------------------------------------------------------------------------------How does investigating the myth of the flat earth help teachers of the history of science? First, as a historian, I have to admit that it tells us something about the precariousness of history. History is precarious for three reasons: the good reason that it is extraordinarily difficult to determine “what really happened” in any series of events; the bad reason that historical scholarship is often sloppy; and the appalling reason that far too much historical scholarship consists of contorting the evidence to fit ideological models. The worst examples of such contortions are the Nazi and Communist histories of the early- and mid-twentieth century. Contortions that are common today, if not widely recognized, are produced by the incessant attacks on Christianity and religion in general by secular writers during the past century and a half, attacks that are largely responsible for the academic and journalistic sneers at Christianity today. A curious example of this mistreatment of the past for the purpose of slandering Christians is a widespread historical error, an error that the Historical Society of Britain some years back listed as number one in its short compendium of the ten most common historical illusions. It is the notion that people used to believe that Earth was flat--especially medieval Christians. It must first be reiterated that with extraordinary few exceptions no educated person in the history of Western Civilization from the third century B.C. onward believed that Earth was flat. A round earth appears at least as early as the sixth century BC with Pythagoras, who was followed by Aristotle, Euclid, and Aristarchus, among others in observing that Earth was a sphere. Although there were a few dissenters--Leukippos and Demokritos for example--by the time of Eratosthenes (3 c. BC), followed by Crates (2 c. BC), Strabo (3 c. BC), and Ptolemy (first c. AD), the sphericity of Earth was accepted by all educated Greeks and Romans. Nor did this situation change with the advent of Christianity. A few--at least two and at most five--early Christian fathers denied the sphericity of earth by mistakenly taking passages such as Ps. 104:2-3 as geographical rather than metaphorical statements. On the other side tens of thousands of Christian theologians, poets, artists, and scientists took the spherical view
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throughout the early, medieval, and modern church. The point is that no educated person believed otherwise. Historians of science have been proving this point for at least 70 years (most recently Edward Grant, David Lindberg, Daniel Woodward, and Robert S. Westman), without making notable headway against the error. Schoolchildren in the US, Europe, and Japan are for the most part being taught the same old nonsense. How and why did this nonsense emerge? In my research, I looked to see how old the idea was that medieval Christians believed Earth was flat. I obviously did not find it among medieval Christians. Nor among anti-Catholic Protestant reformers. Nor in Copernicus or Galileo or their followers, who had to demonstrate the superiority of a heliocentric system, but not of a spherical earth. I was sure I would find it among the eighteenth-century philosophes, among all their vitriolic sneers at Christianity, but not a word. I am still amazed at where it first appears. No one before the 1830s believed that medieval people thought that Earth was flat. The idea was established, almost contemporaneously, by a Frenchman and an American, between whom I have not been able to establish a connection, though they were both in Paris at the same time. One was Antoine-Jean Letronne (1787-1848), an academic of strong antireligious prejudices who had studied both geography and early church history and who cleverly drew upon both to misrepresent the church fathers and their medieval successors as believing in a flat earth, in his On the Cosmographical Ideas of the Church Fathers (1834). The American was no other than our beloved storyteller Washington Irving (1783-1859), who loved to write historical fiction under the guise of history. His misrepresentations of the history of early New York City and of the life of Washington were topped by his history of Christopher Columbus (1828). It was he who invented the indelible picture of the young Columbus, a “simple mariner,” appearing before a dark crowd of benighted inquisitors and hooded theologians at a council of Salamanca, all of whom believed, according to Irving, that Earth was flat like a plate. Well, yes, there was a meeting at Salamanca in 1491, but Irving’s version of it, to quote a distinguished modern historian of Columbus, was “pure moonshine. Washington Irving, scenting his opportunity for a picturesque and moving scene,” created a fictitious account of this “nonexistent university council” and “let his imagination go completely...the whole story is misleading and mischievous nonsense.” But now, why did the false accounts of Letronne and Irving become melded and then, as early as the 1860s, begin to be served up in schools and in schoolbooks as the solemn truth? The answer is that the falsehood about the spherical earth became a colorful and unforgettable part of a larger falsehood: the falsehood of the eternal war between science (good) and religion (bad) throughout Western history. This vast web of falsehood was invented and propagated by the influential historian John Draper (1811-1882) and many prestigious followers, such as Andrew Dickson White (1832-1918), the president of Cornell University, who made sure that the false account was perpetrated in texts, encyclopedias, and even allegedly serious scholarship, down to the present day. A lively current version of the lie can be found in Daniel Boorstin’s The Discoverers, found in any bookshop or library. 153
The reason for promoting both the specific lie about the sphericity of Earth and the general lie that religion and science are in natural and eternal conflict in Western society, is to defend Darwinism. The answer is really only slightly more complicated than that bald statement. The flat-earth lie was ammunition against the creationists. The argument was simple and powerful, if not elegant: “Look how stupid these Christians are. They are always getting in the way of science and progress. These people who deny evolution today are exactly the same sort of people as those idiots who for at least a thousand years denied that Earth was round. How stupid can you get?” But that is not the truth. --------------------------------- This completes Dr. Russell’s 1997 essay --------------------------------Now step back in time and read Aristotle and our comments about Aristotle. This will help you recreated in your mind how ancient Greeks after Aristotle typically conceived of and justified the idea of a spherical Earth. Aristotle, in his book De Caelo (II. 13-14. Translation of J.L. Stocks), makes a number of arguments in favor of a spherical Earth It would indeed be a complacent mind that felt no surprise that, while a little bit of earth, let loose in mid-air, moves and will not stay still, and the more there is of it the faster it moves, the whole earth, free in mid-air, should show no movement at all. Yet here is this great weight of earth and it is at rest. And again, from beneath one of these moving fragments of earth, before it falls, take away the earth, and it will continue its downward movement with nothing to stop it. The difficulty then, has naturally passed into a commonplace of philosophy; and one may well wonder that the solutions offered are not seen to involve greater absurdities than the problem itself. This first argument Aristotle makes is based on his notion of the element earth seeking its natural place in the center of the universe, thus naturally moving in as close as possible to the center, making a spherical earth a necessarily result. “Anaximenes and Anaxagoras and Democritus give the flatness of the earth as the cause of its staying still,” Aristotle reports. “Thus, they say, it does not cut, but covers like a lid, the air beneath it.” Aristotle argues against this view that a flat earth is necessary to keep it from sinking through the air beneath it in the following ways: Let us first decide the question whether the earth moves or is at rest. For, as we said, there are ... others who, setting it at the center, suppose it to be rolled and in motion about the pole as axis. Aristotle opposes this ancient expression of the rotating earth idea by showing that it does not make sense in light of his principles of physics. In particular he argues that for Earth to rotate about an axis would be a “violent”, not “natural” motion. If it were truly “natural” motion, then 154
every part of earth, including rocks on its surface, would (like Earth as a whole) also move in circles about their own axes, but this is not observed to be the case. Rather, every rock or other small portion of earth naturally tends to move toward the center of Earth in straight lines (not in circular motion). Aristotle continues: Further, the natural movement of the earth, part and whole alike, is to the center of the whole--whence the fact that it is now actually situated at the center [of the universe]--but it might be questioned, since both centers are the same, which center it is that portions of earth and other heavy things move to. Is this their goal because it is the center of the earth or because it is the center of the whole [universe]? The goal, surely, must be the center of the whole [universe]. Aristotle also makes the case in his book De Caelo that the “nature” (internal principle of motion) of the basic “element earth” (which constitutes the main ingredient of the place Earth we live on) may be contrasted with the 3 other elements of the terrestrial realm (water, air, and fire) in a way that clearly necessitates a spherical earth. These 3 other terrestrial elements are not “absolutely heavy” as earth naturally is, but still tend to congregate in concentric rings around the central earthly portion of the terrestrial realm of the universe. Water is only “relatively heavy”, air is “relatively light” and fire is “absolutely light.” When objects composed primarily of the earth element are released at locations within the terrestrial realm dominated by water, air, and/or fire, the earthy object will naturally move (fall) through these lighter elements until reaching as close to the center of the universe as possible. Aristotle thus concludes: It is clear, then, that the earth must be at the center and immovable, not only for the reasons already given, but also because heavy bodies forcibly thrown quite straight upward return to the point from which they started, even if they are thrown to an infinite distance. From these considerations then it is clear that the earth does not move and does not lie elsewhere than at the center [of the universe]. Aristotle then reasons that “if no portion of earth can [naturally] move away from the center [of the universe], obviously still less can the earth as a whole so move.” For Earth to be moved from the center of the universe would be a complete violation of the very “nature” of things, and thus is absolutely impossible. He completes the main part of his physical arguments for Earth’s spherical shape by saying that “every portion of earth has weight until it reaches the center, and the jostling of parts greater and smaller would bring about not a waved surface, but rather compression and convergence of part and part until the center is reached.” Thus the Earth as a whole object is relatively smooth (we still think this despite discovery of very “high” mountains; just examine a NASA image of earth to confirm this).
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A Summary of the History of Ideas about Earth’s Shape Columbus left the Old World’s last convenient stopping ground, the Canary Islands, and then headed west over the Atlantic ocean under the conviction that he would encounter the Far East (Japan, and then China and Southeast Asia) before running out of supplies. The modern myth about past ideas of Earth’s shape, which Jeffrey Russell identified in the 1997 essay you read above, would have us to believe that Columbus argued in favor of a spherical Earth in order to get funding for his project to sail west to get to the Far East. More generally, this modern myth may be defined as the false modern opinion that people living prior to Columbus, especially medieval Christians, thought that Earth was flat. There are various versions of this modern myth, some not as vulgar as others. Former Librarian of Congress, Daniel Boorstin, in his book The Discoverers (1983), at least got straight that Columbus had no need to prove the sphericity of Earth as its sphericity was known in Europe, claimed Boorstin, from about 1300. But European scholars were flat earth proponents from about AD 300 to 1300, he falsely maintained. Beware of reliance on secondary sources like Boorstin’s The Discoverers (1983), when forming opinions about what people in the past thought about Earth’s shape! Boorstin would have us believe that people, especially Christians, were in the dark about Earth’s shape from AD 300 to 1300. Primary sources (books written during the period of history in question) tell us a different story. Sacrobosco’s Treatise on the Sphere (c. 1250) repeated a demonstration of earth’s roundness from the Arab al-Farghani who probably got it from a line of sources leading back to Aristotle and other ancient Greeks.. The renowned Christian theologian, Thomas Aquinas (1225-1274), likewise repeated numerous ancient Greek arguments for Earth’s sphericity that had made their way into the late medieval period, particularly through Islamic sources of Greek thought and through Latin translations of much of the Aristotelian corpus. What about the early Middle Ages (c. 529-1050) before the foundation of European universities and the influx of Latin translations of Aristotle’s works? Although Christendom’s access to the best texts (especially Aristotle) that argued for earth’s sphericity was limited in this period, virtually all Christian scholars during this period who wrote anything about earth’s shape recognized that there were good reasons to believe that it was spherical. For example, Martianus Capella (c. 420), who formalized the idea of the “seven liberal arts” that dominated medieval educational curricula, clearly argued for a spherical earth. Even the early church fathers (from the time of Christ to the beginning of the Middle Ages c. 529), for instance St. Augustine (354430) and Basil of Caesarea (330-379), generally accepted the roundness of Earth. What, then, are we to make of the few Christian scholars who did believe in a flat earth? The two clear examples of this very small category are Lactantius (c. 245-325) and Cosmas Indicopleustes in his so-called “Christian Topography” (547-549). Lactantius held views that eventually brought him condemnation as a heretic (including a dualism that put Christ and Satan on the same plane) and so not surprisingly his writings had little influence during the Middle Ages. Cosmas conceived of a huge, rectangular, vaulted arch over the Earth that had a flat floor, like the Tabernacle of Moses (Earth was an offering table within). He ignored the figurative biblical language about the sky stretched out like a canopy. He was influenced by Origen, though for Origen the tabernacle image was simply a metaphor. Cosmas was also a misfit in terms of the Christian climate of opinion of the time, drawing many of his religious ideas from the Far 156
East, which he attempted to harmonize with Christianity. Likewise, he was a marginal figure with little influence in the Middle Ages. His work survives in only three manuscripts and he was refuted by John Philoponos (late antiquity) and others in the Middle Ages. Given that the evidence for knowledge of Earth’s roundness was very well established in Greek antiquity (see Aristotle’s arguments in the previous section, for example), there is no need to offer any other evidence for the falseness of the “Flat Error” in the period before the early Christian era. So, Columbus had no need to argue with his proposed royal patrons about earth’s shape. Its roundness was a well-established piece of knowledge and had been so continuously through the Middle Ages and the early modern period. What then was the primary issue at stake in his attempt to get funding for his voyage? It was not the shape of the Earth, but its size. Columbus argued that earth, and especially the ocean-covered part of Earth’s surface that stretched out to the west, was much smaller than most contemporary scholars would accept (including those on the panel of judges before whom Columbus had to make his case for funding to the Spanish crown). Who had the best case for the correct distances and sizes at stake? Judging both from modern standards and from the context of what was known at the time, Columbus estimates were far less than actual evidence available. Study Questions: A. Review Aristotle’s arguments for a spherical Earth and then answer these questions: 1.
List reasons Aristotle had for believing Earth is spherical.
2.
Do you know additional reasons for believing in a spherical Earth? List them.
B. Answer these questions based on your reading of Russell’s article (reprinted above) and based on the summary of history found above: 1.
Did these Greeks believe in a spherical earth? ______ Pythagoreans (5th, 4th cent. B.C.), Plato (d. c. 347 B.C.) Aristotle (d. 323 B.C.) Ptolemy (c. 150 A.D.)
2.
What is the modern myth about the beliefs in the past of Earth’s shape?
3.
How did this modern myth get started and perpetuated?
4.
Why is this modern myth so durable?
5.
What was the real debate in Columbus’ plea for finances to sail to the Far East?
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Exam 1 Study Guide 1. Use study guides for exam preparation, but exam questions are not limited to study guides. There is one exception: all exam questions about the Privileged Planet will come directly from its study guide (and related class discussion). 2. Study the old exam questions in the back of the Packet, but beware of revisions to this course that may introduce questions that are totally different from those on old exams. 3. Watch for questions that begin “According to Chaisson ...” and answer such questions from Chaisson’s perspective, not your own (or mine). Sometimes there may be no difference between Chaisson’s views and yours. At other times there may be vast differences. 4. Class exams are usually about 3/4ths closed book/note and about 1/4th open book/note. Organize your notes well to be able to quickly access them in the open part of the exam. Class exams consist entirely of multiple choice and true/false questions. There will be about 40- 45 questions. Bring the test forms you purchased in the bookstore. 5. You may use a Miller Planisphere on both the open and closed parts of the exam. We will test your skill at using and understanding this instrument. For example, practice using the planisphere to find the zodiac and Winter Hexagon constellations. You will need to know how to solve problems with the planisphere, such as when the heliacal rising of Sirius occurs at this time in history. 6. Study all quizzes given up to this moment. Answer keys are on the north board in class. 7. I have used the term “primary motion” as a synonym for daily motion and “secondary motion” as a synonym for zodiacal (sidereal) motion. This is critical for exam 1. 8. Will there be diagrams on the exam? Not very many, if any. However there will be many questions that will test your visual memory of the constellations and their largest, wellknown stars. Many of these questions will involve the use of your planisphere. Sometimes I explicitly state “use your planisphere on this question.” At other times, you will just need to know that this is a question that requires the use of a planisphere. Yet other questions will depend on your ability to image various celestial motions in correct three-dimensional orientation. If you paid close attention in the planetarium, then you will be well prepared to deal with such visually oriented questions. 9. How will labs figure into Exam 1? I will convert lab material into multiple choice and true/false questions. Also, notice that labs often cover the same material as the class readings, but in a different environment. Thus, in most cases, labs represent a strategic way to reinforce what you already were supposed to have learned by means of class lectures and discussion.
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10. What about study questions in the Packet that we never had time to address in class? Yes, they could be on the exam. Be sure to answer them in your study group and then ask me to cover the ones you didn’t get. Presumably you have done this all along and have asked questions in class. If not, use the review day for this purpose. 11. Pay particular attention to the overlap among class periods, labs, and readings. Balance out your study of individual facts and terms with problem solving, idea synthesis, thesis evaluation, and other higher order learning aims. We will emphasize these higher order skills on the open-book/open-note portion of exams. The closed-book/closed-note section of exams will focus on memory recall of discrete items. Finally, study in groups, because others are strong in areas in which you are week. 12. I never force grades into an ideal “curve” shape (I don’t “curve” exams or quizzes). If I adjust grades, it is only to raise everyone’s grades the same amount. I do this by changing the total number of possible points to a number (e.g., 39) that is lower than the original figure (e.g., 42). The new highest number possible is printed at the top of the column on the print out of grades. The Grade Book program calculates a percentage grade for an assignment by dividing your raw score (number of points earned) by the total number of possible points for that assignment. 13. How do lab & course grades appear on OBU transcripts (including 7 week grades)? We follow university policy in assigning the final laboratory grade. A student’s overall class grade is automatically applied to the laboratory grade. Although labs carry no university credit (and thus do not directly affect your GPA), your lab performance will affect your GPA in that it constitutes a portion of your overall class grade. 14. What are the meanings of the terms and symbols in the grades posted on the north board in the classroom (first posting is after exam 1)? Max Points = maximum points. The “highest possible raw score” or the “total possible correct answers”. This will be lower than what was originally on the exam if I raised everyone’s grades. Some students may have more than 100% because of this kind of grade adjustment. Avg score = average score. Average percentage of right answers for all sections of this class. Each student score in the grid below is also given as a percentage rather than as a raw score. d = dropped. Lowest quiz score is automatically selected and dropped by the computer at the time of each grade posting. Which quiz score is “lowest” may change between postings. L = lowered score. Score was lowered by a penalty because one or more instructions were not correctly followed. Examples include wrong ID number, ID number not left justified.
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Wednesday September 29: Exam 1 Bring #2 pencil, test forms, and all your relevant books and notes for the exam. Did you study for the exam following the study guide that was due last class period?
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Monday October 4 Lab 5: Flat Earth (Room 214), Flat Earth Show (Planetarium). Do Pre-Lab Before Lab! Flat Earth Pre-Lab For the full script of this show, see http://hsci.cas.ou.edu/exhibits/ (search for “Shape of the Earth”; the Babylonian and Copernicus shows are also online at this website). “The Myth of the Flat Earth” by Jeffrey Burton Russell for the American Scientific Affiliation Conference, August 4, 1997 at Westmont College. These comments by Dr. Russell are based on his scholarship in his high acclaimed book, Inventing the Flat Earth: Columbus and Modern Historians (New York: Praeger, 1991). ---------------------------------------------------------------------------------------------------------How does investigating the myth of the flat earth help teachers of the history of science? First, as a historian, I have to admit that it tells us something about the precariousness of history. History is precarious for three reasons: the good reason that it is extraordinarily difficult to determine “what really happened” in any series of events; the bad reason that historical scholarship is often sloppy; and the appalling reason that far too much historical scholarship consists of contorting the evidence to fit ideological models. The worst examples of such contortions are the Nazi and Communist histories of the early- and mid-twentieth century. Contortions that are common today, if not widely recognized, are produced by the incessant attacks on Christianity and religion in general by secular writers during the past century and a half, attacks that are largely responsible for the academic and journalistic sneers at Christianity today. A curious example of this mistreatment of the past for the purpose of slandering Christians is a widespread historical error, an error that the Historical Society of Britain some years back listed as number one in its short compendium of the ten most common historical illusions. It is the notion that people used to believe that Earth was flat--especially medieval Christians. It must first be reiterated that with extraordinary few exceptions no educated person in the history of Western Civilization from the third century B.C. onward believed that Earth was flat. A round earth appears at least as early as the sixth century BC with Pythagoras, who was followed by Aristotle, Euclid, and Aristarchus, among others in observing that Earth was a sphere. Although there were a few dissenters--Leukippos and Demokritos for example--by the time of Eratosthenes (3 c. BC), followed by Crates (2 c. BC), Strabo (3 c. BC), and Ptolemy (first c. AD), the sphericity of Earth was accepted by all educated Greeks and Romans. 161
Nor did this situation change with the advent of Christianity. A few--at least two and at most five--early Christian fathers denied the sphericity of earth by mistakenly taking passages such as Ps. 104:2-3 as geographical rather than metaphorical statements. On the other side tens of thousands of Christian theologians, poets, artists, and scientists took the spherical view throughout the early, medieval, and modern church. The point is that no educated person believed otherwise. Historians of science have been proving this point for at least 70 years (most recently Edward Grant, David Lindberg, Daniel Woodward, and Robert S. Westman), without making notable headway against the error. Schoolchildren in the US, Europe, and Japan are for the most part being taught the same old nonsense. How and why did this nonsense emerge? In my research, I looked to see how old the idea was that medieval Christians believed Earth was flat. I obviously did not find it among medieval Christians. Nor among anti-Catholic Protestant reformers. Nor in Copernicus or Galileo or their followers, who had to demonstrate the superiority of a heliocentric system, but not of a spherical earth. I was sure I would find it among the eighteenth-century philosophes, among all their vitriolic sneers at Christianity, but not a word. I am still amazed at where it first appears. No one before the 1830s believed that medieval people thought that Earth was flat. The idea was established, almost contemporaneously, by a Frenchman and an American, between whom I have not been able to establish a connection, though they were both in Paris at the same time. One was Antoine-Jean Letronne (1787-1848), an academic of strong antireligious prejudices who had studied both geography and early church history and who cleverly drew upon both to misrepresent the church fathers and their medieval successors as believing in a flat earth, in his On the Cosmographical Ideas of the Church Fathers (1834). The American was no other than our beloved storyteller Washington Irving (1783-1859), who loved to write historical fiction under the guise of history. His misrepresentations of the history of early New York City and of the life of Washington were topped by his history of Christopher Columbus (1828). It was he who invented the indelible picture of the young Columbus, a “simple mariner,” appearing before a dark crowd of benighted inquisitors and hooded theologians at a council of Salamanca, all of whom believed, according to Irving, that Earth was flat like a plate. Well, yes, there was a meeting at Salamanca in 1491, but Irving’s version of it, to quote a distinguished modern historian of Columbus, was “pure moonshine. Washington Irving, scenting his opportunity for a picturesque and moving scene,” created a fictitious account of this “nonexistent university council” and “let his imagination go completely...the whole story is misleading and mischievous nonsense.” But now, why did the false accounts of Letronne and Irving become melded and then, as early as the 1860s, begin to be served up in schools and in schoolbooks as the solemn truth? The answer is that the falsehood about the spherical earth became a colorful and unforgettable part of a larger falsehood: the falsehood of the eternal war between science (good) and religion (bad) throughout Western history. This vast web of falsehood was invented and propagated by 162
the influential historian John Draper (1811-1882) and many prestigious followers, such as Andrew Dickson White (1832-1918), the president of Cornell University, who made sure that the false account was perpetrated in texts, encyclopedias, and even allegedly serious scholarship, down to the present day. A lively current version of the lie can be found in Daniel Boorstin’s The Discoverers, found in any bookshop or library. The reason for promoting both the specific lie about the sphericity of Earth and the general lie that religion and science are in natural and eternal conflict in Western society, is to defend Darwinism. The answer is really only slightly more complicated than that bald statement. The flat-earth lie was ammunition against the creationists. The argument was simple and powerful, if not elegant: “Look how stupid these Christians are. They are always getting in the way of science and progress. These people who deny evolution today are exactly the same sort of people as those idiots who for at least a thousand years denied that Earth was round. How stupid can you get?” But that is not the truth. --------------------------------- This completes Dr. Russell’s 1997 essay --------------------------------Now step back in time and read Aristotle and our comments about Aristotle. This will help you recreated in your mind how ancient Greeks after Aristotle typically conceived of and justified the idea of a spherical Earth. Aristotle, in his book De Caelo (II. 13-14. Translation of J.L. Stocks), makes a number of arguments in favor of a spherical Earth It would indeed be a complacent mind that felt no surprise that, while a little bit of earth, let loose in mid-air, moves and will not stay still, and the more there is of it the faster it moves, the whole earth, free in mid-air, should show no movement at all. Yet here is this great weight of earth and it is at rest. And again, from beneath one of these moving fragments of earth, before it falls, take away the earth, and it will continue its downward movement with nothing to stop it. The difficulty then, has naturally passed into a commonplace of philosophy; and one may well wonder that the solutions offered are not seen to involve greater absurdities than the problem itself. This first argument Aristotle makes is based on his notion of the element earth seeking its natural place in the center of the universe, thus naturally moving in as close as possible to the center, making a spherical earth a necessarily result. “Anaximenes and Anaxagoras and Democritus give the flatness of the earth as the cause of its staying still,” Aristotle reports. “Thus, they say, it does not cut, but covers like a lid, the air beneath it.” Aristotle argues against this view that a flat earth is necessary to keep it from sinking through the air beneath it in the following ways:
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Let us first decide the question whether the earth moves or is at rest. For, as we said, there are ... others who, setting it at the center, suppose it to be rolled and in motion about the pole as axis. Aristotle opposes this ancient expression of the rotating earth idea by showing that it does not make sense in light of his principles of physics. In particular he argues that for Earth to rotate about an axis would be a “violent”, not “natural” motion. If it were truly “natural” motion, then every part of earth, including rocks on its surface, would (like Earth as a whole) also move in circles about their own axes, but this is not observed to be the case. Rather, every rock or other small portion of earth naturally tends to move toward the center of Earth in straight lines (not in circular motion). Aristotle continues: Further, the natural movement of the earth, part and whole alike, is to the center of the whole--whence the fact that it is now actually situated at the center [of the universe]--but it might be questioned, since both centers are the same, which center it is that portions of earth and other heavy things move to. Is this their goal because it is the center of the earth or because it is the center of the whole [universe]? The goal, surely, must be the center of the whole [universe]. Aristotle also makes the case in his book De Caelo that the “nature” (internal principle of motion) of the basic “element earth” (which constitutes the main ingredient of the place Earth we live on) may be contrasted with the 3 other elements of the terrestrial realm (water, air, and fire) in a way that clearly necessitates a spherical earth. These 3 other terrestrial elements are not “absolutely heavy” as earth naturally is, but still tend to congregate in concentric rings around the central earthly portion of the terrestrial realm of the universe. Water is only “relatively heavy”, air is “relatively light” and fire is “absolutely light.” When objects composed primarily of the earth element are released at locations within the terrestrial realm dominated by water, air, and/or fire, the earthy object will naturally move (fall) through these lighter elements until reaching as close to the center of the universe as possible. Aristotle thus concludes: It is clear, then, that the earth must be at the center and immovable, not only for the reasons already given, but also because heavy bodies forcibly thrown quite straight upward return to the point from which they started, even if they are thrown to an infinite distance. From these considerations then it is clear that the earth does not move and does not lie elsewhere than at the center [of the universe]. Aristotle then reasons that “if no portion of earth can [naturally] move away from the center [of the universe], obviously still less can the earth as a whole so move.” For Earth to be moved from the center of the universe would be a complete violation of the very “nature” of things, and thus is absolutely impossible. He completes the main part of his physical arguments for Earth’s spherical shape by saying that “every portion of earth has weight until it reaches the center, and the jostling of parts greater and smaller would bring about not a waved surface, but rather 164
compression and convergence of part and part until the center is reached.” Thus the Earth as a whole object is relatively smooth (we still think this despite discovery of very “high” mountains; just examine a NASA image of earth to confirm this). A Summary of the History of Ideas about Earth’s Shape Columbus left the Old World’s last convenient stopping ground, the Canary Islands, and then headed west over the Atlantic ocean under the conviction that he would encounter the Far East (Japan, and then China and Southeast Asia) before running out of supplies. The modern myth about past ideas of Earth’s shape, which Jeffrey Russell identified in the 1997 essay you read above, would have us to believe that Columbus argued in favor of a spherical Earth in order to get funding for his project to sail west to get to the Far East. More generally, this modern myth may be defined as the false modern opinion that people living prior to Columbus, especially medieval Christians, thought that Earth was flat. There are various versions of this modern myth, some not as vulgar as others. Former Librarian of Congress, Daniel Boorstin, in his book The Discoverers (1983), at least got straight that Columbus had no need to prove the sphericity of Earth as its sphericity was known in Europe, claimed Boorstin, from about 1300. But European scholars were flat earth proponents from about AD 300 to 1300, he falsely maintained. Beware of reliance on secondary sources like Boorstin’s The Discoverers (1983), when forming opinions about what people in the past thought about Earth’s shape! Boorstin would have us believe that people, especially Christians, were in the dark about Earth’s shape from AD 300 to 1300. Primary sources (books written during the period of history in question) tell us a different story. Sacrobosco’s Treatise on the Sphere (c. 1250) repeated a demonstration of earth’s roundness from the Arab al-Farghani who probably got it from a line of sources leading back to Aristotle and other ancient Greeks.. The renowned Christian theologian, Thomas Aquinas (1225-1274), likewise repeated numerous ancient Greek arguments for Earth’s sphericity that had made their way into the late medieval period, particularly through Islamic sources of Greek thought and through Latin translations of much of the Aristotelian corpus. What about the early Middle Ages (c. 529-1050) before the foundation of European universities and the influx of Latin translations of Aristotle’s works? Although Christendom’s access to the best texts (especially Aristotle) that argued for earth’s sphericity was limited in this period, virtually all Christian scholars during this period who wrote anything about earth’s shape recognized that there were good reasons to believe that it was spherical. For example, Martianus Capella (c. 420), who formalized the idea of the “seven liberal arts” that dominated medieval educational curricula, clearly argued for a spherical earth. Even the early church fathers (from the time of Christ to the beginning of the Middle Ages c. 529), for instance St. Augustine (354430) and Basil of Caesarea (330-379), generally accepted the roundness of Earth. What, then, are we to make of the few Christian scholars who did believe in a flat earth? The two clear examples of this very small category are Lactantius (c. 245-325) and Cosmas Indicopleustes in his so-called “Christian Topography” (547-549). Lactantius held views that eventually brought him condemnation as a heretic (including a dualism that put Christ and Satan on the same plane) and so not surprisingly his writings had little influence during the Middle Ages. Cosmas conceived of a huge, rectangular, vaulted arch over the Earth that had a flat floor, 165
like the Tabernacle of Moses (Earth was an offering table within). He ignored the figurative biblical language about the sky stretched out like a canopy. He was influenced by Origen, though for Origen the tabernacle image was simply a metaphor. Cosmas was also a misfit in terms of the Christian climate of opinion of the time, drawing many of his religious ideas from the Far East, which he attempted to harmonize with Christianity. Likewise, he was a marginal figure with little influence in the Middle Ages. His work survives in only three manuscripts and he was refuted by John Philoponos (late antiquity) and others in the Middle Ages. Given that the evidence for knowledge of Earth’s roundness was very well established in Greek antiquity (see Aristotle’s arguments in the previous section, for example), there is no need to offer any other evidence for the falseness of the “Flat Error” in the period before the early Christian era. So, Columbus had no need to argue with his proposed royal patrons about earth’s shape. Its roundness was a well-established piece of knowledge and had been so continuously through the Middle Ages and the early modern period. What then was the primary issue at stake in his attempt to get funding for his voyage? It was not the shape of the Earth, but its size. Columbus argued that earth, and especially the ocean-covered part of Earth’s surface that stretched out to the west, was much smaller than most contemporary scholars would accept (including those on the panel of judges before whom Columbus had to make his case for funding to the Spanish crown). Who had the best case for the correct distances and sizes at stake? Judging both from modern standards and from the context of what was known at the time, Columbus estimates were far less than actual evidence available. Study Questions A. Review Aristotle’s arguments for a spherical Earth and then answer these questions: 1.
List reasons Aristotle had for believing Earth is spherical.
2.
Do you know additional reasons for believing in a spherical Earth? List them.
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B. Answer these questions based on your reading of Russell’s article (reprinted above) and based on the summary of history found above: 1.
Did these Greeks believe in a spherical earth? ______ Pythagoreans (5th, 4th cent. B.C.), Plato (d. c. 347 B.C.) Aristotle (d. 323 B.C.) Ptolemy (c. 150 A.D.)
2.
What is the modern myth about the beliefs in the past of Earth’s shape?
3.
How did this modern myth get started and perpetuated?
4.
Why is this modern myth so durable?
5.
What was the real debate in Columbus’ plea for finances to sail to the Far East?
6. Critique the quotation from George Gamow, a notable 20th-century astrophysicist: “In the days when civilized men believed that the world was flat they had no reason to think about gravity. There was ‘up’ and ‘down.’ All material things tended naturally to move downward, or to fall, and no one thought to ask why. The notion of absolute up and down directions persisted into the Middle Ages, when it was still invoked to prove that the Earth could not be round.” George Gamow, “Gravity,” Scientific American, March, 1961.
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Flat Earth: Lab 5 Report
Name ______________________
1. Which viewpoint was easiest to argue for in the role-playing exercise? Flat / spherical Earth? 2. Draw 4 hypothetical Earth shapes then read question #3 and answer "yes" or "no" in the boxes below each shape according to whether observations a/b/c/d could be possible (or not) given an Earth of certain shape. Draw 3-D looking shapes (circle is sufficient for sphere). Cube Cylinder Hemisphere (turtle) Sphere
a. a. a. a. b. b. b. b. c. c. c. c. d. d. d. d. 3. Test the above hypotheses (four possible Earth shapes) against these four observations a. Jack lives east of Jill and sees sunrise an hour before her (two time zones) b. Curved Earth shadow on Moon during all lunar eclipses (seen from all orientations) c. Polaris appears motionless while other stars appear to move in circles around it d. As you travel north Polaris appears about 15° higher for every 1000 miles you travel 4. Which observation only establishes Earth's north-south curvature? a b c d 5. Which observation only establishes Earth's east-west curvature? a b c d 6. The cumulative argument established by only the observations identified in #4 and #5 still leaves open which possible Earth shapes? cube / cylinder / hemisphere / sphere 7. Which additional observation falsifies the non-spherical answer to #6? a b c d 8. Which observation could work with any conceivable Earth shape model? a b c d 9. How would Earth spin to get the answer to #8 to work? ______________________________ 10. Which observation allows calculation of Earth's circumference? a b c d Do it here: 11. How is a scientific model like a map? How do you decide to reject or modify a model? Answer These Questions at the End of "The Shape of Earth" Planetarium Show 1. What was the real debate in Columbus plea for finances to sail west to the Far East? Why? 2. Did average students in medieval universities understand more about observational astronomy than average university students do today? Why? 3. Why is the modern myth about medieval beliefs of Earth’s shape still taught in schools?
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Chaisson, pages 25-34a: Copernican Revolution Skim over p. 28 and read it more carefully for next class period when we cover Galileo.
Copernicus Nicholas Copernicus constructed a Sun-centered astronomical system that looks more revolutionary to us today than it actually was in his own time. The planetarium show “Copernicus and His Revolutions” brings this historical perspective alive. For the full script of this show, see http://hsci.cas.ou.edu/exhibits/ (search for “Copernicus”; the Babylonian and Shape of the Earth shows are also online at this website). What did Copernicus actually achieve when he published his 1543 book: On the Revolutions of the Heavenly Spheres (referred to below by the Latin, De revolutionibus)? Should it be characterized as a revolution, a reformation, an evolution, or in some other way? Was it really a revolution in the sense of a sudden break from the past, or were certain ancient ideals reasserted—ideals that had undergone corruption during the intervening years? What about Copernicus’ relationship to the church? Copernicus was a church administrator and dedicated his book to the Pope. What implications does this have for the stereotypical assessment of the Copernican achievement as another instance of “science vs. religion”? Investigate these questions while we reading the Chaisson textbook selection (25-34a) alongside this Packet commentary. In the table below, “recent interpretations” refer to viewpoints that have largely replaced the “previous” ones. Consider this a chart of progress in our knowledge of the history of science! Previous and Recent Interpretations of Copernicus Previous Interpretations
Recent Interpretations
“Aware that his doctrines were totally opposed to revealed truth, and foreseeing that they would bring upon him the punishments of the Church, he expressed himself in a cautious and apologetic manner....” John William Draper, 1874.
Copernicus was a devout Catholic whose main opposition came from Aristotelian physicists, not theologians. Taking into account the variety of cosmological opinions within the Church leadership, Copernicus used his preface to present his central proof in a rhetorical style familiar to his fellow humanist clerics who valued mathematical disciplines such as astronomy. Although Copernicus’ reformist agenda within the Church initially failed, he intended to enrich, not oppose the Church.
The Copernican revolution was an internal development within science. Socialcultural factors played negligible roles.
In order to properly understand the Copernican achievement, one must take into account its cultural dimensions, including astrology debates, Renaissance rhetoric, and the role of the Christian worldview.
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He rejected ancient science and began the Scientific Revolution.
He reaffirmed the ancient principle of uniform circular motion that Ptolemy’s equant had compromised, in order to reform astronomy.
The Lutheran theologian Osiander, wrote a deceptive “preface” to the De revolutionibus that hindered the development of science by obstructing Copernicus’ realist agenda.
Osiander intended to contribute to the Copernican achievement by minimizing the initial criticism to its realist claims (the claim that Earth really does move). A number of Wittenberg reformer-educators adopted the Copernican system as at least a calculating device. Some even accepted its heliocentrism as real. Scientists later accepted the realism Copernicus had intended, though for a variety of reasons.
Copernicus revolutionized astronomy primarily on the basis of careful observations.
Copernicus only made about 27 new observations, none of which was crucial to his theory. Some of these were actually manufactured “observations” (e.g., sub-horizon events) to illustrate his theory.
The Early Life of Nicholas Copernicus Nicholas Copernicus came under the care of his uncle when his father died. His uncle became a bishop over a remote frontier European province (what is now Poland). Through this position his uncle set the young Copernicus on the path of financial security and advancement in the church hierarchy. But to effectively advance in the church hierarchy, Copernicus had to earn a university degree in either law or theology. He earned a doctorate in canon (church) law and worked as a church administrator most of his life. Copernicus moved from Poland to Italy to begin his law studies at the University of Bologna. Here he met and closely associated with the astronomer Domenico de Novara (1454-1504). Domenico began teaching at the university just after an earlier period of reorganization and revitalization at the Pope’s command. The “Renaissance” movement (1400–1500) of Northern Italy motivated this reorganization and resulted in a new interest in ancient Greek culture-especially Platonism. Renaissance Platonism and Astrology Indeed, Domenico was a Platonist. It was probably through Domenico that Copernicus became convinced that if something is beautiful, then it more likely true (the Platonistic view of how you gain knowledge). Domenico was an astrologer as well as an astronomer. Astrological prognostication was a thriving enterprise in Europe. The enterprise of astrology included making predictions about human events based on astronomical phenomena. Although it was controversial, it was widely practice. While a student at the University of Bologna, Copernicus assisted Domenico’s astrological and astronomical work. A controversy over the validity of astrological prediction broke out in Bologna then. Giovanni Pico della Mirandola (lets call him Pico) published a book that denounced astrology. One of Pico’s principal arguments questioned astrology on account of the 172
ubiquitous disagreement among astronomers over the correct order and distances of the planets (Ptolemy’s Almagest regarded the problem as insoluble). If a planet’s distance from the Earth were uncertain, then the degree of its influence over human affairs would also be dubious. Part of the reason Copernicus began his serious pursuit of astronomy may have had to do with the set of problems posed by Pico’s denunciation of astrology. In particular, Pico’s argument about the uncertainty of the order and distances of the planets may have triggered Copernicus’ search for a way to solve this problem—a search that might have led him to heliocentrism. Indeed, Copernicus’ system of astronomy allowed him to calculate the distances between planets (based on the assumption of Earth as a planet, not proof of it). For example, assuming Earth has an orbit larger than that of Venus and that they both have orbits that roughly center on the Sun, Copernicus was able to calculate the distance of Venus from the Sun in terms of Earth-Sun units (what we now call an AU, astronomical unit). Examine the diagram below that depicts the orientation of Earth and Venus relative to the Sun at the moment of the (maximum) bounded elongation of Venus and then answer these questions: Identify how each of the angles of the Venus-Sun-Earth triangle is known (circle correct): • 43˚ angle: known by o observation o geometric reasoning Venus Earth from assumption of Earth’s orbit 47° 90° • 47˚ angle: known by o observation o geometric reasoning .72 units from assumption of 1 unit 43° Earth’s orbit • 90˚ angle: known by o observation Sun o geometric reasoning from assumption of Earth’s orbit
Copernican Model: elevates humans to a new level, empowering us to calculate distances that were impossible to solve in the Ptolemaic system.
If you draw a triangle with these angles, you can measure the distance yourself to see that the Venus-Sun distance comes to about .72 times that of the Earth-Sun distance (or you can use trigonometry to get this answer).
Copernicus’ Creative Years at the Frauenburg Cathedral Upon finishing his university education Copernicus returned to Poland and over three decades worked out his heliocentric system of astronomy. When the Vatican learned of his work, it was met with interested curiosity, not controversy. Georg Joachim Rheticus (1514-1574), a Lutheran astronomy professor, came to study with Copernicus and was most instrumental in getting 173
Copernicus to actually publish his work, although a few copies of a brief outline (the “Commentariolus”) had circulated much earlier in manuscript form. De Revolutionibus (On the Revolutions of the Heavenly Spheres), 1543 In 1542 Copernicus wrote the preface to his work, De Revolutionibus, dedicating it to Pope Paul III. As far as we can tell, this was not just a trick. He appears to have been a devout Christian of the Catholic persuasion. After Rheticus accepted a position at the University of Leipzig, a Lutheran theologian at Nuremberg, Andreas Osiander (1498-1522), took responsibility for the manuscript. It was published in 1543 and at least some of the printed pages were probably presented to the author on his deathbed.
Five Ways that Copernicus Departed from Ptolemy 1. He considered the equant device cheating. Copernicus argued that Ptolemy’s planetary theory, although consistent with observation, was not sufficiently pleasing to the mind. In particular he thought that equants were ugly and therefore false. The equant was a mathematical device that enabled a point on the deferent to speed up and slow down while maintaining another kind of uniformity of motion. Copernicus thought that the equant broke the most important Platonic rule of astronomy--that everything must be explained in terms of uniform circular motions. Uniform angular motion that just happens to be in circular paths is not enough to be sufficiently beautiful to the mind. Copernicus was influenced by Neo-Platonism, in which beauty and truth were closely associated. Moreover, equants would be impossible in a physically true model, because rotating solid spheres would be impossible. Imagine a styrofoam ball with a straight metal wire passing through its axis. The ball stays in the same place as it rotates, and nothing prevents the ball from being nested within a larger sphere; as in the Ptolemaic heavens, spheres were believed to nest within larger spheres. On the other hand, the problem that arises with the equant is equivalent to inserting the metal axis of the styrofoam ball off-center (through an eccentric point), and then have the equator of the ball rotate uniformly around a point that is off-center in the opposite direction (the equant point). Indeed, for motion to be uniform around an equant point, the spheres could not be made of solid material. 2. He switched the positions of Earth and Sun. He argued that the Sun was located where the Earth was formerly thought to be (center of the universe), and the Earth (with the Moon) was located where the Sun was formerly thought to be (between Venus and Mars), making Earth a planet. 3.. He was not dissuaded by a failure to observe the most decisive expected evidence for a moving Earth: stellar parallax. Once Earth is considered a moving planet, then this creates a new problem for astronomers (left figure below). As Earth orbits the Sun at the center (Sun not shown in diagram), stars A and B should appear to be located at different angular distances from each other 6 months apart in Earth’s annual orbit. The lack of stellar parallax was observed from antiquity, and provided evidence against the heliocentric hypothesis of Aristarchos. Given the technology available at the time of Copernicus, this difference in angle between star A and star B still could not be observed. Copernicus was not dissuaded by this observational refutation of his theory, but proposed an ad 174
hoc solution to evade this old objection (right figure below). The orbit of Earth around the Sun must be very small compared to the distance to the fixed stars. Put otherwise, the stars must be very far way. Why? Because no stellar parallax was observed from Earth using the naked eye (or even the telescopes of Galileo several generations later). This reinforced the traditional view of the immensity of the universe, but it also gave the planetary part of the universe a much smaller space to occupy compared to the size of the universe as a whole. Star A
Star A Star B Sphere of Sphere of fixed stars fixed stars Stellar Parallax Solution
Star B
Stellar Parallax Problem Earth at position 2
Earth’s orbit is like a point compared to the distance to the fixed stars
Earth at position 1
Only modern instruments enabled such a minute parallax (right diagram) to be observed. Study Question: Stellar parallax was predicted by Copernicus but not observed in either his or Galileo’s lifetimes. How then could Copernicanism be considered scientific? What does this episode suggest is wrong with some popular definitions of the “scientific method”? 4. He attempted to reconcile a moving Earth with contrary observations. Copernicus argued that Earth turns eastward daily on its axis despite the fact that we don’t always experience a strong wind from the east. He reasoned that this makes sense because Earth rotates daily with its surrounding elements (including the “air”). This was a remarkable argument to make in light of the fact that Copernicus lived in an intellectual context in which Aristotelian natural philosophy was so pervasive that it was equated with common sense and obvious truth. Despite the similar arguments by Nicole Oresme and Jean Buridan in the 14th century, it had a stronghold on the universities and intellectual life in general. 5. He repurposed epicycles. Copernicus still used roughly the same number of epicycles in his system of astronomy, but he did not use them to explain retrograde motion. He explained retrograde motion as an optical illusion. Complete the diagram on the next page to see the Copernican optical illusion explanation for yourself (there is an answer key on the page after that).
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Use a ruler to draw straight lines through each set of numbers so that they extend out and touch the upper line which represents the background of fixed stars
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This is the answer key to the previous page All that is left to do is number the arrows at the top 1-5 to see retrograde
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Did Copernicus really initiate a “revolution” in science? In some ways Copernicus’ work appears to be a “revolutionary” break with the past of astronomy, while in other respects his work reformed, reaffirmed or even restored earlier astronomical principles (especially the original Platonic notion of “uniform circular motion”). Moreover, in significant ways it evolved from contemporary work in astronomy, building naturally upon the work of immediate predecessors from Regiomontanus to Dominico da Novara. In short, Copernicus work is a good example of how difficult it sometimes is to characterize the 16th and 17th centuries by the traditional term “Scientific Revolution.” Kepler, Galileo, and Newton did more to pull off a “revolution” than Copernicus (but if a revolutionary turning point is an “event” that stretches over two hundred years to occur, then what historical change could possibly constitute an evolutionary process?).
Danielson: Copernicus: 104-117 Almost contrary to common sense: Nicholas Copernicus With reluctant courage, and recognizing the “novelty and absurdity” of his own opinions, the founder of postmedieval cosmology dares to divulge his ideas on the motions of Earth. Prior to the 19th century, the term “philosopher” simply meant scholar, whether in the sciences or not. A.
Dedicatory Letter to Pope (Preface to On the Revolutions of the Heavenly Spheres) 1. Why did Copernicus say many would think his book “absurd” or at least “almost contrary to common sense”? (p. 104-105)
2. What did Copernicus claim was wrong with Ptolemy’s followers (“those employing eccentrics”)? (p. 106) a. Mathematically calculated predictions of observations b. Foundational ideas of the system that contradicted certain “first principles” and made the system look like a “monster” c. Both a and b 3. How did Copernicus relate #2 to “the best and most orderly Artist” (God)? (p. 106)
4. Which of the following did Copernicus claim that he decisively tested? (p. 107) a. Whether Earth moves b. Whether the assumption of a moving Earth can be used to construct a system of astronomy superior to Ptolemy’s 5. By what criteria did Copernicus judge his own theory superior to Ptolemy’s? (p. 107) 178
6. How did Copernicus anticipate the Bible being used (misused) against his system of astronomy and how did he deal with this? (p. 107-108). His reference to “idle talkers” could be an allusion to I Timothy 1:3-7; 5:13 in which idle talk & authoritative-sounding speculation led away from truth.
7. What application of Copernican astronomy did Copernicus offer the Pope that would be of practical interest to the Church? (p. 108)
B.
Copernicus’ Book: Main Part 1. How does Copernicus argue for the sphericity of the universe? (p. 108) •
Aesthetic argument (what is beautiful or “fitting” is true)
•
Analogical Argument (other similar things are that way, and so this is too)
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Observational evidence leads to this conclusion at the exclusion of all others
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Some combination of the above options? Which?
2. How did Copernicus argue for Earth’s sphericity? (p. 108-109) •
Aristotelian-style gravity arguments
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Position of celestial poles change as you travel _______ & ________
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Number of circumpolar stars changes as you travel _______ & ________
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Eclipse events seen at different times depending on: longitude/latitude (circle one)
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Ship mast progressively disappears as ship goes out to sea
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Some combination of the above options? Which?
3. How do the Earth sphericity arguments function rhetorically (as persuasion)? (p. 109) •
Danielson says Copernicus “belabors” the case for Earth’s sphericity. Why?
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•
Hint: how might this part of his book build up Copernicus’ authority in the minds of the reader before moving to the “crazy” idea of a moving Earth?
4. Copernicus reviews celestial phenomena and astronomical theory as known since Greek antiquity. Be prepared to interpret any line of text in this passage in light of this course. He ends with a warning that in doing astronomy we must not just assume that Earth is at rest. (p. 110-111) •
Sample interpretation: “…across equal portions of their circumference their motions over a given time will appear unequal because viewed from different distances.” Use the diagram below to help you interpret this passage: 4
Hint: 1-to-2 distance = 3-to-4 distance, but will the speed of a point moving uniformly along the circle appear to be the same during these two segments of circular motion as viewed from the black spot?
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5. How does Copernicus begin arguing for the radical reality of a moving Earth? (p. 111) • Observational argument • Aesthetic argument (what is beautiful or “fitting” is likely true)
6. Copernicus cleverly turns a bad situation into victory. Here’s the story. (p. 112) •
If Earth orbits the Sun, we see stars from different positions and stars should appear to shift where they appear to be. Given the instruments available at that time, such stellar parallax could not be observed, thus counting as evidence against Copernicus’ theory. Refer to the packet reading on Copernicus for details about stellar parallax, and review Chaisson, pages 11-12.
•
Copernicus does not present the problem using this sort of problematic language. Instead he frames the whole thing in a way that makes his system of astronomy look good. How? Answer: We aren’t at the cosmic center but our distance from it is _______________ compared to the distance to the sphere of fixed stars.
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7. Copernicus cleverly turns Ptolemy’s own argument for Earth’s very small size (compared to the immense size of the universe) against Ptolemy’s system of the world. How is the size difference turned in favor of a moving Earth (answer below)? (p. 112-113) •
Simplicity Argument: that which is simpler is more likely to be true. Which is simpler (more economical) to rotate daily: Earth / universe (circle one)? Why?
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Do-it-some-more-like-Ptolemy Argument: Ptolemy argued that Earth’s surface is near, but not exactly at, the ____________ of the universe. Yet, our horizon appears to cut the universe exactly in __________. Thus the universe is immeasurably large. We shall follow this method of reasoning yet further by arguing that Earth’s orbit around the Sun is near, but not exactly at, the ____________ of an immeasurably large universe. No wonder some called Copernicus the “Ptolemy of our age.”
8. Aristotle argued it is against nature for Earth to move. Copernicus replied that if Earth actually moves, then there is a natural cause for this motion. See below. (p. 114-115a) •
He called into question the tradition of attributing daily motion to a universe that is huge instead of attributing daily motion to the small Earth.
•
This quotation expresses the above reasoning: “As regards the daily rotation, why not grant that in the heavens is the appearance but in Earth is the reality?”
9. How does Copernicus challenge the Aristotelian tradition of the “potency of place” (the potential inherent within certain places to draw into themselves certain elements, such as the center of the universe’s alleged power to draw in the earth element)? Explain Copernicus idea of gravity. (p. 115)
10. Having rejected Aristotle’s view that the universe’s center is the most dishonorable place, how does Copernicus give honor to the cosmic center as he places the Sun there? (p. 117)
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Kepler’s New Astronomy Johannes Kepler (1571-1630) constructed a “new astronomy.” This new system of astronomy was heliocentric like Copernicus’ system, but in contrast to Copernicus, Kepler replaced circles with ellipses and reintroduced a form of non-uniform motion similar to Ptolemy’s equant under the guise of a new “equal areas in equal times” law (explained below). Kepler was a committed Christian and majored in theology at the German university where he was educated. He later taught mathematics at the high school level, and then got a job in Prague working for Tycho Brahe in 1600. In 1601 Brahe died and Kepler got his job. It was during his time in Prague that Kepler came up with the laws of planetarium motion that we refer to as Kepler’s three laws. Kepler: The Making of a Christian in Science Kepler was born in a German town to a Lutheran father and Catholic mother. The young Kepler developed a devout faith in God that guided his scientific endeavour. Kepler’s lifelong objective was to discover the Supreme Architect’s mathematically elegant plans of creation, by deducing them from mathematical principles and checking these deductions against observations. No sixteenth century physicist of note seriously advocated Copernicanism. Kepler was one of the first astronomers to advocate Copernicanism, but then he proceeded to modify it greatly. After a broad liberal arts education at Tübingen University, Kepler pursued advanced studies in theology at this respected Lutheran university. Here he accepted the Copernican system of astronomy. He wrote that he accepted it “as true in my deepest soul... I contemplate its beauty with incredible and ravishing delight.” Kepler expresses a Platonic idealism in this quotation. He became convinced that the beauty and mathematical elegance of the Copernican theory required that it be physically true, contrary to Aristotelian cosmology, which still had a stronghold in European universities. Besides Platonism, one of his other main reasons for accepting Copernicanism and rejecting the geocentrism of Aristotle was Christian theology. Many early modern scientists, including Kepler, grounded their confidence in the uniformity of cause and effect in the biblical doctrine of creation. Science became the search for order in a universe regulated by an intelligent Creator. The very term “laws of nature” was modeled on the idea of God as the divine lawmaker, of both moral and physical laws. Humans, in God’s image, have a mind that is matched to the intelligibility of nature. As Kepler put it, in doing science we are “thinking God’s thoughts after him.” The Christian doctrine of the comprehensibility of the world was not an ideological straight jacket that restrained the options that scientists had in their research. Rather, it was a tremendous boost to the confidence that we can do science with open minds and with confidence in fruitful results. Kepler wrote of the natural laws of the universe in 1599, before the discovery of his famous “3 laws” of planetary motion: “Those laws are within the grasp of the human mind: God wanted us to recognize them by creating us after his image so that we could share in his own thoughts.” Kepler, like Copernicus, drew from the increasingly prevalent Christian critique of Aristotle’s strict dichotomy and took it to mean there are universal laws of motion that would account for 182
the motion of both earth and the other planets. Kepler also used the late medieval clockmaker metaphor for God to capture the idea of God as the creator of one consistently interacting set of parts we call the universe. This was not the remote clockmaker (prevalent later in the deism of the 18th century), but the immediate providence of God the clockmaker over a unified heaven and earth within which Copernicanism could thrive. Nature, in this context, was conceived of as only relatively autonomous, not absolutely so. The clock still depends on the oversight of the clockmaker in order for the very parts of the clock don’t slide back into non-existence and in order that the natural laws that govern mechanical interaction of parts don’t cease to be. Kepler’s First Major Theory: The 5 Regular Solids Before we cover Kepler’s “3 Laws” we must understand the law of nature that he came up with earlier on in his career, one that we no longer believe in. Kepler developed this law as apart of his Copernican cosmology and believed in it, with certain modifications, during his whole life. In the Mysterium Cosmographicum (1596), “Mystery of the Cosmos” Kepler thought he had found the blueprint God used in making the universe. He thought God had answered his prayers of finding a more rigorous cosmology based on Copernican astronomy. In this book Kepler put forward what would remain his most cherished discovery. When Kepler began to work toward publishing the five regular solid idea along with a host of other speculations and comments on scientific methodology, he was advised by his friend, the rector of Tübingen, to remove the first chapter of the proposed book, which was devoted to harmonizing the Bible with the Copernican theory. Kepler was advised to stick to mathematical astronomy without concerning himself with physical reality. Kepler agreed to drop the original first chapter, although he never abandoned his basic belief in the connection between mathematical beauty and physical truth as well as the harmony of faith and reason. In later years Kepler remarked that this small book was the point of departure for his whole career.
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The 5 Regular Solids (The images are in the “Science & Faith” essay earlier in the Packet) Solid Face Number of Faces Tetrahedron Equilateral triangle 4 Cube Square 6 Octahedron Equilateral triangle 8 Dodecahedron Equilateral pentagon 12 Icosahedron Equilateral triangle 20 Kepler, like the Pythagoreans (fifth century B.C.), found in these figures the solution to the mystery of the cosmos. In the Timaeus, the earliest published work of particle physics, even Plato had constructed his universe according to the geometry of these solids. Now for Kepler, these solids explained the number of the planets and their distances, as they had guided the Supreme Mathematician’s hand as he had laid out the blueprints of the heavens. In the Aristotelian/Ptolemaic cosmos, seven planets wandered through the sky: The Moon, Mercury, Venus, Earth, Mars, Jupiter and Saturn. Copernicus made Earth a planet, but removed the Sun and Moon from their number (making the new number of planets six rather than seven). Because there were only five regular solids, Kepler argued that there must be exactly five gaps between six planets, just as the Copernican theory specified. Six planets would have five gaps between them, the extent of which would be determined by a nesting arrangement of the regular solids. The geometry of the regular solids thus proved the number and the distances of the planets according to the Copernican system. Kepler did not believe that the solids were physical structures; the mystery of the Copernican distances was explained by their geometry. Indeed Kepler was able to discover an arrangement of regular solid—planetary sphere—regular solid—planetary sphere... and so forth that matched the Copernican values (the five regular solids could not be placed in ascending order according to their number of sides and still reasonably fit the data). What do we have here in the person of Kepler thus far: a theological studies drop-out, sent to the far boondocks—he had left seminary studies and got a job teaching high school mathematics. While teaching high school he came up with 5 Regular solids argument for the Copernican system, but this idea did not make it into mainstream science. Only about 200 copies of the Mysterium Cosmographicum were printed and most of these have since been lost. From this we may infer that there was little interest in Kepler’s book, but it was republished in 1621, nine years before he died in 1630. Kepler sent a copy of his Mysterium Cosmographicum to his Italian friend, Galileo, who responded with a letter in which he identified with the Platonic search for the beautiful truth. However, Galileo did not bother even to read his copy of the book, and never accepted the argument from the solids or Kepler’s three laws. Kepler also sent a copy of his book to a famous astronomer of Denmark named Tycho Brahe (1546-1601). Although he didn’t get an enthusiastic reaction from him, he later got Brahe’s job primarily on the basis of this book.
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Tycho Brahe (1546-1601) Tycho Brahe had devoted his life to the proposition that true astronomical theory could only come about through the amassing of precise planetary positions. Although Brahe’s letter back to Kepler was cordial, he sent a nasty letter to Kepler’s teacher, Michael Maestlin, complaining about Kepler’s deductive methodology which ran counter to Brahe’s own preference for a strict inductive approach (actually Brahe used both also). Tycho Brahe soon played an important role in Kepler’s life and we must briefly introduce Brahe to make the connection meaningful. Tycho Brahe, in 1573, published De nova stella (“On the New Star”) which gave the precise longitude and latitude of a star which appeared for the first time. Based on the reputation Brahe built through his precise observations and publication of De nova stella, King Frederick of Denmark gave Tycho a small island 14 miles from Copenhagen and finances with which to build an observatory. Brahe built an elaborate castle decked out with enormous astronomical devices for making accurate observations of the heavens. For 20 years Brahe siphoned off large amounts of royal revenue for his astronomical empire and consequently became the first person ever to make very precise astronomical observations (all without a telescope, which Galileo first used for astronomical purposes in 1609). Tycho Brahe argued the following from his observations of a 1577 comet: the comet is further from Earth than the Moon and thus in conflict with Aristotelian cosmology. Explain why (refer back to Aristotle). Unfortunately Brahe’s royal patron died. Driven by fear of insufficient finances for the future, Brahe moved to Prague where he became mathematician for the Holy Roman Emperor, Rudolph II (with a generous salary). About the same time (1598) Kepler lost his job in Graz due to the effects of the counter-Reformation as it was applied by the new Jesuiteducated, Prince Ferdinand. So, Kepler came begging to the feet of Brahe, requesting a job. Brahe saw this opportunity as a means to get Kepler to carry on his tradition of astronomy, which attempted to arrive at Brahe’s conception of the cosmos through amassing data. Kepler, conversely, viewed the occasion as a means to get his hands on Brahe’s superb data to confirm his own conception of the divine architectural plans of the universe (including his doctrine of 5 regular solids), which Kepler had conceived of by contemplating mathematics and divinity. Although neither party was entirely successful in reaching their expectations, Kepler certainly came out on top, partly because Tycho Brahe died in 1601 and Kepler got his job and all his data. Below is a diagram of the system of astronomy the Tycho Brahe invented and that he hoped in vain Kepler would support. Answer the following questions after examining the diagram. 1. Is the Tychonic system essential Copernican, Ptolemaic, or neither? 2. Is bounded elongation explained in more a Copernican or Ptolemaic manner? 3. Could Mars collide with the Sun in this system?
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4. Would the sphere of Mars collide with the sphere of the Sun in this system? 5. Is the retrogradation of planets treated in a Copernican or Ptolemaic manner? 6. What observations supported or counted against this system...by the year 1600...by the year 1615 (see Galileo’s telescopic discoveries when we cover Galileo and then come back to this question to complete it)? Fixed Stars Saturn Jupiter Venus
Mars
Mercury Sun
Moon
Earth
Kepler’s “New Astronomy” Instantly endowed with finances, fame, and intellectual freedom in 1601, Kepler applied himself fully to his own agenda of research which was set on creating a totally new astronomy. The published result: Astronomia Nova (1609). Mars had been, for centuries, the most stubborn planet to fit into any explanatory model. Ptolemy thought he had Mars conquered with the 186
equant. Copernicus later threw the equant out and reasserted the old astronomical commitment to explaining everything in terms of uniform circular motion, but this time with the Earth as a planet right next to Mars. Kepler began the Mars problem (he called it his “war with Mars”) by using circles and equants, like Ptolemy. After 70 trials he devised a model for Earth, but the data for Mars (from Tycho) could never be made to fit such a model. When Kepler used a circular orbit with Tycho’s data for Mars, it was in error by 8 minutes of arc—about a quarter of the angular breadth of the full moon (60 minutes of arc per degree of arc; 8 is about 1/4 of 30 seconds which is the size of full moon). After years of trial and error, playing with various shaped orbits (including egg (ovoid), recall make it in lab with 3 pins), Kepler had the brilliant idea, in 1605, of trying an ellipse with the Sun as one focus. This became his first law of planetary motion. Law #1: Planets move in ellipses with the Sun at one focus
Planet "b" Planet "a" Focus
Focus
Focus
Sun
All the astronomical clutter of epicycles, deferents, and equants were cleared away. Kepler’s “first law” postulated that planets move in elliptical rather than in circular orbits. With his first law, then, Kepler repudiated the 2000-year tradition, established by Plato and upheld by Copernicus, of “saving” or explaining astronomical appearances by combinations of uniform circular motions. This “breaking of the circle,” or “shattering of the spheres,” represented a major intellectual departure; one which Copernicus himself would have rejected, just as Kepler’s contemporary, Galileo also rejected it. As we will see, Newton incorporated Kepler’s “3 laws” in to his physics and through this route they have become apart of 20th-century science. The regular solid thesis of Kepler did not make it to the 20th century. In departing from the tradition or circular motion, Kepler diverted attention from the combinations of regular circular motions, which might underlay the observed or apparent motions of a planet. Instead he raised the question of what actual physical path would correspond to the apparent motions themselves (the idea of an “orbit”). 187
Kepler himself agonized in a confusion of calculations before he settled on the form of the ellipse, considering many other conceivable shapes for planetary paths. Kepler came upon the ellipse not as a generalization from observational data, but because of its mathematical relation to the circle itself; this made it an appropriate element in the Creator’s Divine Plan. For ellipses could be proven to be equivalent to certain combinations of circular motions which were employed by Copernicus. Finally, the ellipse alone correlated as precisely as he desired with the observations of the positions of Mars providentially obtained, he believed, by Tycho Brahe. Galileo, a contemporary and correspondent of Kepler actually rejected Kepler’s laws. This biggest innovation is not so much going from circle to ellipse as it was going from combinations of geometrical curves as mathematical devices that were not supposed to be physically real (although they believed in the reality of solid spheres, even Ptolemy and Copernicus did not believe that every one of their smaller epicycles were real) to proposal of single geometrical curve describing the actual physical path in space (orbit), which, in combination with Earth’s actual physical motion through space, accounts for phenomena observed. Kepler did not come to the ellipse because this figure forced itself on his mind by leaping out of Tycho’s data. No, rather Kepler considered shapes that had been previously mathematically defined (ovoid, ellipse) because such shapes would be worthy of a mathematically inclined Creator God. Kepler wrote: Divine Providence granted us such a diligent observer in Tycho Brahe that his observations convicted the Ptolemaic calculation of an error of 8 minutes of arc; it is only right that we should accept God’s gift with a grateful mind.... Because these 8 minutes could not be ignored, they have led to a total reformation of astronomy.95 So, for the first time in the history of astronomy we have a single geometric curve describing the actual physical path of planets. And finally, for the first time we truly have a “solar system,” that is, a system of astronomy in which the Sun is both the mathematical and physical key to the entire series of planets, including Earth. The sun’s position is most important mathematically because it is the focus of the elliptical orbits of all planets. Law #2: The radius vector (line from sun to planet) sweeps out equal areas in equal times. See the illustration below. Although the speed of Mars and its distance to the Sun both vary, the line from the Sun to Mars sweeps across equal areas of space (not equal angles, as had Copernicus’ circles) in equal times. This law he boldly extended to every planet. The planet moves with variable rather than uniform speed, proceeding faster in that part of its orbit which is closest to the Sun. Kepler’s first and second laws of motion and Kepler’s idea of a solar system were all published in his Astronomia Nova in 1609. Despite the fact that the equal areas law restored something similar to Ptolemy’s equant, this was, without a doubt, a totally “new astronomy.” 95
Hummel, p. 70; Gingerich, “Johannes Kepler,” p. 295. 188
Planet at 4 positions 1 4
2 Sun These two areas are equal, thus planet going faster 3-4 3
The Story of Kepler’s Law #3 With what is now called his “third law” (Harmony of the Universe, 1619) Kepler discerned a strikingly elegant feature of the universe, which clearly displayed the harmony of the Divine Architect’s plans. By 1613 realized that there was no connection between the motions of the different planets other than the fact that all had the same focus, the center of the Sun. Each planet had its own elliptical orbit and its own pattern of rate of motion. The pattern of speeding up and slowing down was, of course, governed by Kepler’s second law, which retained the uniformity of equal areas being swept out in equal times by the radius vector. This was all fine, but Kepler desired to discover a law that would more dramatically reflect the harmonious relationships of the solar system as a whole. He began to study music theory in the hopes of coming across a musical law that was likewise embedded in the framework of the universe. Kepler found what he was looking for and we now call his third law of planetary motion. Motivate by faith that God created universe such a way that its parts were harmoniously related to each other. Kepler set out to discover those physical laws that reflect God’s cosmic harmony. Law #3: The ratio of the square of the period of revolution of a planet (time it takes for planet to go around sun once, T) to the cube of its distance (D) from the Sun is the same for every planet.
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Planet "b" Planet "a"
T2 /D3 ratio is same for all planets
Sun
Thus the times and distances of the planets are related in a geometrical harmony, a harmony of the universe, a cosmic musical order composed by the Creator and first heard by the mind of Kepler. The reference to music is not accidental. From antiquity, music theory had been considered a sister science to astronomy, with both subordinated to mathematics. In The Harmony of the Universe Kepler set out a mathematical theory of music that explained the lengths of strings that produce the harmonious ratios of the “just” scale. Kepler demonstrated that the motions of the planets consisted of precisely these harmonic ratios, as would be fitting for the mathematical and musical handiwork of the Creator. The beauty of music provided the explicit context for his “third law.” Kepler called this work “a sacred sermon, a veritable hymn to God the Creator” and proclaimed: “behold how through my effort God is being celebrated in astronomy.” Kepler’s work showed that Copernicanism did not imply a vast empty silent meaningless cosmos with conscious life on only one lonely outpost. As with the Pythagoreans and their music of the spheres, to step outside under the stars at night with Kepler is to enter the presence of the most elegant of symphonies, and even into the majestic presence of the Creator beyond the Cosmos. For the one with ears to hear, the harmonies of the universe unceasingly declare the glory of God. Kepler concluded: “behold how through my effort God is being celebrated in astronomy.” Summary: Kepler’s 3 Laws •
Law 1: planets have elliptical orbits around Sun with the Sun at one focus
•
Law 2: planets change speed in such a way that a line from the Sun to a planet sweeps out equal areas in equal times
•
Law 3: T2/D3 is the same for every planet (T = time it takes for a given planet to go around the Sun once, D = average distance from a given planet to the Sun)
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Danielson: Calvin, Kepler, Brahe: 122-131, 163-165, 169-172 This art unfolds the wisdom of God: Calvin and Kepler: 122-127 Two great reformers, one of theology and the other of astronomy, lay out similar principles for interpreting God’s “books.” Study Questions: Select the correct answer for each. 1. John Calvin argued that when the Bible describes nature, it does so in what terms? a. Theoretical terms (explaining underlying physical causes and subtle cosmic truths) b. Ordinary observational terms (how things appear to Earthlings) 2. John Calvin argued science (astronomy, natural philosophy, etc.) is to be a. Encouraged because it leads to truth (God’s wisdom) b. Discouraged because it is not practiced in the Bible 3. How did Kepler interpret Psalm 104:2a “He wraps himself in light as with a garment”? Hint: see Danielson introduction to this reading. (p. 126) 4. What did Kepler mean by this? “He aims not to teach men what they do not know, but puts them in mind of what they neglect….” (p.126). Is that that same meaning as this? “… for it was his intent to extol things known, and not to dive into hidden matters….” (p.127) 5. What phrases stand out in the last paragraph of Kepler that shows his disgust with those who would misuse the Bible to oppose Copernican astronomy? (p. 127)
A star never seen before our time: Tycho Brahe: 128-131 The greatest of the naked-eye astronomers describes an event that for the first time proves the heavens themselves are in the grip of Time. Tycho Brahe was one of those who observed a “new star” in Cassiopeia in 1572. We now know that this was a supernova. This star was previously too faint to see from Earth, but the light of its explosion (when it underwent the supernova process) happened to reach Earth when Tycho was a young astronomer in the year 1572. What impact did Tycho’s observation (and distance calculation) of a “new star” have on early modern astronomy? (p. 128-130)
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This boat which is our earth: Johannes Kepler: 163-165a, 169a-172 An awed (and envious?) mathematician responds to Galileo’s discoveries with speculations about moonmen and the inhabitants of Jupiter--and about the best orbiting space station of them all (Earth). 1. Kepler claimed he had invented the idea of a telescope long before Galileo. What reason did Kepler give for his alleged decision to not construct and use a telescope before Galileo’s success? (p. 164-165a) Optional reading: (p. 165b-169a) 2. On the one hand (in the above optional reading), Kepler cited evidence that counted against the idea that there are innumerable Earth-like planets in the universe (see the Privileged Planet for extensive contemporary evidence). On the other hand, Kepler thought it likely that there were intelligent life forms in a few selected places in the cosmos (as do the authors of the Privileged Planet). What does Kepler have to say about Jovian intelligent life (Jupiter’s inhabitants) and our chance to meet them? (p. 169-170)
3. For whose sake, according to Kepler, do the planets (moons) of Jupiter exist? (p. 170) a. Not for our sake, because we cannot _____ them with the naked eye b. Rather, they exist for the sake of the __________ beings (inhabitants of __________) 4. Kepler argues, like the authors of the Privileged Planet, that our place in the universe was designed for _____________ (this is one of the main purposes of our location within the cosmos). Kepler contemplates the conditions for viewing our solar system’s planets from Jupiter in comparison with viewing from Earth and concludes that Earth is superior and thus fit for highest of “corporeal creatures.” Why did Kepler think Earth was privileged relative to Jupiter in regard to the practice of observational astronomy? (p. 171-172)
5. What reason does Kepler give for concluding that Earth was destined by God to be a planet orbiting a sun rather than a stationary location? Hint: how does earth’s annual orbit privilege its inhabitants with more powerful scientific research potential (review Packet Copernicus reading drawing of Venus at maximum elongation)? (p. 171)
6. Why did Kepler think that it was appropriate for Jupiter to have more moons than Earth (Galileo had recently discovered 4 moons orbiting Jupiter by means of a telescope; we now know that Jupiter has 16 moons)?
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Wednesday October 6 Chaisson, pages 34b-41: Scientific Revolution Finish this chapter, answer the questions at its end, then read more about Galileo and Newton.
Galileo Note: For an illustrated introduction to the life and works of Galileo, see http://hsci.cas.ou.edu/exhibits/exhibit.php?exbgrp=1 (or go to http://hsci.cas.ou.edu/exhibits/ and search for Galileo). How did Galileo fundamentally change the study of physics? Galileo (1546-1642) lay much of the groundwork utilized later by Newton to unify the physics of heaven and earth into one universal system of physics. Galileo argued that projectile motion (such as shooting a cannon ball) is composed of two components--horizontal and vertical-resulting in a parabolic path. He thus brought the “parabola” of pure mathematics into the mainstream of physics. This was a major departure from the Aristotelian view that an object can undergo only one kind of motion at one time. Modern physics since Einstein drastically reconceptualized the Galilean view of projectile motion in terms of single motion through curved space. Christianity has often been blamed for attempting to stifle scientific freedom in the context of Galileo’s famous trial by the Inquisition. As we shall see, there was much more to the Galileo affair than simply Galileo vs. the Church. Not only is Galileo worthy of study for understanding the historical relationship between science and religion, but also because of the sheer bulk of his first-rate creative scientific achievements. Florence (Tuscany): Growing Up Galileo grew up in Florence (now part of Italy as are all the other cities mentioned below). His Father was a prominent Florentine musician and a member of an informal fine arts and mathematics group that met in the home of a wealth merchant. The young Galileo attended these meetings with his father. His father sent him to an ancient monastery near Florence for his early education. When Galileo decided he wanted to take monastic vows, dad yanked him out and sent him to the University of Pisa to study a more lucrative profession—medicine. Pisa (Tuscany): University Drop Out and Professor At Pisa Galileo spent most of his time not studying medicine, but learning mathematics in private from Ostilio Ricci. Galileo acquired reputation of always being ready to quarrel at the drop of a hat. He left without a degree in 1584 to study math on his own in Florence. Galileo’s father pulled a few political strings to get Galileo a chair of mathematics at University of Pisa in 1589. Imagine the reaction of the Pisa faculty to have a college dropout now on the faculty. He didn’t 193
last long there because of his incredible ability to irritate people, especially the Aristotelian philosophers who dominated the universities. By the time he left Pisa in 1592, other faculty members would attend his lectures simply to boo and hiss at anything they disapproved of. Padua (Republic of Venice): Patron Wooing The University of Padua in the Republic of Venice was his next stop. Again, through certain connections Galileo managed to obtain the Padua position—creating more enemies in the process of this political manipulation. While at Padua Galileo received Kepler’s Mystery of the Universe and responded with a letter revealing his own allegiance to Copernicanism, though not public. Kepler wrote back enthusiastically, saying be a bold, published Copernican. To woo the Medici rulers of his native Tuscany (capital city was Florence), Galileo dedicated a booklet that explained one of his instruments, a geometric and military compass, to the young crown prince, Cosimo. This resulted in his being invited to tutor the crown prince in mathematics during several succeeding summers. In 1609 Cosimo’s father died and Cosimo became the new Grand Duke of Tuscany. Galileo saw his chance to get a permanent job under Cosimo, but Cosimo declined. About this time a peddler came to town and boasted a new device—a looking glass, later known as a telescope. Galileo constructed his own looking glass based on second hand accounts of the device and used for astronomical observations. Shrewdly, he also gave a telescope to the Venetian government and as a result was offered a salary of 1,000 florins! The Starry Messenger, 1610 He published his first startling observations, with a 30X telescope (about the magnification of cheap binoculars today), in 1610 in The Starry Messenger. The most exciting discovery was the four bodies that he inferred to be satellites of Jupiter. In an attempt to get a job under the rich court of Cosimo II in Florence he named these four bodies (a happy number, since Cosimo was one of 4 brothers) the “Medicean Stars” (after the family name of the rulers of Tuscany). This gesture, plus a gift of a telescope brought Galileo an invitation to work for the Grand Duke of Tuscany and not even have to teach—just do research. Even the King of France advised Galileo that if there were any planets left which Galileo would name for him, it would not go unrewarded. Outline of Galileo’s Telescopic Observations and Conclusions, 1609-1615 1. Moon: surface has earth-like features: mountains, valleys, etc. Supported idea that Earth, also, could be a planet.
2. More Stars: Milky Way whitish celestial haze resolved into points of starlight; myriads of stars. In any given area, up to 10 times number of stars. This supported Copernicus’ view that the stars are very far away (required to explain absence of observable stellar parallax).
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3. Medicean Stars: Begin to record movements and disappearances of special wandering stars by Jupiter. Explanation: satellites of Jupiter, analogous to our Moon. Analogical argument in favor of Copernicanism: if Jupiter has satellites and goes around Sun, why couldn’t Earth have its Moon and both go around the Sun? Thus, multiple centers or circular motion no longer an objection to Copernicanism. Also, the Earth in motion around the Sun would not leave the Moon behind, as the Aristotelian physicists had argued. 4. Sunspots: argued that the Sun rotates (we still hold this view). 5. Phases of Venus (later came detection of phases of Mercury). Like our moon, Venus appears to have phases, so must go around the Sun. See diagram below. This view was consistent with Tycho’s system, and also with a then-current variant of the Ptolemaic system, where all planets revolve around the Earth except for Venus and Mercury.
Take Class Notes Here Ptolemy/Aristotle
Tycho Brahe
Copernicus
.
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Phases of Mercury and Venus Mercury maximum brilliancy
Sun
Venus maximum brilliancy
Venus maximum brilliancy
Compare the previous diagram with this Ptolemaic one:
SUN
VENUS
EARTH
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At Florence again till Galileo’s death in 1642: Major Publications & Trial In 1610, as Galileo made his way back to Florence, he asked for and received the unique title of “Philosopher and Mathematician to the Grand Duke.” This title, that is the “philosopher” part, was important to Galileo because it gave him the sense of authority he desired to make statements about physical reality, which contradicted the established Aristotelian position. In particular, he wanted a more secure institutional platform from which to propagate the Copernican system. In addition, the salary in the Tuscan court at Florence was to be 2.5 times what he would have received in Padua had he stayed on there. Galileo wrote: It is not possible to receive a salary from a republic, however splendid and generous, without serving the public, because to get something from the public one must satisfy it and not just one particular person. And while I remain able to teach and to serve, no one can exempt me from the burden while leaving me the income; and in sum I cannot hope for such a benefit from anyone but an absolute prince. 1632 Dialogue on the Two Chief Systems of the World—Ptolemaic and Copernican This work is a complete expression of all that Galileo was: physicist, astronomer, polemicist, and above all, an extremely articulate Renaissance man (one who is well versed in many areas). The title, Dialogue on the Two Chief Systems of the World, gives away the fact that the book was written in the form of a Platonic dialogue between several imaginary figures. This format allows the author to deal with controversial issues in a somewhat detached manner since he can hide behind the fictitious characters.: • Simplicio: This character stands for traditionalists (Aristotelians). This role is caricatured and made to look stupid (the Pope identified himself as the object of this derision). • Sagredo: The kind of intelligent, unbiased reader we’d all like to be (he quickly grasps the truth and leaves Simplicio in the dust). • Salviati: Galileo himself Events Leading to Galileo’s Trial of 1633 • Letter to the Grand Duchess Christina, 1615 • Condemnation of Copernicanism, 1616 • Bellarmino’s Decree to Galileo, 1616 • Barbarini becomes Pope Urban VIII, 1623 • Publication of Galileo’s Dialogue, 1632 Letter to the Grand Duchess Christina, 1615 One night at a dinner party the Grand Duchess Christina became engaged in a conversation over Copernicanism and the Bible. The Grand Duchess Christina was the mother of the Grand Duke of Tuscany, Galileo’s boss. Christina became troubled by apparent conflicts between Copernicanism and the Bible. A student of Galileo’s student was there at the party and told what Galileo what had gone on. 197
Galileo responded with his masterful letter of 1615, now known as Galileo’s Letter to the Grand Duchess Christina. In this letter Galileo appointed himself a theologian in his attempt to convert his beloved Catholic Church to Copernicanism. He quoted the catchy phrase of a Cardinal Baronius: “The intention of the Holy Spirit is to teach us how to go to heaven, not how the heavens go.” In keeping with this maxim, Galileo argued that Bible passages that refer to an apparently moving Sun are using ordinary observational language with not intention to teach a particular cosmology or astronomical system. Contrary to legend, Galileo was hostile neither to Christianity nor to Scripture; he rather felt himself personally called to prevent Roman Catholicism from committing itself on scientific matters, and thus putting itself in a position where demonstrated scientific results might undermine the Church’s over-extended authority. Had he been less devout he could have returned to Venice, a republic that had repudiated the Pope’s authority and was offering him asylum. But in the midst of the controversy Galileo appears not to resist the temptation to beat those who adopted a “scientific textbook” hermeneutic at their own game. He argues that the Joshua passage that refers to the Sun standing still in the middle of the heaven (sky) refers to the Sun ceasing to rotate on its axis at its position in the middle of the cosmos (heliocentric view). When the Sun ceased its rotation, so all other planetary motion ceased, he argued. Many scholars think that Galileo was not being serious here, but just showing his opponents that he could play the same game as his opponents (reading cosmological meanings into the Bible that were not intended by the original human authors or by the Holy Spirit who guided them). Galileo’s Letter laid out his rejection of what is sometimes now called the “scientific textbook” principle of biblical interpretation which assumes that the Bible was partly intended to teach us scientific theories. Galileo’s position was actually in line with orthodox theology going back to St. Augustine and beyond to the other early Church Fathers. I and many others agree with Galileo that although the Bible does not claim to be a scientific textbook, it certainly is a revelation of truth, the inspired Word of God—whatever it claims to be true is true absolutely, for God has spoken and he knows all of reality absolutely! When we say we “got inspired” to write a paper, poem, or sermon, this is not the same sense of “inspiration” has been understood through most of history of science and Christianity. The traditional view up through the time of the 17th century when the greatest leaps of scientific discovery were occurring, the traditional view of the authority of Scripture was that it is the only book “inspired” in the strict sense of being “God breathed.” • •
II Timothy 3:16 “All Scripture is God breathed.” II Peter 1:21 says the Bible was written by men who “spoke from God as they were carried along by the Holy Spirit.”
This traditionally has meant that God used the personalities and writing styles of the authors and so guided the process that the end product of text in the original text by the author was without 198
error. Accommodated, yes; mixed with error, no. Word of man, yet, but also Word of God and inerrant. Truth absolutely, yes; exhaustive revelation about every topic in the universe, no. Galileo essentially stood in this mainstream of Christian orthodoxy on the doctrine of the authority of Scripture. John Calvin advised: The Holy Spirit had no intention to teach astronomy; and in proposing instruction meant to be common to the simplest and most uneducated person, he made use by Moses and the other prophets of the popular language, that none might shelter himself under the pretext of obscurity. Unfortunately there were powerful factions within the Catholic Church that closely allied themselves with Aristotelian physics and cosmology and who thus opposed Galileo and Copernicanism for non-biblical reasons. This leads us up to the Condemnation of Copernicanism in 1616. Condemnation of Copernicanism in 1616 Galileo’s move back to Florence in 1611 helped set him up both for the successes and disasters of his later professional life. He left a lifetime appointment at Padua. This was perceived as disrespectful by the educational and political establishment of the Venetian Republic of which Padua was a part. By working for the Grand Duke of Tuscany, Cosimo II of the Medici family, Galileo received special privileges such as a very high salary, official recognition as a philosopher, a strong position from which to challenge the Aristotelian-dominated universities and no teaching responsibilities so he could have more time to think and write. These same privileges, accompanied by Galileo’s special ability to ridicule people in person and in print, produced a strong force of enemies committed to destroying Galileo. In fact there was an underground society that formed (mostly academicians from Pisa and Florence) for the express purpose of opposing everything Galileo said or wrote that challenged the Aristotelian status quo. The Florentine philosopher, Ludovico delle Colombe, led this academic group and thus its nickname, the “pigeons” (Latin = colombi). Galileo often spoke of the pigeons as the “conspiracy” that haunted him the rest of his life. Galileo’s move back to Florence thus triggered many of the forces that helped make Galileo so visible and vulnerable. In 1611 the leader of the pigeons (Colombe) published a treatise that began with traditional arguments against the Earth’s motion, but ended with quotations to show that such motion was incompatible with the Bible. The pigeons were most influential in making the motion of the Earth (and Copernicanism in general) a theological issue as well as a physical and astronomical one. Remember that neither Galileo nor his opponents were free of brute economic and personal advancement motives for saying and writing what they did and this includes dragging theology into the debate. Galileo’s 1615 Letter to Christina (discussed above) was an answer to this kind of nonsense as well as the honest concerns of Christina. By 1616 a significant number of Church authorities became convinced that there was something dangerous about asserting the mobility of the Earth and immobility of the Sun since the Scrip199
tures seemed to indicate otherwise. After only a few days of deliberation in February of 1616 the Holy Office officially declared the immobility of the Sun to be both “foolish and absurd in Philosophy” (against reason) and heretical (against Bible), whereas the mobility of the Earth was merely designated as just erroneous (against reason). The Holy Office also declared that all copies of Copernicus’ De revolutionibus be corrected so that its postulates be regarded as strictly mathematical models (save the phenomena) with no connection to physical reality. This is not so much anti-science as conservative science. Church officials unfortunately tied themselves to Aristotelian science too closely so that when scientific change occurred they lost out and so did the Roman Catholic Church as a whole. Study Question: Do evangelical Protestants risk a similar error today in too closely identifying biblical authority with young-earth creation science? Bellarmino’s Decree to Galileo, 1616 We now turn to a letter that an influential Jesuit theologian wrote to a committed Copernican (not Galileo) one year before the 1616 condemnation of Copernicanism. This theologian, Cardinal Bellarmine, had several personal encounters with Galileo in which he exhorted Galileo with the kind of wisdom in this letter: Further, I say that if there were a true demonstration that the Sun is in the center of the universe and that the Sun does not go around the Earth but the Earth goes around the Sun, then it would be necessary to be careful in explaining the Scriptures that seemed contrary. We should rather have to say that we do not understand them than to say that something is false. But I do not think there is any such demonstration [i.e., of Copernican view], since none has been shown me. To demonstrate that the appearances are saved [accounted for] by assuming the Sun as the center and the Earth in the heavens [i.e., mathematical model only] is not the same thing as to demonstrate that in fact the Sun is in the center and the Earth in the heavens [i.e., physical fact]. (Letter to Foscarini, trans. Owen Gingerich in “The Galileo Affair,” The Scientific American, August, 1982, p. 137). In fact Galileo obtained a copy of this 1615 letter in 1616 and realized that the ball had just bounced back into his court. He now saw that the time was ripe to convince the world that he could give a true physical demonstration of the new cosmology. He recognized that he had to go far beyond showing the mere convenience of the mathematical model of Copernican astronomy. There must be physical proof. Toward the end of 1615 Galileo offered his theory of the action of tides as physical proof of the Earth’s motions. He theorized that tides were due to the combined daily rotation of the Earth on its axis and its annual revolution around the Sun. Unfortunately this supposed physical proof did not convince very many of his contemporaries. Well accepted physical demonstrations of the Earth’s rotation did not appear until the 19th century: observation of stellar parallax and the Foucault pendulum.
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Study Question: Assuming that science is based on observation, was it unscientific to accept the Earth’s rotation prior to the 19th century? Why were Copernicus, Kepler, Galileo and Newton scientific? 1616 was a big year for Galileo • • •
•
January: He finished his paper on tide theory. February: The Holy Office condemned Copernicanism. March: Galileo was summoned before Cardinal Bellarmine and rebuked for teaching that Copernicanism was literally true, rather than just a useful calculating device in astronomy. Galileo received Bellarmine’s warning with respect and realized that he must restrain his “realist” position on Copernicanism and hope that the Church leadership would one day accept his viewpoint. May: Galileo received a personal letter from Bellarmine indicating that he could not propagate Copernicanism as physically true, but the letter left the impression that it was okay for Galileo to use the new cosmology as a useful hypothesis for astronomical calculations. Galileo then resumed his scientific work which criticized Aristotelian physics, but which did not explicitly affirm Copernicanism as physically true.
Barbarini becomes Pope Urban VIII, 1623 His work The Assayer (1623) is a good example of the kind of work Galileo did in this period of his life. This work was such a success that even the new pope, Urban VIII (Maffeo Barberini), liked to have it read to him at mealtimes. Urban VIII was a patron of learning and personal friend of Galileo. In 1624 Galileo had a serious talk with Urban VIII in order to test the waters for a new Copernican push. Galileo was given a careful response: discuss both the Copernican and Ptolemaic views as alternative hypotheses of the cosmos. Publication of Galileo’s Dialogue, 1632 Between 1624 and 1630 Galileo worked on his Dialogue on the Two Chief Systems of the World. This work, published in 1632, is a complete expression of all that Galileo was: physicist and astronomer, mathematician and experimentalist, rhetorician and polemicist. The most significant fact about this work is that, like those works of Galileo’s friend, Kepler, this book was of a hybrid nature, combining mathematics and physics. The title, Dialogue on the Two Chief Systems of the World, gives away the fact that the book was written in the form of a Platonic dialogue between several imaginary figures. This format allows the author to deal with controversial issues in a somewhat detached manner since he can hide behind the fictitious characters. In this way Galileo was able to loosely obey the admonitions of the Pope and of Cardinal Bellarmine who in 1616 said it okay to deal with Copernicanism hypothetically (Bellarmine died in 1621). Galileo presented the manuscript to Pope Urban VIII in 1630. The Pope liked it and told the master of the Holy Apostolic Palace to simply rubber stamp it as okay. The official read the manuscript anyway, felt uneasy about it, but then finally approved it. It was published in 1632. 201
The book sold out as it came of the press and within a few months there was a full-scale outrage over its contents. All sales were stopped, an ecclesiastical commission examined it carefully, and then Galileo was told to quickly come to Rome.. Urban VIII was very angry because he had been shown a letter supposedly written by Cardinal Bellarmine in 1616. The letter, actually it was signed by another Church official on Bellarmine’s behalf and was more strict, suggested more strongly that Galileo was not to teach or defend the Copernican theory in any way since he had refused to shut up (actually Galileo did shut up for years). Urban VII had thought that Galileo had deceived him by not mentioning this letter. Galileo then presented the letter actually signed by Bellarmine (not as forceful) and this part of the case collapsed. But then attention was turned to the Dialogue itself. It became clear that Galileo had produced a very thin veil to try to cover up his strong commitment to the physical reality of Copernicanism. So, when Galileo maintained that he had not defended the Copernican view, 7 of the 12 judges got really ticked off and gave the verdict of “vehemently suspect of heresy.” The remaining 5 judges refused to sign the verdict. The Trial of 1633 The next year, 1633, Galileo was summoned again and amid a complex political struggle the final verdict came out including house arrest that followed Galileo until his death in 1642. Historians of the late 19th century and many people still today tended to overlook the complex political struggles and especially the influence of university Aristotelian physicists in the Galileo affair and thus they branded the Church as a whole as being anti-science. But, as we have seen, the Galileo affair is primarily a case study of the power struggles that naturally occur during times of crucial social and scientific change. The primary source of opposition to Galileo was the trail of enemies that Galileo left behind in the various universities that he worked at and especially the pigeon league formed by some of these enemies. These people, in protecting the truth of Aristotelian science, attempted to hunt down Galileo—first in an academic setting and after that did not work, in an ecclesiastical context. Galileo’s Contribution to a New Physics Galileo work in physics was closely related to his earlier work in astronomy in that his Copernican astronomy required the creation of a new physics, one that departed from Aristotle in a radical way. After his house arrest in 1633, Galileo was forced to work on something else besides Copernicanism. His most creative scientific achievement occurred in this last period of his life—he developed a comprehensive mathematical treatment of motion on Earth (not the motion of Earth). These efforts produced the 1638 masterpiece entitled Two New Sciences, which was the climax of his career. Galileo had the work smuggled out of the country and published in the Netherlands. There was nothing about theology in this book, but one could have hardly expected an Italian censor to have passed anything written by Galileo at this point. What were the “2 New Sciences”? #1. Science of the strength of materials (e.g., breaking strength of beams). This was new. 202
#2. Science of motion. This was a new look at an old science (the Presocratics studied motion). The guiding principle of Two New Sciences may be summarized by this statement: search for mathematical simplicity in the physical world and you will find physical truth. This sounds like Kepler’s approach to science. Try to connect the following table with Galileo’s famous inclined plane experiment, which he published in the Two New Sciences. Galileo’s Inclined Plane: Table of Uniformly Accelerated Motion Time 1 2 3 4 5 6
Distance 1 3 5 7 9 11
Total Distance 1 1+3 1+3+5 1+3+5+7 1+3+5+7+9 1 + 3 + 5 + 7 + 9 + 11
Sum 1 4 9 16 25 36
Galileo’s Analysis of Projectile Motion Galileo argued that projectile motion (such as shooting a cannon ball) is composed of two components: horizontal and vertical:
Horizontal = uniform motion (when air resistance in not considered; see “x” below) Vertical = uniformly accelerated motion (free fall; see “y” below) X
+
X
Position of ball at time t
Y
+
Y
Compare the cannon ball diagram with the diagram below. A person on the top of a boat mast drops a ball. Answer the questions on the next page concerning this diagram.
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Boat Thought Experiment: Answer the Questions Below 1.
Which row of time frames (top or bottom row) represents the perspective of someone on the boat, and which the view of someone on land watching the boat pass by to the right?
2.
From the viewpoint of someone on the boat, what components of motion does the ball have? Just vertical, just horizontal, or both? How about from the viewpoint of someone on the shore watching the boat pass by to the right?
3.
How does the above diagram relate to Galileo’s inclined plane experiment?
Aristotelian natural philosophers believed that only one kind of motion can take place at one time in an object. Galileo, to the contrary, argued that two simultaneous motions could occur in projectile motion. Indeed, it is almost contrary to common sense to say that a body has two different simultaneous motions. And yet this is precisely what the above diagram shows us, especially as viewed by someone on the shore. The idea of a projectile, such as a fired cannon ball, having two simultaneous motions was recognized before Galileo by those working with practical artillery problems like how to shoot a cannon most efficiently and accurately to hit a distant target. The resulting curved path of the 204
cannon was thought to be the product of two forces acting on the cannon ball at the same time. Galileo came to conceive of this as the horizontal and vertical components of motion. X
+
X
Position of ball at time t
Y
+
Y
Galileo was able to prove that the path produced by a combination of a horizontal motion of constant speed and a vertical motion undergoing acceleration (regularly accelerated, not erratically) would be a parabola–a curve known since antiquity in the realm of pure mathematics. Galileo brought all of the mathematical properties of parabolas to bear upon the physical problems of projectile motion. In the diagram above, only a half parabola appears. A full parabola would result if one shot the cannon up in the air rather than horizontally. In summary, the importance of Galileo’s work on the physics of motion is that it continued to apply the mathematical approach to the study of physical problems that had previously been treated in a non-mathematical way (Aristotle’s approach). What evidence can we cite for the ways in which mathematics and physical science joined forces in a creative way in the early modern period? Around the same time as Galileo’s work on projectiles and falling bodies, Kepler postulated that the ellipse represents the actual paths of planetary motion. He applied all that he knew of the mathematical properties of the ellipses to the orbital paths of planets (e.g., sun at one focus). He also described the way in which planets travel in elliptical paths, for example, how they speed up and slow down and are in harmony with each other’s motion in the solar system in a precise mathematical manner. Newton synthesized mathematics and physics at a higher level than Galileo. We turn to him next.
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Newton Isaac Newton’s (1642-1727) book The Mathematical Principles of Natural Philosophy (1687) to a large extent synthesized the work of numerous previous thinkers in mathematics, astronomy, and natural philosophy--including various medieval scholars, Copernicus, Galileo, Kepler, Descartes, and Huygens. His work culminated several previous attempts at the integration of the mathematical (Platonistic) and physical (Aristotelian) perspectives on reality. His work also represents the culmination of the “Scientific Revolution” (see the course chronology that you were to memorize). Newton’s Opticks (1704) exemplifies the experimental tradition, and his Principia (1687) represents the triumph of mathematical physics, unifying the terrestrial physics of Galileo with the celestial laws of Kepler. With few modifications, Newtonian physics is still the basis for the physics of everyday life, including playing tennis, riding a bike, or doing ballet (center of gravity, momentum, etc. are terms used in these kinds of practical physics). Newtonian style science became the paradigm for physics and eventually many other disciplines of science. A central component of this paradigm consisted of the notion, often called “phenomenalism,” that true science may stop short of specifying actual causes. Causes may be elusive and uncertain, though mathematical descriptions remain true. Therefore one should aim to discover a mathematical expression that accurately describes physical phenomena, even if one is ignorant of the underlying causes of such phenomena (e.g., gravity). For Newton, phenomenalism as an approach to science was rooted in the Christian theological tradition of voluntarism, which emphasized divine omnipotence. As an important essay by Edward Davis on the “Newtonian World View” explains, Newton was willing, if necessary, to leave knowledge of causes to God alone without giving up the search for intelligible order expressed in descriptive mathematical laws. In the same way, Newton’s experimental work in optics and other fields was based upon his conviction that God was free to create the universe in any way he pleased, and only by experimental testing could one determine which of the many possibilities the Creator actually instituted. One of the organizing themes of the physical sciences in the 16th and 17th centuries is the rise of mathematical physics, which in the work of Newton finally displaced the qualitative, Aristotelian physics of the universities. Remember, mathematicians (and astronomers, who were mathematicians) were low on the totem pole of university disciplines. Physicists were far more prestigious and better paid, and they did not take kindly to the pretensions (so they thought) of mathematicians such as Galileo who thought they could do physics better than the physicists. To physicists, the domain of the mathematician is restricted to the hypothetical (since the same appearances may be explained by multiple mathematical models96), while in contrast, the physicist deals with what is actually true. Thus cosmology, a branch of physics, was the study of the true structure of the universe and its causes, while astronomy, a branch of mathematics, was the attempt to perform accurate calculations using hypothetical models that made no truth claims whatsoever. So mathematics was not used to any great extent in University-based physics (“natural philosophy”), despite its great success through centuries of astronomy, culminating in 96
One famous example is the equivalence of eccentric and epicycle models for the annual motion of the Sun. 206
the work of Copernicus, Kepler and Galileo. Newton and the giants upon whose shoulders he built changed this forever and established a new discipline of mathematical physics. One of those giants was Johannes Kepler. Kepler had provided convincing evidence that the ellipse represents the actual paths of planetary motion. He applied all he knew of the mathematical properties of the ellipse to the orbital paths of planets (e.g., Sun at one focus). One way to understand the creation of mathematical physics is to interpret it as the integration of the mathematical (Platonic View of Reality) and physical (Aristotelian Natural Philosophy or “Physics”) perspectives. Newton’s great book of 1687, The Mathematical Principles of Natural Philosophy, incorporates (as the title itself suggests) both lines of development in the main story of this class. It is physics or “natural philosophy,” but it is also essentially “mathematical.” He not only synthesized the terrestrial physics of Galileo and the celestial laws of Kepler that we just mentioned, but he produced a grand synthesis of much of the mathematical and physical theories up to that point in history. What is even more amazing is that his choice of what he considered to be “most basic” in nature (his fundamental postulates), turned out to endure the test of time (with some modifications) to the present day. The Newtonian Synthesis Just after Newton received his Bachelor of Arts degree from Cambridge in 1665 the University was closed because of a plague. Newton returned to Cambridge two years later as a “fellow” because two other fellows fell down some stairs, died, and left two fellowships open. About a year later, Newton’s mentor Isaac Barrow gave him his own chair as professor of mathematics at the University of Cambridge. Newton was only 26 years old (born 1642 + 26 years old = 1668) when he occupied this important chair at Cambridge. Newton’s 1687 book known as the Principia (“Principles” in Latin) had the full title of The Mathematical Principles of Natural Philosophy. We shall briefly explore how Newton came to develop the ideas in this famous book. By the late 17th century, a large number of scientists believed that the Earth orbited the Sun, but early on in this century only a small minority held this view. With the widespread acceptance of Earth as one of the planets, it helped break down the conceptual barrier to applying terrestrial (earthly) physics to the heavens—to all the planets! In the 1680s there were a few ideas floating in the air, waiting to be organized, and developed. Newton seized the moment through his mathematical genius and accomplished an amazing synthesis of mathematical physics now known as Newtonian physics. Many scientists were interested in the possibility of developing a physics of planetary motion that would be consistent with the laws of physics known on Earth. This was in opposition to Aristotle’s physics in which there were two totally separate sets of natural laws: one set for the heavenly (superlunar) part of the universe, and the other set for the terrestrial (sublunar) part of the universe. In the 1680s Edmund Halley (after whom a famous comet was named), Christopher Wren, and Robert Hooke discussed one possible law for such a universal physics that Halley had suggested: Perhaps there is a force on each planet exerted by the Sun that varies inversely with square of the distance between any planet and the Sun. Such distance could be conceived of as a radius of a 207
roughly circular orbit—remember that the elliptical paths of planets are just barely elliptical; they are almost circular. One could express this rough guess of Halley as follows: F α 1/R2 “F” stands for “force”; the one thought to be exerted by the Sun on the planets “α” stands for “proportional to” (quantity on left changes in proportion to quantity on right) “R” stands for “radius” or distance from the Sun to a given planet (different for each planet) This rough idea proposed as a physical law came to be known in the 17th century as the “inverse square” law. The meaning of this phrase can be unpacked as follows: Inverse means “reversed in position or relation” (in this case, the “R” is on the bottom side of the division symbol; thus the larger “R” is, the smaller “F” is) Square means “something multiplied by itself” (in this case, the “R” has a small superscripted 2 by it to indicate that “R” is to be multiplied by itself; this further accentuates the inverse proportion already described) The consequence of having an “inverse square” proportion in Halley’s mathematical expression (F α 1/R2) can be explained in the following way. An “inverse” proportion indicates that as one number or variable increases the other number or variable decreases, and vice versa. So in the case of the formula above, the first quantity (force) increases in proportion as the other square of the other quantity (distance from Sun to planet) decreases. But also the reverse is true: the force decreases in proportion to the square of the increase of the Sun-to-planet distance. The idea was simple enough to discuss, but very difficult to prove mathematically in a way that would incorporate Kepler’s three laws, which, by this time, were widely accepted (despite Galileo’s rejection of them) among European scientists. Recall that Kepler’s three laws mathematically and physically described the motions of the planets. See illustration below in reference to all three laws, but realize that the drawing shows ellipses that have much greater eccentricities than are really the case:
Law 1: planets have elliptical orbits around Sun Law 2: planets change speed in such a way that a line from the Sun to a planet sweeps out equal areas in equal times
Law 3: T2/R3 is the same for every planet. “T” means the time it takes for a given planet to go around the Sun once, “R” means the “mean radius” or distance from a given planet to the Sun.
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Planet "b" Planet "a"
3 TT2/R /D 2
3
ratio is same for all planets Sun
Halley challenged his colleagues to find a way to deduce mathematically Kepler’s laws (laws operating within the domain of celestial physics) from an inverse square law (F α 1/R2). In other words, could one prove that planets would travel in elliptical paths (Kepler’s 1st law) if they were acted upon by a centrally operating inverse square force like that supposedly exerted by the Sun (F α 1/R2)? Could one also prove that these planets would speed up and slow down in the way that Kepler specified (in his 2nd law) if they were acted upon by such a centrally operating inverse square force? Finally, could one prove that the motion of all planets (assuming the truth of F α 1/R2) would be related to each other in the harmonic way that Kepler advocated (Kepler’s 3rd law)? There was much at stake on such a rough, simple expression as F α 1/R2. If one could do all of this, it would be grounds for accepting this inverse square law as a universal law of nature—a universal law of gravitation! Could it be done using some of the rules from terrestrial physics? Or was this an inappropriate mixing of apples and oranges (earthly and terrestrial physics) as Aristotelian physicists would interpret it? The account of how the human mind solved this problem is a complicated, yet fascinating story. We need to go across the English Channel to the Netherlands to continue our account. Here we will meet a Dutch scientist whose work provided an important additional foundation for Newton’s grand synthetic solution to the problem at hand. The Dutch scientist Christiaan Huygens (1629-1695) formulated an important law of terrestrial physics that describes circular motion observable here on Earth—such as a rock on the end of a string moving in a circular path. Try this experiment if you like: Take a heavy object and tie it to the end of string. Whirl it about your head and think about the motion of the object along the lines of these questions:
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Do you feel a force being exerted by your hand through the string that keeps the rock in circular motion? __________ How does changing the length of the string affect the force you feel (answer below)? o Shortening the string? ____________________ o Lengthening the string? ____________________ How does changing the speed of the object affect the force you feel (answer below)? o Decreasing the speed? ____________________ o Increasing the speed?____________________
Now let us analyze further Huygen’s physics in light of the above experiment: Huygens invented a formula that describes the force that keeps a rock moving in a circular path on the end of string: a force the prevents the rock from flying off tangentially in a straight line as is the case with a slingshot. Here it is: F α mV2/R
“F” stands for the force needed to keep the rock from flying off tangentially in a straight line “ ” stands for “proportional to” m = mass of rock (the amount of matter which you feel as its heaviness) V = velocity along the straight line tangent to the circular motion R = radius of circle (how long the string is)
If you consider the experiment suggested above, then Huygen’s law intuitively makes sense. If you use a larger rock or increase the rate of whirling, then you need a greater inward force to keep the rock pulled inwardly and to prevent it from flying off on a tangent. If the string were too weak, it would break and the rock will fly off in a straight line (in a tangent to the circle that previously described the rock’s motion). Imagine putting various values into the formula above and getting the kinds of results just described. If the string is short, it takes more inward force to cause the rock to continually turn such a sharp corner and stay in circular motion (as opposed to the natural tendency to fly off an a tangent). Huygen’s formula (F α mV2/R) originally described circular on Earth (not any circular motion of Earth as a whole, or of any other planet), but through a leap of the imagination Newton proved that it was relevant to the nearly circular (elliptical) motion of the Earth around the Sun as well as to the orbital motions of all other planets. We will provide one of the alternative ways to make this connection. This is not the way Newton used in his famous book, but his method involves very complicated mathematics. Think for a moment what would happen if the Earth were to magically stop revolving about the Sun (if gravity ceased to exist). If this were to occur, the Earth would fly off on a tangent in straight (linear) motion. Since the distance around a circle is equivalent to 2πR (2 times the value for “pi” times the radius of the circle), we can express the velocity of the circular motion of a rock on a string as:
V = distance/time = 2πR/T 210
We can then substitute 2πR/T for V in the formula of Huygens (F α mV2/R) in order to get:
F α m(2πR/T)2/R.
We can then convert the above expression to:
F α m4π2R/T2
If we drop out all of the constants (consider mass a constant for this; think of it as working with one particular object of a given fixed amount of mass) as is valid to do when working with a proportionality (as opposed to an equation) then we get:
F α R/T2
Recall that according to Kepler’s 3rd law T2/R3 is the same for every planet (T = period of a planet’s orbit about the Sun, R = mean radius of the planet’s orbit). So we can think of T2/R3 as a constant (and we will label it “K” in honor of Kepler)
T2/R3 = K
This can be manipulated mathematically (multiply each side of the equation by R3) to get:
T2 = KR3
Now we have to introduce a technically incorrect step. We will combine the formula for the force that a string exerts to keep a rock in circular motion (from Huygens) with a formula that describes the relationship between the period and radius for each of the planets (the justification for this will come later). That is, if we take the form of Huygen’s formula derived above:
F α R/T2
And if we substitute KR3 in place of the T2 part of the above equation (justified by the fact that T2 = KR3), then we get:
F α R/KR3
We can cancel out the R on the top of the division sign with one of the three R’s on the bottom side of the division sign to get:
F α 1/KR2
Furthermore, because we can validly drop out a constant (K in this case) in a proportionality, we can get:
F α 1/R2 211
So, we are left with a formula that says that the force acting centrally on an object moving in circular motion is proportional to one over the radius squared (R = radius, or distance of object from source of force). This is the very gravitational law formula that many other scientists suspected. Uniting Heaven and Earth under a Unified Physics So Halley, Hooke, Wren, and other scientists in the 1680s began to speculate about the relationship between the kind of terrestrial physics embodied in Huygen’s work and the kind of celestial physics represented by scientists such as Kepler (his three laws of planetary motion). All of this speculation was based on the assumption that the physical principles that govern an object tied to a string whirled in constant circular motion also apply to a planet moving in an elliptical orbit around the Sun. Let us examine the basis for this analogy between the motion of a rock in circular motion with the motion of a planet in elliptical motion: MOTION OF AN OBJECT HELD BY A STRING Circular path Uniform rate String attached to a rock; string has the role of transmitting a centrally acting forced Takes place on Earth, terrestrial physics, which could be different then celestial physics
MOTION OF A PLANET AROUND THE SUN Elliptical motion Planets speed up and slow down No strings attached or any other direct contact between the Sun and its planets Takes place in the celestial region, and was different than attractive powers on Earth (e.g., magnet)
How early modern scientists were able to take this analogy seriously: The elliptical motion of planets is almost circular Planets speed up and slow down, but not that much No strings attached to planets, but maybe a force acts at distance in place of strings Planetary motion takes place in the celestial region, but maybe terrestrial laws apply Maybe the laws of physics on Earth and the laws of physics in the heavens are identical The mathematical steps above are not really a mathematical proof, but only a suggestive line of reasoning that needed to be developed by someone with sufficient mathematical skills. Newton was the man, and he invented the Calculus for the occasion. Halley visited Newton and proposed the problem described above. Newton said something like, “Yes, I deduced an elliptical orbit from such an inverse-square force and it is buried in my notes from years ago.” (We do not have an actual record of this conversation). Three months later, in the same year of 1684, Halley received a mathematical derivation from Newton. In it Newton deduced Kepler’s 3 laws from F α 1/R2. This was the main idea that Newton presented in his famous book the Principia. This book constituted a truly new physics—a new universal physics that united the heavens and the Earth under one consistent set of natural laws (summarized mostly under the following 4 laws):
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THE FOUR MAIN POSTULATES (LAWS) OF THE PRINCIPIA: Law of Motion #1 Objects continue in same state of rest or uniform motion in a straight line unless acted upon by a force to change this state. Law of Motion #2 Change in motion is proportional to the force applied and exists in the direction of that force. Law of Motion #3 For every action there is an opposite and equal reaction. Law of Gravitation F α m1m2/R2 The four main postulates of Newton’s book were his three universal laws of motion and his universal law of gravitation. These four laws supplied the rationale for the unity of heaven and Earth under a single set of laws. The Aristotelian idea of separate natural laws for the sublunar and superlunar realms was destroyed forever. A long succession of scientists with a Christian worldview, beginning with John Philoponos in late antiquity, critiqued the Aristotelian dichotomy between the superlunar and sublunar regions of the universe, and Newton was quite familiar with this tradition. The basis of this Christian critique was the idea of God as the Creator and Ruler of the entire universe with a single set of consistent laws. For this reason Newton frequently referred to God as the Pantokrater, or Universal Ruler (see, for example, the “General Scholium” to the Principia). The physical cosmos in the heavens and the physical features on and around the Earth all were progressively understood within a Christian worldview as governed within a single framework of divinely ordained natural laws. Natural laws are not one thing on Mars and another on the Earth. Newton drew from this rich heritage of the Christian critique of Aristotle (a tradition that went through the Middle Ages up to the time of Newton) and brought this critical tradition to fruition with his laws that were understood to operate universally. Law #1: Objects continue in the same state of rest or uniform motion in a straight line unless acted upon by an outside force to change this state (principle of inertia) In other words, the principle of inertia states that bodies free of the effects of outside forces remain in the same state of motion or rest. Are there any bodies actually free of outside forces? No, but ideally you can think of this situation, and then this sets you up to look for subtle forces that explain why a body does not continue in motion in a line (gravity, friction of surface, air resistance, etc.). This idea is quite similar to Descartes’ notion of inertia (which we have not discussed in this course), but Newton added force as new entity in nature. Note that this law is totally opposite to Aristotle’s physics in which all motions required the constant contact between the mover and the thing moved (regardless of whether the mover was internal or external). Recall Aristotle’s two kinds of motion:
Natural motion: motion caused by an internal mover (the natural quality of heaviness or lightness based on the 4 elements of Aristotle). This kind of motion occurs only until the object gets to its natural place, claimed Aristotelian physicists.
Violent motion: motion caused by an external mover, but it occurs only as long as the object is constantly pushed along by something external to it.
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Law #2: Change in motion is proportional to the force applied and exists in the direction of that force:
F α mV
The key idea in law #2 is “change in motion,” because you don’t need force to keep motion going (see law #1), but only to change the state of that motion. This idea is built on Huygens work of considering speed of objects moving and colliding, rebounding, etc., with the direction of that speed taken into consideration (“velocity” is defined as “speed” with a particular direction of motion specified). Law #3: For every action (force) there is an opposite and equal reaction (force) This was the most novel of the three laws. When you get mad and pound your fist on a table, the table hits you back with an equal but opposite force. We will not go into this law beyond this very superficial example. Newton was able to deduce all three of Kepler’s laws from his three laws of motion and universal law of gravitation. He was able to deduce many other things proposed by earlier scientists as well. His book, in other words, “synthesized” much of the past work of physicists as well as completed the revolution against Aristotelian physics. Now we must introduce the 4th main physical law of Newton’s work: The law of universal gravitation.
F α m1m2/R2
This formula means that the gravitational force between two bodies is proportional to the product of the masses of those two bodies and inversely proportional to the square of the distance between the two bodies. This is similar to F α 1/R2 (inverse square law), but more specific. Two other components to the proportionality are specified, namely the mass of any two bodies in the universe. So can you can apply this law to any two bodies in the universe (e.g., Sun and Earth, Earth and Moon, Earth and apple, and so on). Intuitively Newton’s law of gravity makes sense:
m1m2 stands for the amount of mass of two bodies multiplied together. It is on top of equation, so the greater the masses, the greater the force between them.
R stands for the distance between the two bodies; so the greater the distance, the less the force between them.
Newtonian physics is based upon four postulates: his three laws of motion and his law of gravitation. Newton was able to deduce most of the previously know laws of celestial and terrestrial science with such convincing effectiveness that he became known as “the man who explained the universe.” We shall cover just one specific example of his ability to mathematically prove the work of earlier scientists.
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The universal gravitation law enable us to say that the weight of a stone (or apple, etc.) is proportional to the product of the mass, m, of the stone and the mass, M of the Earth and inversely proportional to the square of the distance between the centers of these two objects (stone and Earth). The distance between a stone near the surface of the Earth and the Earth can be considered to be simply the radius of the Earth itself because Newton was able to show that the location of an object for gravitational calculations is equivalent to the center of its mass (roughly the geometrical center of Earth and geometrical center of a spherical stone). Because the rock in our thought experiment is so near Earth’s surface, we will treat its distance from Earth as being equal to the radius of Earth. So, we can constructed the following formula to describe the force exerted on a rock by the Earth (causing its “weight”):
F α mM/R2 o F is the force of gravity o m is the mass of the stone o M is the mass of Earth o R is the radius of Earth
Examine the diagram on the next page as you follow the argument on this page (on the diagram the whole problem is described with equal signs rather than proportional signs in order to update it from the way Newton expressed it to the way we express it today). Because the force pulling down on the stone or apple is proportional to momentum or quantity of motion (mV), then we can also keep in mind the following formula:
F α mV
This is Newton’s 2nd law of motion in which force is proportional to mass times velocity. If we combine the two equations above, it follows that:
mV α mM/R2
After canceling out the “m” on each side of the formula, we get:
V α M/R2
Study Questions
Question: Do you see anything significant about this proportionality that describes the free fall motion of a rock toward the Earth? What does the velocity in free fall depend on? o Answer: The velocity of a rock falling to Earth ideally depends upon two constant values (M, the mass of Earth and R, the radius of Earth) that exist due to the brute face of the particular size and mass of the Earth itself. Thus the velocity with which a rock falls to Earth has nothing to do with the mass of the rock itself.
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Question: Does this mean that feathers and rocks drop at the same speed? o Answer: Yes, ideally, without air resistance and other more subtle factors.
Galileo had argued for roughly this conclusion a few generations earlier. This was in opposition to Aristotle who said that heavy things fall faster than light things. In the late 17th century this idea of all bodies falling at the same rate, regardless of their weight, was confirmed with the help of the newly invented air pump. Scientists removed most of the air in sealed glass containers and watched feathers fall like rocks within such containers. See diagram below.
Falling Apple Apple
Earth Law of Gravitation
R
F = G mM R
2
W=G
2nd Law of Motion
F=ma W=ma ma=G mM R
mM R2
2
Does the "a" depend on the mass of the falling body?
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a = G M2 R
The Reception and Significance of Newtonian Physics Newtonian style science became the paradigm (the example to follow) for mathematical physics and gradually, many other disciplines of science. Yet many scientists disagreed with certain aspects of Newtonian science and differently emphasized the various other aspects of Newton’s work. A new form of scientific understanding associated with Newton Newton was able to convince most early modern scientists that a mathematical expression that accurately describes physical phenomena could be considered a new way of understanding nature (even with no known material cause). The ability to predict future phenomena based on those mathematical laws helped confirm those new mathematical laws of nature. As explained with respect to “phenomenalism” in the introductory paragraphs above, Newton’s quantitative formulation of gravity could be used regardless of the actual cause or mechanism of that universal force. Physicists in the 19th-century just couldn’t stand Newton’s gravity working across empty space any longer, so they invented a mechanism to help explain the cause of gravitational force, something to fill up that empty space, the idea of a gravitational field. Conclusion Newton’s Principia was the finest expression of an early modern scientific method known as “The New Experimental Philosophy.” It had the following features:
Voluntarism: In contrast to the intellectualist (or rationalist) Cartesian and Leibnizian approach to physics, Newton represents the culmination of the voluntarist tradition. For the voluntarist, the order of nature is the result of divine will, not necessity. The natural order is contingent upon God’s choice, and could have been constituted otherwise.
Empiricism: The experimental method is essential to determine order freely established by the Almighty. Newton’s work in optics and chemistry also represent this emphasis on experimental inquiry.
Mathematical intelligibility: Mathematical postulates were used to explain physical phenomena in all realms of nature. The Christian emphasis on the intelligibility of creation is affirmed by the certainty of knowledge that mathematical demonstrations provide. Mathematical knowledge is not complete (for example, the law of gravity does not specify the cause of gravity), but it is sure.
Unity of natural laws throughout the universe. Deductions from those mathematical postulates are shown to correspond to observations of nature (this correspondence was demonstrated through experimentation, if possible)
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Phenomenalism: Knowledge can be obtained that is not exhaustive. Science need not always attain knowledge of causes. Sometimes a more modest aim of knowledge of regularities is all that is possible. (Open system of cause and effect; miracles and direct preternatural agency are not ruled out a priori.)
Review Questions
Question #1: How did Newton treat the traditional division of the universe into the celestial (superlunar) and terrestrial (sublunar) regions and how did he build upon the heliocentric theory? o Answer: He treated Earth as another planet and the physical laws of Earth were understood to apply everywhere in the universe.
Question #2: What can we say of Newton in relationship to various physical laws developed from time of Kepler and Galileo to Newton? o Answer: He synthesized them in the Principia, i.e. deduced almost all of them from his four main laws.
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Monday October 11 Lab 6: Copernican Show (Planetarium), New Astronomy (Rm 214). Pre-Lab Before Lab! Pre-Lab Complete the exercises on this page and the following page before coming to lab. If you have troubles with this Pre-Lab, we will help you during the lab (ask us). Keep these diagarams to study for the next exam. Do not turn them in. Explanations of Retrograde Motion: Ptolemy and Copernicus You should draw five lines (lines of sight) from earth, through the 5 numbered positions of the planet, extending out to the background of fixed stars. Number the 5 places where the line of sight intersects with the background of fixed stars in chronological order (it will show the back and forth of retrograde motion). Do this similarly for Copernicus explanation on the next page. Compare the two.
East
Background of f ixed stars 1 5
2
Planet at 1 position 1
4 3
Complete the other lines of sight to stars
West
Earth
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4
S
5
2
rs
1
Ma
3
rth
5
2
Ea
3
4
1
Use a ruler to draw straight lines through each set of numbers so that they extend out and touch the upper line which represents the background of fixed stars
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5
S
2
rs
1
Ma
4
3
2 rth
5
3
Ea
4
1
This is the answer key to the previous page All that is left to do is number the arrows at the top 1-5 to see retrograde
Did you complete the previous page by drawing lines like this? Also number 1-5 at the top of this page to see how it explains retrograde motion. You should have done this 1-5 numbering for both the Ptolemaic and Copernican explanations to see that they both explain the same phenomena. 221
New Astronomy Lab: Begin Work Here in Lab Purpose: To explore the basic geometrical figures of Keplerian astronomy Materials: 2 cardboard sheets, 3 paper sheets, 3 pins, ruler, string loop, calculator Lab Report: To get credit for this lab, transfer the appropriate answers to the lab report Objectives: 1. To draw closed-curve figures that are easily, quickly, and accurately reproducible 2. To understand the properties and definitions of closed-curve figures 3. To relate these experiences to Keplerian astronomy Guidelines: 1. Use 2 sheets of cardboard (one stacked on top of the other) as a stick board underneath the paper (draw on the paper, NOT the cardboard) 2. Use pins to secure the paper to the cardboard and also as means to help you draw 3. Do not cut or tie any other knots in the loop of string 4. Use the ruler only to measure, not to draw (we want “curved” not straight figures) 5. Keep pencil tip in constant contact with the paper to produce a continuously curving line 6. Do not touch or cross any previous part of a curved path with the pencil (except to finish a closed-curve figure; stop at the starting point to “close” the figure) Exercises: Complete each exercise before going on to the next. 1. As instructed in steps (a), (b), and (c) below, draw 3 closed-curve figures (not to turn in; please use both sides of each sheet of paper). For each figure stick one or more pins through the paper into the cardboard, then lay the loop of string on the paper around them. Place a pencil point within the loop of string and pull it taut, taking up all of the slack in the string. The taut string will guide pencil movement to make a closed curve. a. Draw a figure using one pin. What kind of figure results? b. Draw a figure using two pins. This kind of figure is called an ellipse. How does an ellipse differ from a circle? If your ellipse does not look different from the circle drawn in the previous step, make the distance between the two pins greater and draw it again. c. Draw a figure using three pins. Continue to change the orientation of the three pins and re-draw this figure, until it looks noticeably different from an ellipse or a circle. What does this figure resemble? 2. Then do this. a. Choose one of your non-circular figures from step #1 and label this figure “original.” On a piece of notebook paper, write instructions that you could read over the phone to a friend so that she could exactly reproduce your original closed-curve figure (assume she has the same materials you do, including your string loop). 222
b. Find another group that has completed step #2(a). Exchange instructions and loops of string so that each group may reproduce the drawing of the other without seeing the original figures (and with no verbal explanations yet). Race to see which group can complete the instructions of the other group first. Label these figures “reproduction.” c. After the race compare “reproduction” drawings with “originals” by holding them up to a light, superimposed on each other. Discuss why a given figure does or does not look like its “original.” Affirm and criticize the other group’s instructions and their attempt to reproduce your “original.” 3. Explanation: Select an ellipse that you have already drawn and put the 2 pins in their original positions (or draw a new ellipse and keep the pins in place). Put the pencil at any point on the ellipse with the string tautly stretched out between the pencil tip and the two pins. In the diagrams below, P1 and P2 are two different pencil points, and F1 and F2 are the two pins. Your pencil points can be anywhere on your ellipse.
P1
A
F1
A
F2
F1
F2
B
B
P2 3a)
Measure the length along the string from the pencil point (P1) to each pin. Length to Pin #1 (F1): ________ cm Length to Pin #2 (F2): ________ cm
3b)
Record the lengths for another pencil position (P2) on the curve. 223
Length to Pin #1 (F1): ________ cm Length to Pin #2 (F2): ________ cm 3c)
Compare the data above to identify an essential regularity of all ellipses: Sum of lengths in Step #3a: ________ cm Sum of lengths in Step #3b: ________ cm
3d)
Complete the definition of the ellipse: An ellipse is a regular closed-curve figure where the _______ of the distances from any point on the ellipse to the two “foci” is constant.
Further Explanation: The eccentricity of an ellipse is a measure of the distance between the two foci in relation to the overall size of the ellipse. The closer the two foci are together, the less “eccentric” an ellipse is. Distance between Foci (cm) ———————————— Length of Major Axis (cm)
=
Eccentricity
The Major Axis is a diameter line drawn lengthwise across an ellipse (line AB in the above figures). The Major Axis passes through both foci and extends to the two farthest points on opposite sides of the ellipse. •
Without changing the length of the loop of string, decrease the distance between the foci of your ellipse and draw it.
•
How does the ellipse’s appearance change? Is it more circular or less circular?
•
Measure the distance between the foci and the length of the major axis.
Calculate the eccentricity of this ellipse by plugging the two distances into the formula below (use your calculator to find the resulting eccentricity): cm ———————————— cm
=
•
Can we say that a circle is a special case of an ellipse, where the 2 foci coincide?
•
Without changing the length of the loop of string, increase the distance between the foci of your ellipse and draw it.
•
How does the ellipse’s appearance change? Is it more circular or less circular?
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•
Measure the distance between the foci and the length of the major axis.
•
Calculate the eccentricity of this ellipse: cm ———————————— cm
=
Conic Sections: Use Wood Model of Cone Compare the various ways of slicing a cone using the model cones on your desk (and as shown on the overhead). These slices, known as “conic sections,” have played a prominent role in the development of science since Apollonius of Perga, a third century B.C. geometer who analyzed them in On the Conic Sections, a work which Kepler translated. Conic Section Circle Ellipse Parabola Hyperbola
Applications in Science Astronomy from Plato to Copernicus Keplerian Astronomy Ancient Optics (e.g. burning mirrors) & Galileo’s Physics Modern Physics
We will explore various ways of slicing a cone using the wooden cone models provided. 1. Pull off the top block that forms the cone’s point and use it to trace a circle below (have the circle intersect the bold point below; your circle should also contain the text):
draw your • circle around this text
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2. Remove the block that was just below the “circle” block and use it to trace out an ellipse. Position the ellipse so that it contains the circle you traced and intersects the “bold point” on the left (this is for easy comparison). 3. Only two blocks remain attached to the main cone piece. Remove the darker of the two and lay the main cone piece on its side so that it rocks freely back and forth like a cradle, coming to a resting position. Three metal posts should now be sticking out on the top of this newly exposed flat surface of the main cone piece. This new flat surface is bounded by a curve called a parabola. Observe that this new surface and its parabolic edge are parallel to the table, and thus parallel to the outer surface of the cone (make sure everyone in your group agrees about this observation). 4. Pick up the small parabolic piece removed from the main cone in the previous step and use it to trace out a parabola that contains both the circle and ellipse drawn above (be careful not to draw just part of a circle; use the right curve on this piece). The parabola should touch the other two curved figures at the same “bold point” on the far left. Notice the family resemblance among the three figures, but also note that this parabolic curved figure is not “closed” in on itself as the first two are. 5. Remove the last light-colored hyperbola piece from the cone and stand it upright parallel to an upright-oriented main cone piece. This orientation allows you to see that the plane of the newly created conic section is parallel to what aspect of the main cone piece? (answer here ______________ ; this helps you fill in the blanks on page 74). 6. Use the hyperbola piece to trace a hyperbola that touches the above parabola at the same common point shared by all the figures (for easy comparison). Compare this curve with the others. Which other curve is it most like? _____________________. 7. Which type of “conic section” results from a slice from each of the following (fill in blanks below): a. Parallel to the base of the cone? _______________ b. Parallel to the outer surface of the cone (open figure)? _______________ c. Parallel to the axis of the cone (open figure)? _______________ d. Inclined to the base of the cone and to the surface of the cone, in between a circle and a parabola? _______________ Kepler’s First Law •
In class discussion, you will learn how Kepler proved that the orbits of planets are ellipses rather than circles.
•
When Kepler determined that the orbit of Mars could not be a circle, his next choice was to investigate whether it would fit an oval (egg-shaped) figure, which had a respectable intellectual lineage in Pythagorean-Neoplatonic and popular cosmological traditions. Only later did he establish that the orbit of Mars was elliptical, and neither circular nor oval. 226
•
If the orbit of Mars (which is the most elliptical of the outer planets that can be seen without a telescope) were drawn to the scale of our sheets of paper, it would resemble a circle, since its eccentricity is quite small (0.093 at present).
•
Rank the planetary orbits from the most circular (1) to the least circular (9) according to modern eccentricity values: Rank
Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto
Eccentricity 0.206 0.007 0.017 0.093 0.048 0.056 0.046 0.010 0.248
•
Which planet’s eccentricity most closely approximates the ellipse you drew for step 6a?
•
•By “breaking the circle,” i.e., departing from the ideal of uniform circular motions as the embodiment of perfection, Kepler’s ellipse-based astronomy was more radical a break with astronomical tradition than Copernicus’s heliocentrism (even Kepler’s contemporary Galileo maintained the circularity of heavenly motions, rejecting Kepler’s views).
•
In the late seventeenth century, Isaac Newton and Edmond Halley determined that the orbits of comets are ellipses rather than parabolas. Halley’s comet (which returns every 76 years) has an eccentricity of 0.969. Compare this value to the ellipse you drew in step 6b. Which is more elliptical?
To check out: •
Make any needed corrections to your Pre-Lab that the lab assistant may have identified
•
The lab assistant/instructor will look over your lab & lab report to check for problems
•
Obtain approval from the lab assistant/instructor to leave (initials on your lab report)
•
Clean up your tables and follow any specific instructions given (turn calculators off)
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New Astroromy: Lab Report • Name: _________________ Credit is possible only if lab assistant/instructor’s initials are here: Initials _______
F1
A
F2
B
P2 Complete the definition of an ellipse: An ellipse is a regular closed-curve figure where the ________ of the distances from any point on the ellipse to the two ________ is constant. Complete this definition and formula: The eccentricity of an ellipse is a measure of the distance between the two ____________ relation to the overall size of the ellipse. The closer the two foci are together, the less/more (circle one) “eccentric” an ellipse is. Distance between ________ (cm) ___________________________ Length of the ______________ (cm)
=
Eccentricity
Answer yes or no; fill in the blanks; circle right answers: Without changing the length of the loop of string, decrease the distance between the foci of your ellipse and draw it. •
How does the ellipse’s appearance change? More circular or less circular?
•
Can we say that a circle is a special case of an ellipse, where the 2 foci coincide? Conic Section Circle Ellipse Parabola Hyperbola
Applications in Science Astronomy from Plato to __________ Keplerian Astronomy Ancient Optics (e.g. burning mirrors) & __________ Physics _________ Physics
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Privileged Planet, Ch. 11: The Revisionist History of the Copernican Revolution Here are the four most influential modern myths about the history of science that continue to distort our understanding of science and it relationship to Christianity: 1. 2. 3. 4.
Ideas of Earth’s Shape: Mythical Legacy of Columbus. (Flat Earth Lab in US 311) Changing Ideas of Earth’s Significance: Mythical Legacy of Copernicus. (This chapter) Galileo Affair: Catholic Oppression of Science? (This chapter touches on this a little) Methodological Naturalism: Guiding Light of Science? (Last part of US 311, US 312)
History Distorted: Study Questions 1.
The so-called Copernican Principle and the history of cosmological discovery since Copernicus is often used to support a human (and Earth) insignificance thesis. Explain how the label “Copernican Principle” is a modernist myth, rather than a scholarly interpretation of the history of science.
2.
Describe how the official story about the transition from ancient to Copernican cosmology is largely wrong. The story tells about a transition from an allegedly human-centered view of the cosmos to a view in which humans have no special significance.
3.
How does the alleged “war between science and religion” fit into #2?
4.
Science becomes merely applied naturalism when it follows the influential “rule” that it is only legitimate to explain nature in terms of unintelligent natural causes. Explain how this fits into the present story.
5.
Was the center of the universe considered a place of honor in ancient Greek and Latin medieval science? Explain.
6.
“Earth in pre-Copernican cosmology was the bottom of the universe rather than its center.” Explain.
7.
How have “protesting historians of science” corrected the mythical story about the so-called “Copernican Principle”?
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8.
Neither Aristotle nor Ptolemy thought that Earth was a large part of the universe. Explain.
9.
When Christian theology was added to the mix in the Middle Ages, the center (bottom) of the universe became “hell”. Explain.
The Mythological War between Science and Religion Even secular historians of science agree that a simplistic warfare metaphor between science and religion distorts the history of science and religion. We are reminded of the positive impact of Christianity on science in this section : “Balancing the view that God is free [and that his creation is contingent; his free choice] is the belief that he is good and rational rather than fickle, irrational, or even malicious, as was so often the case in the stories of pagan gods. Because of this, Jews and Christians could expect nature to be orderly and even ____________ in its structure and behavior. Nature as a whole is contingent, but in its regular operations it is not _____________ or perversely deceptive. The origin of modern science required this careful __________ of contingency and order, and science only emerged in a culture that held these beliefs in careful balance.” Christian Theology and Ancient Cosmology The Condemnations of 1277 denounced orthodox (or “radical”) Aristotelianism because such views restricted God’s freedom in creating the world. Aristotle viewed the cosmos as eternal, while the Christian saw it as the free creation of God who spoke it into being. This freed science from some of Aristotle’s harmful influence. Organic-Naturalistic View of Aristotle vs. A Christian Mechanistic View: Everything in the Aristotelian universe was “purposeful” in the sense that it was directed toward some end or goal (this was a naturalistic form teleology or intelligent design as opposed to a Christian one in which nature does not have within itself its own purposes). By the time of Boyle in the 17th century a Christian reaction to Aristotle’s organic and naturalistic teleology had been well formulated (see the Shapin text on the scientific revolution). Nature was seen more as an intricate and interlocking machine (mechanical, not organic metaphor), an artifact of intelligence rather than an organism whose individual parts themselves tended toward some internally motivated end. Study Question: Can a scientist determine whether the source of intelligent design is immanent or transcendent? If so, how? If not, why not? Highlights from the Copernican Revolution to Today Copernicus: 16th Century Copernicus had no intention of “_______________” man’s status. The Neo-Platonic strain of Renaissance humanism motivated his search for mathematical simplicity and “harmony” in nature. His was a Christian Neo-Platonism in which the material world itself, as the creation of 232
an omnipotent God, could reflect the precision of mathematics, something unthinkable to the strict Neo-Platonist. This Neo-Platonism, tempered by Christian theism, was an important guiding influence, then, for Copernicus and for other Renaissance scientists who followed him, including Galileo and Kepler. Kepler: 17th Century A deeply religious Lutheran, Kepler internalized the logic that Copernicus had only partially embraced. He had a mystical attraction to harmonic regularities that inspired him to search for mathematically simple laws of celestial motion. At the same time, his commitment to realism and his access to reliable data (from Brahe) eventually led Kepler to propose elliptical planetary orbits that vary in speed, both ideas unthinkable to the strict Aristotelian. Galileo: 17th Century Galileo Galilei’s telescopic observations and clever arguments enhanced the plausibility of the new cosmology. He argued, for example, that Earth “is not the sump where the universe’s _________ and ephemera collect.” Earth is exalted from the ancient trash heap of the cosmos to the heavens. Galileo’s forced recantation of his views before the Inquisition in 1633 is profoundly misunderstood. How?
17th and early 18th Century: For Newton, natural laws were God’s ordinary or regular ways of acting in the world. Miracles were God’s extraordinary or irregular ways of doing so. Explain.
18th Century Enlightenment (So-Called Age of Reason)”: In this period, what happened to the concept of nature’s Lawgiver, and with it Newton’s concept of natural law?
Enlightenment intellectuals made “man the measure of all things” (this is when “humanism” begins to acquire a more modern and anti-Christian meaning). In so doing, they exalted man far more than Medieval Christianity ever did. The paradox is this: they claimed humans have no objective purpose from a creator and then turned around and claimed themselves capable of creating their own meaning. 19th & 20th Centuries: Darwin’s theory of evolution, and the mysterious disclosures of the quantum world in the 20th century led some to reintroduce chance as a scientific explanation (as a companion to natural law which had been increasingly since the 18th century viewed as totally determining every aspect of reality). 21st Century: There are hints that design may also have a role to play in science. 233
Location and Significance Dennis Danielson summarized the historical distortion this way: “The great Copernican cliché is premised upon an uncritical equation of geocentrism with anthropocentrism.” Explain. Is the idea of nature pointing to a purposeful designer exclusively Judeo-Christian or Islamic? (Hint: Recall the words of the stoic philosopher Cicero in the Danielson selection you read. Which is more anthropocentric—Christianity or stoic philosophy).
Why is the term “Copernican Principle” historically inaccurate to describe the cosmological arguments for Earth’s insignificance (as well as the philosophical view that the universe has no purpose)? According to the Privileged Planet book, the common meaning of the term “Copernican Principle” commits which kind(s) of error: historical, scientific, or both? (circle correct answer) According to the Privileged Planet book, the common meaning of the term “Principle of Mediocrity” commits which kind(s) of error: historical, scientific, or both? (circle correct) Note: The term “Principle of Mediocrity” occurs in the last sentence of this chapter. This term has been used to refer to the cosmological arguments for Earth’s insignificance (as well as the philosophical view that the universe has no purpose). Most scientists have held this view since the Enlightenment.
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Danielson: Galileo, Campanella: Pages 145-154, 173-177 24. Neither known nor observed by anyone before: Galileo Galilei An ambitious professor inaugurates the age of the telescope by telling how he discovered the true face of the Moon, the moons of Jupiter, and the secrets of the Milky Way. 1.
Galileo’s telescope revealed the existence of about ten times as many _______ _______ as had ever been known before (p. 146a).
2.
Earth’s “semidiameter” is an archaic way of saying Earth’s radius (p. 146a). Because Galileo had a 30X telescope (magnifies objects to make them appear 30 times closer than they actually are), the Moon’s actual distance of 60 earth radius lengths (semidiameters) appeared to be reduced to a mere ___ Earth radius lengths away from Galileo’s telescope. If Earth is modeled as a 12-inch globe, then how many feet away should the Moon be held to model its actual distance from Earth? ____
3.
What was so jolting to the Aristotelian viewpoint about discovering the rough surface features of the Moon (p. 147b-149a)?
4.
Where did Galileo see “Earthshine” (p. 149-150)? What is this? Go out and see it yourself!
5.
If Earth reflects sunlight as do other planets, then how might this encourage one to include Earth in the category of “planet” (p. 150)? Is this proof, or just suggestive?
6.
If Earth is a planet then it is included within what Galileo calls the “dance of the stars” (p. 150). Why would it be a promotion rather than a demotion for Earth to be re-categorized from “center of the universe” to a “planet” (given premodern standards of cosmic importance)? What does Galileo mean by the “sump where the universe’s filth and ephemera collect”?
Page 151 describes how stars look differently through a telescope. Page 152a dramatically unveils the true nature of the Milky Way. Note that the term “galaxy” at this time does not entail the idea that there are many galaxies. Rather, it refers to a prominent collection of stars within our universe, the only one known of its kind at this time. However, the small “nebulous” patches 235
in the sky can sometimes be resolved into some distinct stars as Galileo notes here. Much later astronomers identified many of these nebulae as distinct galaxies. 7.
Step through the observations and reasoning that led Galileo to conclude that he had indeed discovered 4 moons of Jupiter (p. 152b-153). Why does Galileo call the 4 moons of Jupiter “planets” or “stars” (we have since discovered more than 4 moons)?
The two books of God agree with each other: Tommaso Campanella A Catholic theologian mounts a spirited defense not only of Galileo but also of the kind of science he represents. 1.
Campanella refers to “those potbellied theologians” (alluding to potbellied pigs, p. 174). Does he refer to all, most, or some Christian theologians (and how do you know which he means)? What were these theologians doing?
2.
Danielson briefly quotes Galileo’s letter to the Grand Duchess Christina of the Medici family to introduce the metaphor of God’s two books (p. 174b-175a). Why did Christian scholars in science and theology use this metaphor so often in early modern times? To what final end was this metaphor being put to use?
3.
How does Campanella provide a Christian justification for the practice of science or any academic endeavor (p. 175-176)? Do you perceive a balance between intellectual confidence and humility?
4.
Notice how theologians like Campanella recognized the wisdom of Christian leaders not forming an unalterable alliance with whatever happens to be the majority scientific viewpoint at any given time —whether it be the teachings of Aristotle, Ptolemy, or, we might add with hindsight today, Darwin (p. 176b-177).
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Wednesday October 13 Chaisson, Ch. 2: Light and Matter Read the entire chapter and use all of the study helps provided by Chaisson.
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Monday October 18 (no lab this week) Chaisson, Ch. 4: The Solar System Begin be reading “Introduction to Part Two: Our Planetary System” (p. 96-97) Then read the entire chapter 4 and use all of the study helps provided by Chaisson.
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Wednesday October 20 Chaisson, Ch. 5: Earth and its Moon Read the entire chapter and use all of the study helps provided by Chaisson.
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Monday October 25 Lab 7: Distances of Celestial Objects To get credit for this lab, transfer the appropriate answers to the lab report Set of Materials for Each Lab Group Meter stick Tape measure Paper Coffee stirrer Poles at lab stations
Ruler, marked in centimeters Set of paper triangles (described below) Calculator Lump of play-dough
Items for the Whole Class • Tape on the floor near the middle of the wooden cabinets (on the south side) • Vertical lines chart on north blackboard directly opposite the tape line • Recycle paper box on the on the instructor’s table at the front Purpose This lab provides experience in indirect measurement and the use of geometrical inferences in astronomy. Students become familiar with similar triangles and their various relations. Background A major contribution of Greek astronomers such as Aristarchos and Eratosthenes was to develop geometrical methods for measuring sizes and distances of celestial objects. We will discover that by these methods they determined that the universe is quite large.
Part I: Properties of Similar Triangles Sizes and distances of celestial objects cannot be measured directly, as we might do by direct surveying from a spaceship. Indirect measuring techniques rely on the idea of similar triangles, which can be used to estimate the relative distances of the Sun and the Moon, the size of the Earth, or the height of a pyramid. We explore the properties of similar triangles by using a set of fifteen paper triangles. Confirm that you have a complete set of triangles with the characteristics given in the following table. Color triangle Red Yellow Blue White97 Green
Small angle 30° 45° 30° 37° 60°
Medium angle 60° 45° 45° 53° 60°
Large angle 90° 90° 105° 90° 60°
97 The sides of the white triangles are in the proportion of 3, 4, and 5.
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1. Examine your paper triangles. •
Do all three triangles of the same color have equal corresponding angles?
•
If triangles of the same color are similar, how many corresponding angles are equal? ___1; ___ 2; ___ 3
•
Flip one triangle over; how does this affect recognition of “similarity”?
•
Are all triangles that contain a right angle similar?
•
What is the minimum number of angles in each that you have to measure to assure yourself that two triangles are similar? Why?
•
What is the minimum number of angles in each that you have to measure to assure yourself that two right triangles are similar? Why?
•
Define similar triangles based on the above activities and questions (complete this one sentence): Two triangles are similar when ______________________________
2. Measure the lengths of sides of your triangles and record the measurements in the data table below (use metric in all of this lab; Only record the first decimal place rounded to the nearest unit, e.g. 2.5 rather than 2.456). “Long” means “relatively long” (or equal if two sides are of equal length). Lengths of Sides: DATA TABLE #1 Color triangle Red Red Red Yellow Yellow Yellow Blue Blue Blue White White White Green Green Green
Size triangle Short Side Small Medium Large Small Medium Large Small Medium Large Small Medium Large Small Medium Large 241
Long Side
3. Refer to your measurements in the data table above to calculate (using a calculator) the ratios between the long and short sides of each triangle. Record your calculations in the table below. Only record the first decimal place rounded to the nearest unit, e.g. 2.5 rather than 2.456. Read the paragraphs below before doing this. Imagine two similar triangles like those shown below. The smaller triangle has sides named a, b, and c. The larger triangle’s corresponding sides are A, B, and C. They are corresponding sides because a & A are the bases of each triangle, and c/C and b/B are the longer sides.
c
B
b
C
A
a
Suppose side a of the smaller triangle = 1 cm and side b = 2 cm. The ratio of the long side to the short side = b /a = 2 /1 = 2.0 (no units; the cm cancel out). Similarly, we could write the ratio of the long to short sides of the larger triangle as B /A . Calculate the ratios of long to short sides for the triangles indicated below, using the measurements recorded in the data table above. Ratios of Side Lengths Color triangle Size triangle Long ÷ Short Red Small Red Medium Red Large Yellow Small Yellow Medium Yellow Large Blue Small Blue Medium Blue Large White Small White Medium White Large Green Small Green Medium Green Large 242
Analysis: Is the ratio of the long side to the short side of one triangle the same for any similar triangle? Sample Calculation.
c
B
b
C
A
a
Refer again to the similar triangles shown above. If side a of the smaller triangle = 1 cm and side b = 2 cm, then the ratio of the long side to the short side = b /a = 2/1 = 2.0. Similarly, if side A of the larger triangle = 3 cm and side B = 6 cm then the ratio of the long side to the short side = B /A = 6 /3 = 2.0. In this case, the ratio between any two sides of one triangle is the same as the ratio between the two corresponding sides of any similar triangle. Because the ratios between sides of similar triangles are equal, the following proportion can be set up: b /a = B /A This type of proportion is easily solved if three out of the four lengths are known. Suppose that b = 2 cm, a = 1 cm, A = 3 cm, and B is unknown. Substituting into the equation above we obtain: 2/1 = B /3 Solve this equation by cross-multiplying: 2*3=1*B This calculation results in B = 6 cm, so B did not have to be measured directly to be determined, if the other three values were known. Practice: Solve the following proportion for x (show your work): 14 /5 = x /25 x = _______
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Refer to your measurements in data table #1 to calculate the ratios between the long sides of corresponding triangles and the short sides of two corresponding (similar) triangles. Record your calculations in the table below. Ratios of Side Lengths Color triangle Size triangle Short ÷ Short Long ÷ Long Red Small triangleLarge triangle Yellow Small triangleLarge triangle Blue Small triangleLarge triangle White Small triangleLarge triangle Green Small triangleLarge triangle Analysis: Is the ratio of the long side of one triangle to the long side of any similar triangle equal to the ratio of the two corresponding short sides? Sample Calculation. Study the two similar triangles below, abp and ABP.
A, a p
P
b
B Suppose that the line ab = 10 cm and the line AB = 24 cm. This is a ratio of corresponding bases. Suppose further that a-p is measured as 14 cm, and that AP is unknown and for some reason cannot be measured directly. Remember that if three of four variables in a proportion are known, the fourth can be calculated. By setting up a proportion of corresponding sides we can calculate the length of AP: ap /AP = ab /AB Substituting: 244
14 /AP = 10 /24 Cross-multiplying and solving: 10 * AP = 14 * 24 AP = 14 * 24 ÷ 10 AP = 33.6 cm Show your results and explain your procedure to the lab assistant/instructor to get approval to move on to the next part of the lab.
Part II: Similar Triangles in Space A. Using your Thumb as the Rule: Estimating Distance through Parallax Shift The classic “rule of thumb” involves similar triangles in space. 1. Find the masking tape on the floor near the wooden cabinets on the south side of the room. Stand with your toes just behind the tape and hold your left thumb erect, exactly in front of your left eye at arm’s length, viewing it with the left eye only (cover or close the right eye), against a background of vertical lines. Put a piece of masking tape on the floor to indicate where you stood. 2. Now view your thumb with the right eye only (cover or close the left eye). Does your thumb appear to shift its position? __ yes; __ no. This effect is called parallax shift. 3. Your left thumb is the vertex of two similar triangles in space. The small triangle goes from one eye to the other eye to your left thumb. The large triangle has its vertex at your thumb and its base is the distance between the two apparent positions of your thumb against the wall. Label the following points on the sketch below, showing their orientation in space relative to one another as seen from above: eye, eye, thumb, first thumb position on the wall, second thumb position on the wall.
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blackboard
left eye thumb
first line of sight to blackboard
right eye
4. Measure the side that represents the thumb to left eye distance and the shortest side (eye to eye = base; measure from pupil to pupil) of the small triangle, calculate their ratio, and record this information in the table below. 5. Measure the distance on the background wall by which the thumb appeared to shift (use the centimeter grid posted up on the blackboard). 6. Calculate the next-to-longest side of the large triangle (the shortest distance to the wall, i.e., from thumb to wall) given the information in the table below. Do not measure directly with a tape measure at this time. Show your calculations below the table. It is best to mark the location of your foot with a piece of tape so you will be able to go back later (not now) and directly measure the thumb to wall distance. # 4 4 5
Measurements Base (short side) of small triangle (eye-eye) Longer side of small triangle (left eye-thumb) Base of large triangle (apparent thumb-shift)
4 6
Calculations Longer side to short side ratio for small triangle Distance of thumb to wall (side of large triangle)
Data cm cm cm
cm
7. a. Check your calculation of the distance to the wall by measuring it directly. (some measuring tapes don’t start at zero mark; hold the tape with this in mind) 246
b. Then calculate your percent error: % error = [(Directly-measured – Calculated) ÷ (Directly-measured)] * 100 % error = [(#7a – #6) ÷ (#7a)] * 100 If it comes out negative, just ignore the negative sign and make it positive. # 7a
Measurements Distance to wall (side of large triangle)
7b
Calculation Percent Error
Data cm
%
Obtain lab assistant/instructor’s approval before going on. B. Baseline Method: Calculate Distance to Lab Station Poles from Table Edge Use corresponding sides of similar triangles in space to indirectly calculate the distance to the poles across from your lab station. The similar triangles in this method are not oriented in the same way as in the “Rule of Thumb” method above. Inspect the diagram below and then follow the instructions below it. Pole on next Table
coffee stirrer on exact corner of paper
Lab Table
Paper Meter Set-up
of
Stick First
Position
1. Position a piece of paper so that the long side is toward you, flush (even) against the front edge of the table. The left (short) side should be aligned so that it points toward the Pole set up in front of your lab station. 2. Set the coffee stirrer to stand vertically on the top left corner (exactly) by supporting it with play dough. 3. Lay a meter stick on top of the paper, exactly along the same near edge of the table. This meter stick must remain unmoved hereafter. (Don’t mark on the tables.) 247
4. Paper should be at one end of meter stick. Inspect the diagram below and then follow the instructions below it.
A
Lab Table
a
Corresponding Sides of two right Triangles: A and a (triangles not shown)
5. Construct two right triangles, one large and one small, as follows. The large triangle will be imagined (not drawn) on the lab table, and the small triangle will be drawn on the sheet of paper. Let the left side of the small triangle, or side a, be the left side of the sheet of paper. Let the left side of the large triangle (side A) be the line coinciding with side a of the small triangle, extending to the Pole at your the lab station. Use the meter stick (not shown on the diagram above) to keep track of where these lines intersect the front of the table, since the meter stick should not be moved when you slide the paper sideways in the next step. Inspect the diagram below and then follow the instructions below it. P
A
Read off meter stick here to get length of side B
C
i i a
Lab Table
c b
i
B
meter stick reads "0" here
Meter Stick
Corresponding Sides of two right Triangles: A-a and B-b and C-c
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6. Without moving the meter stick, slide the sheet of paper almost a full meter to the right, keeping the front edge of the paper flush with the front edge of the lab table. Get out of your chair and get down low so your eyes are level with the tabletop. Hold a pencil below the table, with its point extending up over the table edge, to use as a sight (its position is labeled “i” in the drawing). Move the pencil until its lead point lines up with the coffee stirrer (labeled “ii”) and the lab table Pole (“P”). When the pencil is aligned, mark a dot at this point on the edge of the paper that is along the edge of the desk. a. Using the meter stick, record the length of the base of the large table triangle (side B), which runs from the end of the meter stick to the point where the pencil, coffee stirrer, and pole line up. b. Measure and record the length of the base of the small paper triangle (side b). c. Draw the hypotenuse or side c of the small paper triangle. d. Measure and record the length of side a of the small paper triangle. e. Calculate the ratio of the side to the base of the small triangle (a /b). f. Do not directly measure side A or side C of the large triangle because they represent huge distances in space (you will calculate the length of “A” indirectly). Will the ratio of the side to the base of the large triangle (a /b) be the same as for the small triangle (a /b)? g. Calculate the distance from the front edge of the lab table to the Pole (i.e., calculate the length of side A), using the measured base of the large triangle (side B) and the calculated ratio of side to base for the similar smaller triangle. Show your calculation beside the table below, and record the result in the table. # 6a 6b 6d
Measurements Base of large table triangle (side B) Base of small paper triangle (side b) Side of small paper triangle (side a)
6e 6g
Calculations Side to Base ratio for small triangle Distance to Pole (side A of large triangle)
Data cm cm cm
cm
7. a. Check your calculation of distance to Pole (side A) by measuring it directly. b. Then calculate your percent error: % error = [(Directly-measured – Calculated) ÷ (Directly-measured)] * 100 % error = [(#7a – #6g) ÷ (#7a)] * 100 If it comes out negative, just ignore the negative sign and make it positive. 249
# 7a
Measurement Distance to Pole (side A of large triangle)
7b
Calculation Percent Error
Datum cm
%
If your measured distance and indirectly calculated distance do not agree, suggest some possible sources of experimental error that would explain their discrepancy: Experimental Error Sources: Analysis 1. How are the similar triangles used in the “rule-of-thumb” method, and the similar triangles used in the “baseline” method, oriented differently in space (answer this below under the two sub-questions below)? •
Which method uses similar triangles, one of which contains the other?
•
Which method uses similar triangles that face one another, neither containing the other, but overlapping in one point?
2. What effect on the accuracy of the result with the “baseline” method might be obtained with increasing or decreasing the baseline? Explain. 3. Which method would be best suited to measuring the distance across a river? Would it be possible to use the other method also? Why or why not? 4. Which method would be best suited to measuring the distance of a star from the Earth? Would it be possible to use the other method also? Why or why not? To check out: The lab assistant/instructor will look over your lab & lab report to check for problems. Obtain approval from the lab assistant/instructor to leave (initials on your lab report). Clean up your tables and follow any specific instructions given, including: 1. put paper that is used on both sides in the recycling box on the front table 2. stack the rest of your paper in a neat pile with unused sides up 4. put play doh back in small plastic bags so it won’t dry out and turn calculators off 250
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Distances in Space: Lab Report • Name: _________________ Credit is possible only if lab assistant/instructor’s initials are here: Initials _______ Part II: Similar Triangles in Space A. Using your Thumb as the Rule: Estimating Distance through Parallax Shift # 4 4 5
Measurements Base (short side) of small triangle (eye - eye) Long side of small triangle (left eye - thumb) Base of large triangle (apparent thumb-shift)
Data cm cm cm
4 6
Calculations Long side to short side ratio for small triangle Distance to wall (side of large triangle)
cm
# 7a
Measurements Distance to wall (side of large triangle)
7b
Calculation Percent Error
Data cm
%
B. Baseline Method: Estimating Distance to Lab Station Poles # 6a 6b 6d
Measurements Base of large table triangle (side B) Base of small paper triangle (side b) Side of small paper triangle (side a)
Data cm cm cm
6e 6g
Calculations Side to Base ratio for small triangle Distance to Pole (side A of large triangle)
cm
# 7a
Measurement Distance to Pole (side A of large triangle)
Data cm
7b
Calculation Percent Error
%
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Chaisson, Ch. 6: The Terrestrial Planets Read the entire chapter and use all of the study helps provided by Chaisson.
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Wednesday October 27 Privileged Planet: Chemistry, Blue Dot, p. 32-40a, 81-101 Pages 32-40a: The Chemistry of Life (part of chapter 2) Life as Analyzed by Astrobiologists Astrobiologists generally think that extraterrestrial life, if it exists, will resemble _____________ life. Why? Because life’s chemical prerequisites are very specific and so it is rare to get everything chemically “just right” for life. We will read the part of chapter 2 that addresses this. Three kinds of life considered by astrobiologists in their study of life in the universe Simple: Mostly single celled organisms Complex: fairly large, ______________-breathing, and multicellular Technological: Complex life that is intelligent enough to make knives, radios & rockets Life’s Chemical Prerequisites The scientifically disciplined imagination says: “If you want life, here are the chemical prerequisites.” Study below the most important prerequisites, namely carbon and water. 1) CARBON: Information-carrying molecules that are carbon-based are required for life a) Life in our universe requires DNA-like molecules for storing information b) The information-carrying molecule must be durable, but open to diverse __________ c) Carbon is far better than any alternative element for these and other life requirements d) ______________ (alternative element found in science fiction literature) falls far short 2) WATER: A solvent and habitat component that is very much like water is required for life a) Need liquid solvent to provide a medium in which chemical _______________ can occur b) Water has many characteristics that make it an ideal medium both for life’s chemical reactions and habitat (p. 33-34) i) Water is virtually unique in being denser as a ______________ than as a solid ii) So, ice _________ on water, insulating the water underneath from further loss of heat iii) This prevents lakes and oceans from freezing from the ___________ up (bad for life) iv) Water helps moderate Earth’s climate and helps organisms moderate body _________ c) Water appears to be an ideal match to __________-based chemistry because organic carbon-based reactions are optimal over the same range of temperatures that water is liquid at the Earth’s __________ (bottom of p. 35) After considering alternatives to carbon and water, planetary scientist John Lewis concluded: Despite our best efforts to step aside from terrestrial ______________ and to seek out other solvents and structural chemistries for life, we are forced to conclude that ________ 255
is the best of all possible solvents, and ______________ compounds are apparently the best of all possible carriers of complex information. (middle p. 35)
3) “Chicken and egg problem”: which came first habitable planet or simple life? (p. 36) a) Even simple life requires habitable planet b) Habitable planet requires existence of at least simple organisms that are part of a feedback loop that keeps a planet’s climate stable i) Organisms, atmosphere, oceans, and solid interior all exchange carbon dioxide, oxygen, water, and other elements and compounds to keep planet’s climate stable ii) James Lovelock argues this system of organisms and Earth’s physical environment functions almost like a super-organism, as if we are part of a larger “Earth system” that is alive. One need not embrace the new age philosophy that often goes with this “Mother Earth” concept known as the “Gaia Hypothesis.” 4) Conclusion about carbon and water a) Carbon and water appear to be prerequisites for two things about life i) Chemical makeup of life ii) Environmental context of life (as part of a planet’s climate-stabilization system) b) Thus, planets or moons without enough carbon and water are probably lifeless on these grounds alone. We shall examine other things as well that have to be “just right” in order for life to be possible. 5) Carbon & water are necessary, but not sufficient for life support. Other items needed include: a) Stable energy sources to maintain liquid water and to support food production i) Host star ii) Planet’s interior heat iii) Energy stored in chemicals that is released through chemical reactions b) Simple life is prerequisite for complex life (p. 37) i) Simple life forms (especially through photosynthesis) produce food needed for survival of complex life ii) The chance of having everything “just right” for complex life is thus much lower than for simple life Life in the Extreme: A Study of Extreme Environments 1) What are extremophiles and why have they been of great interest to astrobiologists? 2) Why is it unlikely that we will find extremophiles in isolated extraterrestrial settings (despite earlier enthusiasm among astrobiologists)? 3) How is your answer to the previous question a blow to the Rare Earth Hypothesis that says complex life is rare, while simple (especially extremophilic) life is common? 256
4) While extremophiles can tolerate extremes in temperature, salinity, moisture, and pH, as a rule, they do not tolerate a very broad range of environmental conditions. In fact, they are somewhat challenging to maintain in the _____________________ (artificially controlled environment). If it’s difficult keeping extremophiles alive in labs, how does this fact challenge the view that simple life is common throughout the universe (p. 39)? 5) Why should we be unsurprised if we find simple life elsewhere in the Solar System? Answer: Astrobiologists now generally recognize that the terrestrial planetary bodies have long been exchanging ___________, especially in the ________ history of the Solar System. Even today relatively intact pieces of Mars and the Moon are collected as ________________ on the Earth. Similarly, the Earth probably has contaminated all the other planetary bodies in the inner Solar System with its ____________. (p. 39b)
Pages 81-101: The Pale Blue Dot in Relief (chapter 5) Thesis: We can see that Earth is special (unusual) by studying other planets, moons, etc. 1) Carl Sagan called Earth “the pale blue dot.” He considered it ordinary and not special. 2) But recent evidence allows us to see Earth “in relief” (in comparison to other places) much more accurately than ever before 3) Habitability and measurability are many times better on Earth than any place we know a) Habitability: suitable for hosting life (or not) b) Measurability: suitable as platforms from which to make scientific discoveries (or not) Other objects to evaluate in comparison to Earth (p. 82) 1) Planets (three kinds, listed in their order out from the Sun) a) Terrestrial: Mercury, Venus, Earth, Mars b) Gas giants: Jupiter, Saturn, Uranus, Neptune c) Pluto: more like a comet (rock and ice; orbit not in plane of solar system) 2) Satellites of planets (moons) 3) Asteroids 4) Comets Mars: Our Most Earth-like Neighbor 1) Not fine-tuned for habitability: Lacks sufficient liquid water 2) Not fine-tuned for measurability
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a) Very poor ice core data on Mars. The ice we speak of is only laid down on the northern polar cap. Because Mars probably lacks any significant ice core data of the quality needed for historical geology, the possibility of making historically diagnostic scientific measurements is greatly reduced. The reasons for the poor condition of ice core data on Mars that are listed below are also each strongly correlated to specific causes that make Mars unsuitable for life. This is evidence for the correlation between habitability and measurability. Reasons for poor ice core data on Mars (these same reasons render life difficult) i) Low precipitation ii) Dust storms caused by low precipitation. Dust storms even further erase any modest ice data accumulation because the dust reduces the ice’s albedo (the amount of sunlight a surface reflects back into space), causing it to warm (and melt) more than pure ice. Could you live (or do science) in a mega “dust bowl” like shown on Plate 10 (a few pages before p. 239)? iii) Wild swings in axis tilt because Mars lacks a large stabilizing moon like Earth’s (1) Earth’s axis is very stable at about 23.5° (support complex life) (2) Mars’s axis tilt ranged from 15°-45° over past 10 million years (now is like Earth) (a) When closer to 45° the polar ice would melt more than it does now (b) Wild swings make Mars a bad place to live and do science of ice cores, etc. b) Very poor stratigraphic data on Mars (stratigraphy is the science of discovering the history of Earth based on a study of rock layers). Such data is very poor on Mars mainly because of … i) Low precipitation (thus infrequent layering of water-borne soil) ii) Violent dust storms that quickly erode the few scientifically useful sequences of rock layers that originate Venus: Lover of Life? No! 1) Not fine-tuned for habitability: probably most inhospitable planet in the Solar System a) 900°F is too hot for liquid water to remain on its surface b) Like Mars, lacks a planetary magnetic field to shield its atmosphere from direct interaction with the solar wind (harmful radiation) 2) Not fine-tuned for measurability a) Much of historical geology (stratigraphy) is impossible to study because lack of waterborne sedimentation and ice core data (see Mars). This is correlated to 1.a. above. b) Much of historical geology (stratigraphy) is impossible because the historical record has been largely baked beyond recognition. This is correlated to 1.a. above.
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Other Planets in Our Solar System: Poor Candidates for Habitability and Measurability 1) Venus and Mars are the best candidates for life in our solar system (and they are poor) 2) All other planets are even worse for life and science (only give a few examples below) a) Mercury almost in gravitational lock with the Sun as is our Moon actually with Earth b) More distant planets (Jupiter, Saturn, Uranus, Neptune) i) Even more hostile to life ii) Mercury and Venus very difficult to discover from far out (angle from sun too small) iii) Long orbital periods require many human lifetimes to observe a single native “year” 3) Best moon candidate: Europa (a moon of Jupiter), but even it has sever limitations for life a) Ocean too deep (high pressure likely lethal to most life) b) Lacks sufficient solar energy for life in ocean (due to thick ice covering over ocean) c) No continents to keep salinity low in ocean; other factors make salt problem likely lethal d) Merely adding water (as is the case with Europa) is not adequate for life support Optional pages: 90b-94a Distant Wanderers (Planets in Other Solar Systems): Also Poor Candidates for Life 1) As of July 1, 2002, ______ giant planets have been found with the Doppler detection method a) Doppler method: detects ______________ of a host star as its planet(s) orbit it b) Current technology in this method only permits detection of planets more ____________ than Uranus or Neptune (Gas giants like Jupiter and Saturn), which are unsuitable for life c) Future research with better technology might detect Earth-sized planets 2) How other solar systems differ from ours: a) Some giant planets orbit very closely to and quickly around their host stars (suns) b) If orbital periods exceed 2-3 weeks, giants usually have highly eccentric orbits c) Only 7 giants with orbital periods greater than one month have eccentricity less than ___ d) To date, no true Jupiter _______ (eccentricity about 0.05 and orbital period about 12 years) has been found around a Sun-like star (high eccentricity is bad for life) 3) Of known planetary systems, that hosted by 47 Ursa Majoris most resembles ours a) This system has been touted as confirmation that our Solar System is not special b) But even this best match to our system is probably lethally different, thus confirming that our Solar System is unusual (atypical) i) The inner of its two gas giants is too close for comfort for any Earth-like planet: a gas giant planet so situated will _____________ away (p. 97) any terrestrial planets from the Circumstellar Habitable Zone (the CHZ is the band of space so situated from a host star that life is possible; we will study this in chapter 7). ii) Giant planets that perturb each other into more eccentric orbits also more likely perturb smaller planets and thus wreaking havoc iii) If most future solar system discoveries reveal high eccentricities of giant planet orbits, then this confirms systems like ours with many planets in stable orbits are rare 259
Moons of Giant Gas Planets are Much Less Habitable to Life than Earth (p. 97b-101) (Hundred-plus known gas giants, each with probably many moons) 1) Deadlier comet collisions (due to strong gravity of giant) a) More frequent hits on both moons and host giant planet b) Impact velocities greater on both moons and host giant planet 2) More intense particle radiation would be lethal (p. 97) a) Particle radiation is more intense where moons orbit a gas giant due to the giant’s strong magnetic field (this magnetic field keeps much of the incoming radiation off most of the giant’s surface and it concentrates the radiation at high altitudes where its moons orbit) b) More of this radiation reaches the surface of the moons due to the weak magnetic fields of moons that offer little protection c) Moons would quickly lose their atmospheres (due to radiation bombardment) and receive even greater lethal radiation on their surfaces after their partially protective atmospheres were totally stripped away 3) (Pages 97-98). Rapid onset of orbital tidal lock (one side of moon always faces its host planet) produces greater day-night temperature swings (unfriendly to life) due to very long days and nights. The average length of day on a moon equals half the time it takes for that moon to orbit around its host planet once (lunar orbits around giants typically take 2 weeks). What is the average length of day on such a moon? _______ Average night length? _______ 4) If (despite evidence to the contrary, p. 98-99) a giant gas planet could establish itself in a stable, nearly-circular orbit about its host sun (particularly an orbit that is at the right distance to maintain liquid water on its moons), there is still much evidence that this giant would loose its moons to a greedy host sun (or the moons might be drawn into the gas giant itself). 5) Summary of argument that moons of giant gas planets are far less habitable to life (p. 100) a) Some giant planet-moon systems might avoid one of the 4 life-threatening factors above b) Overall giant planet-moon systems are very unfriendly to life (compared to Earth-Moon) 6) Overall giant planet-moon systems are unfriendly to scientific discovery and the factors that make this so are also roughly the same factors that make it unfriendly to life. Thus the correlation between habitability and measurability is seen here. (p. 101) How chapter 5 supports the Privileged Planet thesis Habitability and measurability are many times better on Earth than any other place we know. The factors that support intelligent life on Earth also set up Earthlings for superb science. Habitability and measurability are correlated. This same correlation is seen in other planet-moon systems, but on the unfriendly end of the spectrum: poor habitability is correlated to poor measurability. This scientific evidence gives one a strange feeling that the entire correlation scheme, both on the positive and negative poles of outcome, has been rigged up this way. Our blue dot appears unusually bright for life and science. Should we feel special? 260
Monday November 1 Lab 8: Galileo’s Inclined Plane. Do Pre-Lab Before Lab! Pre-Lab Galileo’s Account of His Inclined Plane Experiment Purpose of this Historical Sketch: Read this account of Galileo’s famous experiment and be prepared to compare Galileo’s original conception of this experiment with the OBU Natural Science reconstruction of it. In his 1638 book Two New Sciences (citations from 2nd edition, ed. & trans. Stillman Drake, pp. 169-170. Toronto: Wall & Thompson, 1989) Galileo’s fictional characters Simplicio and Salviati discuss the most remembered experiment of Galileo. After much debate over “uniformly accelerated motion,” Simplicio is “still doubtful as to whether this is the acceleration employed by nature in the motion of her falling heavy bodies.” He challenges Salviati to produce an experiment that would confirm Salviati’s “demonstrated conclusions” about the mathematical laws of free fall motion. Salviati responds: “Like a true scientist, you make a very reasonable demand, for this is usual and necessary in those sciences which apply mathematical demonstrations to physical conclusions, as may be seen among writers on optics, astronomers, mechanics, musicians, and others who confirm their principles with sensory experiences that are the foundations of all the resulting structure. . . . Therefore as to the experiments: the Author [Galileo] has not failed to make them, and in order to be assured that the acceleration of heavy bodies falling naturally does follow the ratio expounded above [the ratio that OBU Nat Sci students will confirm in lab], I [Salviati] have often made the test in the following manner, and in his [Galileo’s] company.” Salviati then gives a three-paragraph description of this “test” or “experiment”: In a wooden beam or rafter about twelve braccia [yards] long, half a braccio wide, and three inches thick, a channel [OBU equivalent is trough between two pipes on wooden 2x4] was rabbeted [carved] in along the narrowest dimension, a little over an inch wide and made very straight; so that this would be clean and smooth, there was glued within it a piece of vellum, as much smoothed and cleaned as possible. In this there was made to descend a very hard bronze ball [OBU equivalent is ball bearing], well rounded and polished, the beam heaving been tilted by elevating one end of it above the horizontal plane from one to two braccia, at will [OBU equivalent is to elevate one end with foam block]. As I said, the ball was allowed to descend along the said groove, and we noted (in the manner I shall presently tell you) the time that it consumed in running all the way, repeating the same process many times, in order to be quite sure as to the amount of time, 261
in which we never found a difference of even the tenth part of a pulse-beat [about 1/10th of a second]. This operation being precisely established, we made the same ball descend only onequarter the length of this channel, and the time of its descent being measured, this was found always to be precisely one-half the other. Next making the experiment for other lengths, examining now the time for the whole length [in comparison] with the time of one-half, or with that of two-thirds, or of three-quarters, and finally with any other division, by experiments repeated a full hundred times, the spaces [distances] were always found to be to one another as the squares of the times. And this [held] for all inclinations [various degrees of slope] of the plane; that is, of the channel in which the ball was made to descend, where we observed also that the times of descent for diverse inclinations maintained among themselves accurately that ratio [the ratio that OBU Nat Sci students will confirm in lab] that we shall find later assigned and demonstrated by our Author. As to the measure of time, we had a large pail filled with water and fastened from above, which had a slender tube affixed to its bottom, through which a narrow thread of water ran; this was received in a little beaker during the entire time that the ball descended along the channel or parts of it. The little amounts of water collected in this way were weighed from time to time on a delicate balance, the differences and ratios of the weights giving us the differences and ratios of the times, and with such precision that, as I have said, these operations repeated time and again never differed by any notable amount. While we can’t go back in time to be present with Galileo either, we can replicate his experiment here, all for our own great satisfaction! The amazed Simplicio remarks: “It would have given me great satisfaction to have been present at these experiments. But being certain of your diligence in making them and your fidelity in relating them, I am content to assume them as most certain and true.” OBU students need not take Simplicio’s approach of trusting in Galileo’s authority that an inclined plane experiment will produce the kind of results that Galileo claimed would occur. We can have first-hand experience of a roughly equivalent experiment at OBU. What are some differences between Galileo’s experiment and ours (equipment, technique, expectations, etc.)? Analysis •
How steeply must a plane be inclined to approximate a free fall situation?
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Galileo measured the times and distances of a ball rolling along an inclined plane in order to approximate the motion of a body in free fall. His ingenious idea was to imagine a plane inclined vertically, which would be equivalent to free fall. A plane inclined by 89
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degrees would still closely approximate free fall. Would the same law that governs free fall also govern the rolling of a ball down an inclined plane? •
If the answer to the above question is yes, then lowering the plane more and more toward the horizontal in effect renders free fall as slow motion, thus making possible more precise measurements of time and distance.
•
How are free-fall and inclined-plane motions different?
Inclined Plane Lab Purpose: Replicate Galileo’s experiment for confirming the law of free fall Lab Team Division of Labor (2 or 3 persons) 1. One person (the starter) will signal when to start timing by indicating precisely (via. “ready, start”) when she releases the ball from behind the starting line near top of the inclined plane. 2. At that signal another person (the timer) starts the stopwatch (and later stops it with the help of person #3). The timer records 3 time measurements on the lab report for each specific length of inclined plane (and he later allows the others in the group to copy this information onto their own lab reports). He should also use a calculator to record average times. 3. A third person (the stopper; can be combined with role #2) indicates when to stop the stopwatch by saying “stop” when the ball has reached the appropriate place on the inclined plane. Use a piece of cardboard to stop the ball at the appropriate point on the inclined plane. In this method you could use at least three of your senses to determine when to say “stop”: sight (of contact), hearing (of impact), and touch (of force of impact). The timer may also be cued to stop the stopwatch by hearing the impact on the cardboard. Read and Remember • • •
Once the experiment has begun, do not change the slope! To set up a slope, put a foam block under one end of the plane. Do not lean on the plane or bow it downward by pressing too hard with the cardboard. Try not to drop the metal balls on the floor.
Procedure 1. Measure the time (use the stopwatches provided) it takes for a metal ball to roll through the top distance interval on the inclined plane. If the ball does not start properly do the measurement over again—there is no good reason to keep obviously faulty data. Obtain 3 consistent time measurements for this one distance interval and record all 3 times as well as their average. If you mess up on this part, it degrades the accuracy of the rest of the lab. Be 263
very careful. The units on the stopwatches are seconds and 5ths of seconds (e.g. 1 and 1/5ths seconds is recorded as 1.2 seconds) Timed Trials: 1st 2nd 3rd aver.
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2. Without altering the inclination of the plane (do not take it off the blocks, or change the number of blocks), repeat the procedure. • Perform three trials of rolling the ball down the combined distance of the top two intervals, then record these times and their average in column 2 below. • Roll the ball through the top three distance intervals, then record these times and their average in column 3 below. • Continue rolling the ball from the zero point through the combined-distance intervals until the times for the top 12 distance intervals (go no further than 12) have been measured, recorded, and averaged in the table below. ....................................... Distance Units ...................................... 2 3 4 5 6 7 8 1st 2nd 3rd aver. * †
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3. Now that you have mastered the measuring techniques, repeat the first distance interval. Note any discrepancy between the old and new data and use only the new data in the next steps. Why should you use the new data instead of the initial data? Timed Trials: 1st 2nd 3rd aver.
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4. We shall analyze how much farther the ball rolls in multiples of the unit time. Unit Distance = the length of any single distance interval marked on the inclined planes. Unit Time = the time required for the ball to fall (roll) through the first unit distance.
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Convert actual times as recorded in step #2 into relative times: Let the length of time required to go the first unit distance = 1 unit of time. Record the length of your unit time (the average from step #3):
T1 = ________ secs
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The time required to travel one distance unit (T1) = 1 unit of relative time. This is recorded in the data table below, by entering a 1 in the second row of the column under 1 distance unit.
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In the column for 2 distance units, divide the average time for the ball to go through the first 2 units distance (in the box marked * in step #2 above) by the average time for it to go through the “one unit distance” (T1). Put this relative time (time to go 2 distances ÷ T1) in the table below under Distance 2. This calculates the “relative time” to go 2 relative units of distance.
Relative 1 Distance (D) Relative 1 Time (T)
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For column 3, representing the amount of time required to travel 3 distance units, divide the average time for the ball to go through 3 units of distance († in step #2 above) by the average time for it to go through one unit distance (T1). Put this relative time in the table above under the column labeled 3.
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In the same way, complete the remaining columns by entering relative times in the lower row corresponding to each relative distance.
Check your understanding • • • • •
Should the size of ball used affect the relative times (ask another group who has different size steel ball than you)? Yes/No (circle one) Should another lab group, who has their plane propped up higher or lower than yours (different degree of inclination), be arriving at different relative times than you (assuming perfect planes and perfect time keeping)? Yes/No (circle one) Examine the table of relative distances and relative times (the previous table). Note that in 1 unit of time, the ball traveled 1 unit of distance. In 2 units of time (the number that is closest to the whole number “2” in your table--find it now), what total distance did the ball roll (read off the distance number directly above the time number)? Record that here: 265
D = _____ •
In other words, given twice as much time to roll as was required to go the first unit distance, what total distance will the ball roll? The answer is whatever you filled in the previous blank (this may not fit the ideal answer, given perfect conditions).
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Examine the table of relative distance & time again. In 3 units of time (the number that is closest to the whole number “3” in your table--find it now), what total distance did the ball roll? Record that here: D = _____
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In other words, given three times as much time to roll as was required to go the first unit distance, what total distance will the ball roll? The answer is whatever you filled in the previous blank (this may not fit the ideal answer, given perfect conditions).
5. Inducing a Law of Free Fall •
Three factors are related in free fall: the speed of the ball, the distance it falls (or rolls), and the time elapsed. It is perhaps obvious that the speed of the ball is not constant. Ever since Aristotle, the speed was presumed to be uniformly accelerating; that is, increasing by a constant amount per unit of elapsed time. Setting aside speed for the moment, then, focus on distance (D) and elapsed time (T). What equation might describe the relation of D and T in free fall?
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The simplest possibility might be that their sums are constant, or that D and T are proportional. If they are proportional, D/T should equal a constant, or multiplying D x T should equal a constant. Test these three possibilities by completing the following table.
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Fill out the first two rows as in step #4. Add row 1 and row 2 to obtain the sum D + T for the third row of each column. Divide D by T to fill in the fourth row. Multiply the top two rows to obtain D x T for the last row of each column.
Relative Distance (D) Relative Time (T) D+T D÷T DxT
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Inspect the table above: • Are the sums constant (does D + T always add up to the same value)? • Is D ÷ T a constant? • Is D x T a constant?
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Another possible relation of D and T might be that the square of one would equal the other, or the square of one might equal the square of the other. Test these possibilities by completing the following table. Fill out the first two rows as in step #4. Relative Distance (D) Relative Time (T) D2 T2
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Inspect the table above: • Does D2 = T2? • Does D = T2? • Does D2 = T? Analysis •
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Experiments are not always as easy to perform or to interpret as they seem. Your results may not be entirely consistent with any of these simple possibilities. However, based on your data, which of the three expressions above would best describe free fall? That is, your data would best confirm Galileo’s law of free fall if it were which of the three? Ideal Free Fall Law: ____ = ____
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Reread Galileo’s account of the inclined plane experiment in the first section. We have not taken Simplicio’s approach of trusting in Galileo’s authority that an inclined plane experiment easily produces the kind of results that Galileo claimed would occur. We now have first-hand experience of a roughly equivalent experiment. What are some differences between Galileo’s experiment and ours (equipment, technique, expectations, conclusions, etc.)?
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Do not actually carry out this step, just predict what should happen based on discernible patterns in the data from step 5. According to your answer to the first analysis question in step #5, how many units of time would it take for the ball to roll 16 units of distance? Relative Distance (D) Relative Time (T) (calculated)
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Now roll the ball through 16 times the unit distance and record the actual time and then covert it to relative time below: Relative Distance (D) 16 Actual Time in 267
seconds (observed) Relative Time (T) (observed) Calculate the percent error of your result in step 7 using the formula of (calculated observed) / calculated * 100 = % error. If it comes out negative, just ignore the negative sign and make it positive. ------------------------------------------------------------Show your results and explain your procedure to the lab assistant/instructor to get approval to move on to the next part of the lab.
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Uniform Acceleration Thought Experiment
Speed
Time 1. Labels. The diagram above, which is based on the work of medieval scholars working long before Galileo (but who never suggest inclined plane experiments), represents the speed of a falling object through four units of time. It is an abstract graph of speed versus time, not a spatial diagram of an inclined plane. When an object is just about to begin its free fall (or rolling down the plane), its speed is 0 and the elapsed time is 0. This is the point located at the lower left of the graph. Label the following on the above graph: • Speed 0 and Time 0. • Relative Times: T1, T2, T3, T4 (go left to right along the bottom of the graph). • Speeds: S1, S2, S3, S4 (go bottom to top along the left or right sides of the graph). 2. Study this to understand how distance is represented on the graph. • If a car travels at 60 mph for 1 hour then how far does it travel? • Answer: 60 miles/hour x 1 hour = 60 miles. • In general: Distance = speed x time. • Since the above graph plots speed on one axis versus time on the other axis, the areas (shown as triangles) represent distances. Consider each small triangle as one unit of relative distance (D) that is traveled up through that point in time on the graph. For example, if you want to calculate how much distance is traveled in the first 3 units of time, count up the TOTAL number of triangles that are found from time 0 to time 3 on the graph. 269
3. Speed. Speed is depicted as the vertical dimension of the graph. The upward slope of the graph represents uniform acceleration (increase in speed), as if a car accelerated from 0 to 60 mph in a given length of time, or as if a rock fell from a given height toward the ground at a constantly increasing speed. •
In uniform acceleration, is the speed constant?
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In uniform acceleration, does the speed increase by a constant amount per unit of time?
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Would S2 represent the average speed of this body from T0 to T4?
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In general, what is the average speed of a body in uniformly accelerated motion? Is it the speed of the body at the midpoint of the total time? Or is it the speed of the body at the midpoint of distance traversed?
4. Deduce the Law of Free Fall. •
Complete the second row of the table by counting the number of triangles, which correspond to the relative distances (D) traversed by a falling body.
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In the third row, calculate the squares of the times.
Relative Time (T) Relative Distance (D) T2
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Write the law of free fall here: Analysis •
Galileo completed these thought experiments before he began his inclined planeexperiments. The table at the beginning of this section appeared in the fourteenthcentury works of Nicole Oresme, and was widely published.
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Do these conceptions help us to understand how Galileo could boast that “I have deduced without recourse to observation” that the distances a body falls due to uniform acceleration are proportional to the squares of the times? Explain.
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To check out: The lab assistant/instructor will look over your lab & lab report to check for problems. Obtain approval from the lab assistant/instructor to leave (initials on your lab report). Clean up your tables and follow any specific instructions given, including: 1. turn calculators off 2. turn stopwatches off 4. do not leave the inclined planes on an incline (put them flat on the table)
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Inclined Plane: Lab Report • Name: _________________ Credit is possible only if lab assistant/instructor’s initials are here: Initials _______ Enter the most accurate average time you got for the 1st distance interval: One Unit Time = ___ Enter the measured times for these intervals of distance: ....................................... Distance Units ...................................... 2 3 4 5 6 7 8 aver.
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Enter the relative times: Relative 1 Distance (D) Relative 1 Time (T) • • • •
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Should the size of ball used affect the relative times? _____ Should the degree of inclination of the plane affect the relative times? _____ In 2 units of time, what total distance did the ball roll? D = _____ In 3 units of time, what total distance did the ball roll? D = _____
When you inspect the tables in the lab, what did you conclude about these possible time and distance relationships (based on your data): • Is D + T a constant? • Are D and T proportional? • Is D ÷ T a constant? • Is D x T a constant?
• Does D2 = T2? • Does D = T2? • Does D2 = T?
Circle the one formula above (even it has a “no” by it) that is the ideal answer that Galileo proposed for the relationship between distance and time in naturally accelerated motion. With more accurate instruments, do you suspect that we would get much closer to this ideal? Yes/No (circle one) Roll the ball through 16 distance intervals. Record actual time ____ Relative time ___ • Reread Galileo’s account of the inclined plane experiment in the first section. What are some differences between Galileo’s experiment and ours (e.g., equipment, technique, and expectations)?
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Chaisson, Ch. 9: The Sun Begin be reading “Introduction to Part Three: The Stars” (p. 236-237) Then read the entire chapter 9 and use all of the study helps provided by Chaisson.
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Wednesday November 3 Chaisson, Ch. 10: Measuring the Stars Read the entire chapter and use all of the study helps provided by Chaisson.
Exam 2 Study Guide 1. Exam 2 will be like Exam 1: about 3/4ths closed book/note and about 1/4th open book/note, usually all multiple choice and true/false questions. 2. Study the old exam 2 (complete with answer key in the back of your Packet), but realize that I have changed the course since the time when this old exam 2 was created. 3. Study the quizzes given since the time of exam 1. 4. Make thorough use of study guides in your exam preparation, but questions are not limited to those asked in textbook and study guides. 5. Are there historical dates I must memorize? Yes, see the list on the “chronology” Packet page. 6. How will labs figure into Exam 2? I will convert lab handout & report questions to multiple choice and true/false questions. Also, notice that labs often cover the same material as the Packet and other readings, but in a different environment. I will also create questions that test how well you absorbed “hands-on” lab experience (even an item for which a study question does not exist). 7. What about study questions in the Packet that we never had time to address in class? There are many intellectually stimulating questions that we did not cover in class. Be sure to answer them in your study group and then ask me to cover the ones you didn’t get.
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Monday November 8: Exam 2 Bring #2 pencil, test forms, and all your relevant books and notes for the exam. Did you study for the exam following the study guide that was due last class period?
Lab 9: Archimedes’ Principle. Do Pre-Lab Before Lab! Pre-Lab Purpose By studying and using Archimedes’ water displacement and buoyancy principles (and their modern application in measuring density) we will see how one ancient Greek was a master of quantitative experiment. Water displacement is a practical way to measure the volume of an irregularly shaped object like a crown. This insight flashed into Archimedes’ mind as he stepped into a bathtub and watched the water rise and overflow. Buoyancy is a fundamental idea within the science of hydrostatics (the physics of fluids), an area in which Archimedes heavily influenced subsequent science, especially Galileo. You will encounter Galileo’s experimental genius in a separate lab having to do with objects descending down inclined planes. In the Archimedes lab you will discover the kind of metal crown (just a metal cube in our lab) on your lab bench by using two different methods from Archimedes: (1) water displacement (2) buoyancy. We will employ the modern concept of density (and specific gravity as a measure of density) to determine the kind of metal crown you have. Background Primary concepts refer to simple qualities instead of composite characteristics. Weight and volume are simple qualities that can be directly measured and are thus primary concepts. Density is a composite characteristic of different kinds of materials, including gold (more dense) and silver (less dense), which were part of the legal and scientific puzzle that Archimedes solved. Density, as a composite characteristic, is a derived (indirectly calculated) concept rather than a primary (directly measured) concept. Specific gravity is a water-based practical calculation of density that allows us to assign specific numbers to the density of materials such as gold (very dense; high number) and silver (less dense; lower number). Thus both density, and specific gravity as a practical calculation of density relative to water, are derived concepts that cannot be determined as the results of single measurements as can weight or length. Nor can they be directly computed like the volume of regular shapes. Rather, they represent properties of the material (i.e., “intensive” properties), not properties peculiar to the particular sample that is in hand (i.e., “extensive” properties). Check your understanding: You bring a pot of water to a boil. 1. Is the boiling point an intensive or extensive property of water? a. intensive b. extensive 277
2. Is the water volume an intensive or extensive property? a. intensive b. extensive Answer Key: 1a, 2b This lab will also investigate questions such as these: 1. 2. 3.
Even though volume is a primary property, is it always easy to calculate? How can we calculate the volume of an irregular solid such as a king’s crown? What is experimental error and how do we cope with it?
Archimedes (287 B.C. – 212 B.C.) • One of the most celebrated mathematicians of antiquity • Studied under Euclid’s successors in Alexandria • Known as mathematician and military engineer (burning mirrors) • Mathematized rules of lever, pulley, and geometrical “machines” • Killed by a Roman soldier during the siege of Syracuse • 1543 publication of Archimedes’ works significant for modern science • Plato and Archimedes were two of Galileo’s heroes Famous (perhaps legendary) quote: “Give me a lever and a place to stand and I will move the world.” (Archimedes) Consider: What is your “Archimedean point”? Vitruvius on Archimedes’ Bathtub Insight: Recreating the Historic Moment of Experimental Discovery Vitruvius in his book On Architecture (IX, introduction 9-12, translation of M. H. Morgan), remarked that although Archimedes made many wonderful discoveries, one in particular “seems to have been the result of a boundless ingenuity.” Vitruvius then describes this discovery: Hiero, after gaining the royal power in Syracuse, resolved, as a consequence of his successful exploits, to place in a certain temple a golden crown, which he had vowed to the immortal gods. He contracted for its making at a fixed price and weighted out a precise amount of gold to the contractor. At the appointed time the latter delivered to the king’s satisfaction an exquisitely finished piece of handiwork, and it appeared that in weight the crown corresponded precisely to what the gold had weighed. Someone later accused the crown contractor of substituting an equivalent weight of silver in place of a certain amount of the crown’s gold. The king asked Archimedes to investigate the matter. Archimedes, upon getting into a bathtub soon after considering the royal matter, “observed that the more his body sank into it the more water ran out over the tub.” This water displacement experience coincided with a flash of insight about the detection of foul play on the part of the crown craftsman. Accordingly, “without a moment’s delay and transported with joy, 278
he jumped out of the tub and rushed home naked, crying in a loud voice that he had found what he was seeking; for as he ran he shouted repeatedly in Greek, “Eureka!” [“I found it!”] Vitruvius writes that Archimedes then allegedly made two masses of the same weight as the crown, one of pure gold and the other of pure silver. The gold object displaced less water than the silver, which served as the key to solve the crown mystery, as Vitruvius explains: After making [the pure gold and pure silver objects of equal weight], he filled a large vessel with water to the very brim and dropped the mass of silver into it. As much water ran out as was equal in bulk to that of the silver sunk in the vessel. Then, taking out the mass, he poured back the lost quantity of water, using a pint measure, until it was level with the brim as it had been before. Thus he found the weight of silver corresponding to a definite quantity of water. This was a clever way of determining the weight of water displaced by a certain chunk of silver. After this experiment, he likewise dropped the mass of gold into the full vessel and, on taking it out and measuring as before, found that not so much water was lost, but a smaller quantity: namely, as much less as a mass of gold lacks in bulk compared to a mass of silver of the same weight. In other words, he repeated with the gold chunk what he had done with the chunk of silver. Although both the silver and gold chunks weighed the same, they did not have equal volumes as his “water displacement” method revealed. Finally, filling the vessel again and dropping the crown itself into the same quantity of water, he found that more water ran over for the crown than for the mass of gold of the same weight. Hence, reasoning from the fact that more water was lost in the case of the crown than in that of the [pure gold] mass, he detected the mixing of silver with the gold and made the theft of the contractor perfectly clear. Check your understanding: Given the above information, which would be heavier, a bar of gold or a bar of silver, if both bars are the same size (equal volume)? Check one: Gold heavier __ Silver heavier __ Which would displace more water, a gold or silver crown of the same weight? Check one: Gold crown displaces more water __ Silver crown displaces more water __ Unpacking Archimedes’ Bathtub “Water Displacement” Insight as Well as his Idea of “Buoyancy” Ancient Greeks like Archimedes would not have interpreted the underlying cause of the above experimental results in the same way that we moderns would. We conceive of gold as being denser than silver (more mass in the same volume) and thus equal weights of both kinds of metal would not displace the same amount of water. Ancient Greeks would probably say that gold has 279
a higher proportion of the absolutely heavy element “earth” than silver does (which must have higher proportions of light elements such as air or fire). Ancient Greek thinkers generally considered the universe and every object in it to be totally full of matter with no empty space. They would have said that there is no more mass (matter) in one volume (place) than in another-just 4 different kinds of material elements here in the sublunar realm--earth, water, air, and fire-each of which compose objects in different proportions and render those objects with a natural tendency to either sink or float in ordinary visible water (different “buoyancies” as Archimedes conceived it). Indeed, Archimedes developed the idea of buoyancy in close association with his bathtub Eureka insight that gave him a water displacement solution to the royal crown mystery. Archimedes reasoned that the upward (“buoy up”) tendency of a body placed in water is equal to the weight of the water displaced by the body. The two thought experiments in today’s lab help explain this equivalence by reference to an imaginary water crown (study these thought experiments before lab). Additional clarification of Archimedes’ buoyancy principle is appropriate here. If a chunk of cork is placed in water, it will float. The part of the cork that is under water displaces exactly that same volume of water. In other words, the volume of water displaced by the cork is equal to the volume of that part of the cork that is below the water line. When you force a cork under water and hold it there, the force you feel pushing back up on your finger illustrates how the total upward buoyant force that the cork experiences when immersed is greater than its own weight (and thus, when left alone, will float rather than sink). Continue thinking about Archimedes’ buoyancy principle by answering this question before reading further: If one weighs a cork and weighs an equal volume of water, which will weigh more? The water will weigh more and this weight of water is also a measure of the buoyancy of that particular sized object (the cork), which is greater than the weight of that cork itself, and thus the cork floats rather than sinks. Does this give you a rough appreciation of Archimedes’ buoyancy principle? Archimedes’ Buoyancy Principle: The upward buoyancy tendency of a body placed in water = the weight of water displaced by the body In the case of 3 chunks of metal of equal weight but different volume (one gold, one silver, and one gold-silver mixed), the weight (in air) of any of these 3 chunks would obviously be greater than its buoyancy tendency (in water) and thus each metal chunk would sink rather than float like cork. Now let us compare the bouyancies of two of Archimedes’ metal chunks. Which chunk of metal of equal weight (the gold or the silver chunk) did Archimedes find to be more “buoyant” in water (even though both chunks had a weight that was greater than either buoyancy factor and thus both sank in water)?
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Circle one: the gold chunk or the silver chunk was more “buoyant” in water? Explain why the correct answer to this question is the “silver chunk.” Now read this to see if it is close to how you explained your answer above. The silver chunk was more “buoyant” in water because, although it weighed the same as the gold chunk, it displaced more water than the gold chunk (due to the silver chunk’s greater volume). Archimedes could conclude this because he understood the “buoyancy” of any object to be equivalent to the weight of a volume of water that is equal in volume to the object in question. Archimedes’ experiment clearly showed (as similarly you will do in lab) that a silver chunk clearly displaces more water than a gold chunk of the same weight. Check for understanding of Archimedes’ Buoyancy Principle: a gold chunk and silver chunk of equal volumes are place in water ... will the two objects displace the same volume of water? ... will they have the same buoyancy tendency? Of course they will displace the same amount of water since both chunks take up the same amount of space (equal volumes). Following Archimedes’ Buoyancy Principle, the two will also have the same upward buoyancy tendency since both will be displacing the same volume and same weight of water. However, because they are made of different materials, one will sink through the water faster than the other because its weight is greater (we won’t get into the fine distinctions here that would separate the ancient explanation of this and the modern one). Do you know understand at a certain abstract level the following principle? Archimedes’ Buoyancy Principle: The upward buoyancy tendency of a body placed in water = the weight of water displaced by the body If you have troubles with such abstractions, our hands-on lab might help your mind take a leap forward. We will use both a “water displacement” method (Lab: Part I) for determining the identity of an unknown mass of metal, as Archimedes did in the ancient text above, as well as a “comparative buoyancy” method (Lab: Part II), which will extend some of Archimedes’ work beyond the scope of the ancient text. We will use the modern idea of specific gravity (the density of an object relative to water density) to identify different kinds of metal cubes (symbolic of crowns) that will be on your lab tables. In doing so, we will depart from the strict historical context of Archimedes ideas and partially replace his ideas with modern ones. Ancient Greeks would generally explain the differences in bouyancies of objects in terms of their relative constitution out of 4 elements, but we explain the same phenomena in terms of density, which is the relative quantity of mass within a certain volume of a material. It is historically appropriate that scientists today still assign different densities of specific materials a number (specific gravity) with water as the universal standard, because the determination of differences of this sort in many ways began with a famous Greek submersing himself into a bathtub of water. Eureka! 281
Lab Objectives 1. Recreate the historic moment of Archimedes’ “bathtub” discovery in order to feel and conceptualize the cultural and personal significance of scientific methodology in ordinary life. 2. Construct the idea of density (and specific gravity as a way to calculate density) by means of 2 abstract thought experiments and 2 hands-on experiments that are based on the thought experiments. 3. Apply Archimedes’ water displacement and buoyancy insights in order to calculate density by means of specific gravity. This will enable you to determine whether your crown is gold, silver, aluminum, lead, brass, iron, or a mystery substance. 4. Appreciate how Archimedes did not perform his work in terms of the modern idea of density, but rather in terms of the “buoyancy” of objects within a 4-element (earth-water-air-fire) paradigm. 5. Use a comparison of ancient and modern ideas of density and buoyancy to better understand the modern scientific conceptions and their applications in everyday life. Key Lab Ideas •
A Modern Definition of Buoyancy: The upward (“buoy up”) force that a fluid exerts on an object that is placed in it.
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Archimedes’ Buoyancy Principle: The upward (“buoy up”) tendency of a body placed in water is equal to the weight of the water displaced by the body. Today we would explain the upward (“buoy up”) tendency of things placed in water in terms of the “buoyant force” acting to partially or fully support a body that is placed in water. Ancient Greeks like Archimedes did not use the idea of “force” for this phenomena, but rather thought in terms of the natural tendency for each of the 4 elements (earth, water, air, & fire) to move or “strive” toward their natural “place” in the universe.
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A General Definition of Specific Gravity (SG): An object’s weight98 divided by the weight of the water displaced by the object (i.e., the weight of an equal volume of water). For example, cork has a low specific gravity and so floats on water. Metals like gold and silver have high specific gravities and thus sink in water. Thus an object’s specific gravity is a measure of how it will tend to sink or rise in water. Both Archimedes and modern thinkers would agree on this general definition and its observable expressions.
98 Weight (in an ancient Greek framework) is caused by the relative proportion of heavy (earth & water) to light (air & fire) elements in an object.
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A Modern Definition of Density: The amount of matter (mass) that is packed into a certain amount of volume or space (metals are highly dense, cork is not very dense). Density can also be conceived of as the ratio of mass to volume for a given material. Ancient Greek scientists did not have this modern “density” notion of the relative proportion of mass to volume. Instead, they used the Aristotelian 4-element theory (earth, water, air, & fire), which assumed a universal plenum (all space is equally and totally filled with matter). For example, Archimedes would say that some bodies, such as cork, are composed of a higher proportion of light elements (air and fire) in relation to heavy elements (earth and water). Such bodies would float on top of water because of the natural tendency of air and fire to move upward (opposite of water which naturally moves or stays down). Both Archimedes and modern folks would measure the tendency for things to gravitate down toward the center of earth by “weight” on a scale.
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A Modern Definition of Specific Gravity (SG): A measure of the density of an object relative to the density of water.
Items used to replicate Archimedes’ experiment (ancient & modern counterparts): Ancient Items Used Crown or metal chunk Bathtub-type container Overflow container
Modern Equivalent = Metal block with hook = Can with side spout = Styrofoam cup
Other items used in this lab: • Balance (triple beam balance; ask for help if you forget how to use one) • Thread (to make a loop upon which to hook the metal block) • Water (from sinks at end of tables) End of Pre-Lab (Come to your lab section to complete the rest of the lab; however, you may want to preview the lab itself, especially the “thought experiments” which might be difficult to grasp). The actual lab begins on the next page.
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Archimedes Lab You can wait until you come to lab to read and do the following (However, many will benefit by reading the two “thought experiments” in advance) I. Method A: Using water displacement to determine specific gravity Specific Gravity Thought Experiment I. Imagine: 1. You have a crown of gold. 2. At a snap of your fingers, the crown of gold is suddenly turned into a crown of water—of the same size and shape as the gold crown (thus it has the same volume as the gold crown). 3
Given that, in modern terms, specific gravity is a measure of how dense something is relative to water, we need to somehow compare the weight of the gold crown and the weight of our imaginary water crown (see first formula below). The imaginary water crown is just a clever way to conceive of an amount of water that is equal in volume to the original gold crown volume (see second formula below). Specific Gravity = Weight of gold crown ÷ Weight of imaginary water crown Specific Gravity = Weight of gold crown ÷ Weight of equal volume of water
4. We can easily weigh the gold crown. But how can we weigh the water crown—that is, how can we determine the weight of a volume of water equal to the volume of the gold crown? 5. Objects that sink displace their volume of water when they are immersed, just like Archimedes’ body displaced an equivalent volume of water over the side of the bath as he lowered himself into it. This provides an indirect way of determining the volume of an irregularly shaped object—like a human body (Archimedes’) or a golden crown (Hieron’s). If you immerse your crown (cube) into a water-filled bathtub (side-arm flask), then theoretically the baptized cube and the overflowing water have the same volume. Often, because of surface tension, sometimes a greater or lesser amount of water will flow, surge, or splash out. Procedure: a. Tie the thread into a loop so that it will hook onto your crown in order to lower the crown into the tub without splashing water outside. b. Weigh the dry crown on the triple beam balance and record its weight in the data table below (line 1). c. Fill your beaker with water to supply water at your lab station as needed. d. Put your thumb or finger over the “bathtub’s” side-arm outlet and fill it with water up to just above the outlet. Place the overfill cup underneath the side-arm, and remove your thumb. e. Weigh the overfill cup, along with any water it contains (it doesn’t matter how much water the cup has in it, just weigh it before the next step). Record in data table, line 2.
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f. Carefully lower the crown into the bathtub (side-arm container) so that water slowly runs out the side-arm into the overfill cup. Shout “Eureka!” if you understand why you are doing this. Make sure to collect all water that overflows. g. Weigh the overflow cup along with all the water it contains. Record in line 3 of the data table. h. Calculate the weight of an equal volume of water (line 4 = line 3 - line 2) and the specific gravity (line 5 = line 1 ÷ line 4). i. Repeat steps (d) through (h) for Trial 2 (differences will be due to error). j. Write out the general formula for specific gravity below as reinforcement for why you did the steps in line (h): SG = Data and Calculations: Line # 1 2 3
Trial 1: Measurements Crown weight Initial weight of overflow cup + any drops of water Final weight of overflow cup + water
Data grams grams grams
4 5
Trial 1: Calculations Weight of equal volume of water Specific Gravity
grams
Line # 1 2 3
Trial 2: Measurements Crown weight Initial weight of overflow cup + any drops of water Final weight of overflow cup + water
Data grams grams grams
4 5
Trial 2: Calculations Weight of equal volume of water Specific Gravity
grams
Analysis: 1. If you weighed the crown AFTER collecting the overflow water, your calculated specific gravity might be: ___ too high; ___ too low Explain 2. If some water splashed out of the side-arm flask and was not caught in the overflow cup when you lowered the crown in, your calculated specific gravity would be: ___ too high; ___ too low Explain 285
3. What are some other possible sources of experimental error with this method of determining specific gravity (Remember that experimental error is not the same as human error; it is something that is inherently wrong in the experiment)?
Show your results and explain your procedure and answers to the above questions to the lab assistant/instructor to get approval to move on to the next part of the lab (if the assistant/instructor is busy, go on with the 2nd part, and get checked later). To assist in this check, write out the general formula for specific gravity: SG = II. Method B: Using buoyancy to determine specific gravity. Specific Gravity Thought Experiment II. Imagine: 1. You have a crown of gold. 2. Immerse that crown of gold into a tub of water. 3. At a snap of your fingers, the crown of gold is suddenly turned into a crown of water—of the same size and shape as the gold crown (thus it has the equal volume). 4. Since your water crown is like the other water in the bathtub, it neither rises nor falls. Therefore, the water beneath and around it must support it with a buoyant force (pushing up) equal to the water crown’s weight (downward force). • buoyancy force (BF) = water crown’s weight • water crown’s weight = weight of water of equal volume to crown (WW) • Thus buoyancy force (BF) = weight of water of equal volume to crown (WW) In symbolic form, BF = WW 5. At another snap of your fingers, your water crown is turned back into a gold crown. Because the surrounding water remains the same, the water will continue to support the gold crown with the same buoyant force it exerted on the water crown. 6. If the gold crown were attached by a thin thread to a scale, the part of its weight not already supported by the water would be supported by the scale. Since the scale is supporting less than the full weight of the gold crown, it would record a smaller weight than if the gold crown were weighed in air. Thus the crown would appear to lose some weight when it is immersed in water. (That this weight-loss due to buoyancy is familiar to anyone who has helped someone learn to swim. It is very easy to hold someone up in the water whom one could never hold up in the air, since the water is supplying most of the buoyant support.) 286
7. Because the weight-loss (WL) is caused by the buoyancy force (BF), the two must be equal in strength, thus WL = BF. 8. But if WL = BF and BF = WW (from step 4), then WL = WW, and so: Starting with the formula for specific gravity from part I of this lab SG = Crown weight in air ÷ WW We can now substitute in WL for WW and get this new formula: SG = Crown weight in air ÷ WL Concept: This is a second method of determining specific gravity. Instead of using the weight of an equal volume of water we will use the apparent “loss of weight” of the crown when it is immersed. In principle the weight of the water in the first method should equal the observed loss of weight of the cube in the second method. In practice the two methods often will not agree, however, so be on the alert for possible sources of experimental error (in both methods). Procedure (if you are ahead of the demonstration of this, try your best in advance): a. Set up a triple beam balance so that it just hangs over the edge of your lab table so that the crown can be suspended by the thread several feet beneath the center of the weighing pan. b. Attach the thread to a paper clip, which in turn is attached to the bottom of the scale. Attach the paper clip directly under the center of the pan on the scale to obtain an accurate reading of the weight of the crown in air (make sure the lab assistant checks out your paper clip position). c. Attach the crown to the loose end of the thread in order to weigh the crown in air. Record the weight in the data table below. d. Fill the beaker about two-thirds with water, and raise the beaker up underneath the crown until the crown is completely immersed. Make sure that the crown is completely under water, but not touching the sides or the bottom of the beaker. Record the weight of the crown in water in the data table below. e. Calculate the specific gravity and repeat steps (c) through (d) for Trial 2.
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Data and Calculations: Line # Trial 1: Data 1 Crown weight in air 2 Crown weight in water
3 4
Results/units grams grams
Trial 1: Calculations Weight-loss of crown Specific Gravity
grams
Line # Trial 2: Data 1 Crown weight in air 2 Crown weight in water
3 4
Results/units grams grams
Trial 2: Calculations Weight-loss of crown Specific Gravity
grams
Analysis: 1. If the crown touches the sides or bottom of the beaker, the calculated specific gravity would be: ___ too high; ___ too low. Explain.
2. If the crown were not completely immersed or underwater, the calculated specific gravity would be: ___ too high; ___ too low. Explain.
3. What are possible sources of experimental error for Part II?
4. Which method do you think is likely to be more accurate, I or II? (Circle best answer) Why? 5. Based on your experience with these two different approaches to the same problem, how would you answer someone who says that in science there is always one “right” way to do something?
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6. Assuming that each kind of material has its own characteristic specific gravity, determine the composition of your crown. Is it gold? Or did we cheat you by giving you a cheap metal? This, of course, was the reputed motivation for Archimedes’ discovery. Guess which metal you have from this SG table (circle it): 1.00 water (the standard for SG) 2.70 aluminum 7.25 iron 8.36 brass 10.50 silver 11.34 lead 19.31 24 karat gold 7. Use the above table for the theoretical value of your specific gravity, and use your own results as the observed value in order to calculate percent error (if it comes out negative, just change the sign to positive). Percent error = (Theoretical – Observed) x 100 Theoretical If it comes out negative, just ignore the negative sign and make it positive. What is the percent error for the average result of Part I? What is the percent error for the average result of Part II? Review 1.
What is the modern definition of specific gravity?
2. True or False? ___ Buoyant force equals the weight of an equal volume of water (Part II). ___ The weight-loss of a submerged object equals the buoyant force (Part II). 3. If an object doubles in size, its specific gravity.... ___ Doubles; ___ is squared; ___ is halved; ___ remains the same. Is specific gravity an intensive or extensive property? (circle one; see prelab) To check out The lab assistant/instructor will look over your lab & lab report to check for problems. Obtain approval from the lab assistant/instructor to leave (initials on your lab report). Clean up your tables and follow any specific instructions given, including: dump out all water tidy up and dry off tables turn off calculators 289
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Archimedes: Lab Report • Name: _________________ Credit is possible only if lab assistant/instructor’s initials are here: Initials _______ Page 1 of 2 Method #1: Using water displacement to find SG Line # 1 2 3
Trial 1: Measurements Crown weight Initial weight of overflow cup + water Final weight of overflow cup + water
Data grams grams grams
4 5
Trial 1: Calculations Weight of equal volume of water Specific Gravity
grams
Line # 1 2 3
Trial 2: Measurements Crown weight Initial weight of overflow cup + water Final weight of overflow cup + water
Data grams grams grams
4 5
Trial 2: Calculations Weight of equal volume of water Specific Gravity
grams
Analysis 1. If you weighed the crown AFTER collecting the overflow water, your calculated specific gravity might be: ___ too high; ___ too low 2. If some water splashed out of the side-arm flask and was not caught in the overflow cup when you lowered the crown in, your calculated specific gravity would be: ___ too high; ___ too low 3. What are some other possible sources of experimental error with this method of determining specific gravity?
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(TURN THIS IN FOR CREDIT FOR LAB): PAGE 2 of 2 Method #2: Using buoyancy to find SG Line # Trial 1: Data 1 Crown weight in air 2 Crown weight in water
3 4
Results/units grams grams
Trial 1: Calculations Weight-loss of crown Specific Gravity
grams
Line # Trial 2: Data 1 Crown weight in air 2 Crown weight in water
3 4
Results/units grams grams
Trial 2: Calculations Weight-loss of crown Specific Gravity
grams
Analysis 1. If the crown touches the sides or bottom of the beaker, the calculated specific gravity would be: ___ too high; ___ too low. 2. If the crown were not completely immersed or underwater, the calculated specific gravity would be: ___ too high; too low. 3. What are possible sources of experimental error for Method #2? 4. Which method do you think is likely to be more accurate, 1 or 2? (circle one) Why? (Hint: which method calculated a smaller experimental error? other reasons?) 5. Based on your experience with these two different approaches to the same problem, how would you answer someone who says that in science there is always one “right” way to do something? 6. Guess which metal you had from this SG table (circle it): 1.00 water (the standard for SG) 2.70 aluminum 7.25 iron 8.36 brass 10.50 silver 11.34 lead 19.31 24 karat gold 292
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Wednesday November 10 Chaisson, Ch. 14: The Milky Way Galaxy Begin be reading “Introduction to Part 4: Galaxies and the Universe” (p. 362-363) Then read the entire chapter 4 and use all of the study helps provided by Chaisson.
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Monday November 15 Lab 10: Privileged Planet Film Come to lab this week to receive your free copy of the lab report. This film was released after the publication date of my packet.
Privileged Planet, Ch. 7: Star Probes (p. 127b-140) When you encounter two underlined options, circle the correct answer. Example: low / high 1) Circumstellar Habitable Zone (CHZ): that region around a _______ where liquid ______ can exist continually on the surface of a terrestrial planet for at least a few ____________ years. a) CHZ inner boundary: where a planet loses its _______ to space through a runaway greenhouse effect b) CHZ outer boundary: where oceans ________ or carbon dioxide _______ form (then a vicious cycle begins of increasing coldness until the oceans freeze over) 2) Realistic CHZ modeling doesn’t mean just keeping liquid water: more prerequisites below a) Avoid lethal effects of asteroids i) Low / high eccentricity of a planet helps it stay safely distant from the asteroid belt ii) Mercury and Venus: (1) Fewer/more asteroids hit them due to their greater distance from the asteroid belt (2) But because they are close to the Sun, asteroids and comets hit harder / softer iii) Earth (1) Has low / high eccentricity; i.e., its orbit is nearly circular / elongated (circle one) (2) Is in a sweet spot not too far from or close to the ______________ belt b) Keeping liquid water within CHZ isn’t as easy as earlier astrobiologists assumed because i) A planet near outer CHZ edge needs more carbon __________ (greenhouse gas) to prevent deep freeze, but large mobile creatures require oxygen-rich atmosphere with low carbon dioxide concentration ii) A planet must be quite near inner edge of CHZ to have sufficient ________________ energy to support a complex enough food web for the maintenance of complex life iii) Thus, so-called CHZ very well may be much narrower than presently assumed (due to tighter constraints such as those mentioned in the two previous points) c) Many factors must be “just right” during solar system formation to get a habitable planet i) Rocky planets might not be able to do the following at arbitrary distances from star (1) Form in the first place (2) Remain in a stable, near-circular orbit 295
ii) A planet formed close to the asteroid belt of a solar system would have an initially high carbon and water endowment that would probably have resulted in a deep ocean and a thick _________ dioxide atmosphere, likely leaving a dead world iii) Asteroid impact rates must be fine-tuned within a narrow range of values: (1) Right time in planet’s history (2) Size & frequency of asteroids Conclusion: CHZ depends upon much more than intensity of light from host star 3) Realistic CHZ modeling must begin with a host star quite like our Sun because a host star (the sun of a solar system) plays two (a & b below) essential life-support roles for that solar system that must be “just right” to have a habitable planet in that solar system. (p. 132-136a) a) A host star is the source of many chemical elements necessary for life i) Under gravity pressure, stars fuse nuclei of atoms in their interiors to build elements ii) Stars spend most of their lives fusing the abundant nuclei of hydrogen atoms (protons) in a phase of a star’s life called the “__________ sequence.” Because hydrogen is so abundant, the main sequence is the longest lasting phase. b) A host star can be a steady supplier of energy useful to life (think of photosynthesis) i) While on the main sequence, a star’s ______________ doesn’t change much ii) When will our Sun brighten 1000s of times? _________________ (A lethal change) iii) Amount of time a star spends on the main sequence depends primarily on its _______ (1) Stars with twice the Sun’s mass remain on main stable sequence a _______ years (2) Stars with 1/2 Sun’s mass remain on main stable sequence about 100 billion years 4) What is the Circumstellar Continuously Habitable Zone (CCHZ) in contrast to the CHZ? 136b-137: Optional reading on the weak anthropic principle (we will cover this later) Latent Ruler: Earth’s Orbit around Sun is a Baseline for Measuring Cosmos (p. 138-140) 1) Not only is our Sun (and Earth’s relationships to it) well suited for Earth’s habitability, but also many of these same features turn out to be great for scientific ________________. For example, the Sun-Earth configuration is near optimum for intelligent creatures like humans to use stellar trigonometric ___________ to calculate distances to nearby stars (see figure 7.2 in text). Be prepared to explain this method of distance calculation. Our “Distances to Celestial Objects” lab reinforces this method. 2) What evidence exists that such trigonometric measurements are better suited to the progress of science when made from Earth rather than any other planet in our solar system?
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3) When did astronomers first attained reliable stellar parallax measurements? What new technology made reliable stellar parallax measurements easy to make? When did we begin to collect 1000s of such measurements to nearby stars? What evidence exists that our local part of the universe was designed for our scientific discovery capabilities through the parallax method of calculation and its related methods?
Privileged Planet, Ch. 8: Galactic Habitat Introduction to the Structure of Galaxies (p. 141-146) 1) Our Own Milky Way Galaxy is One of Billions of Galaxies a) Galileo’s telescopic discovery: “Milky Way” is a vast number of distinct _________ b) We see “Milky Way” when we look lengthwise through our own ________________ c) Other galaxies which were previously identified as “_________” (fuzzy patches in sky) 2) Types of Galaxies a) Ellipticals b) Irregulars c) _________, such as ours. 3) Our Spiral Milky Way Galaxy a) Most of its stars are located in its flat thin disk, with a thickness of 1% of its diameter b) We live in the thin disk, close to its midplane, half way between Galactic center and edge c) Spiral pattern: density wave phenomenon, like concentrations of _________ that form on crowded roads 4) Milky Way Galaxy’s Four Regions (see figure 8.1 on page 144): a) Halo i) Extends beyond edge of the disk of the galaxy and above and below disk; basically, the halo is all the sparse regions of the galaxy that are outside the nuclear bulge and thick and thin disks ii) Contains only old metal-poor stars in highly elliptical orbits; no new stars born here b) Bulge (visible in “flat” or “on edge” view in diagram above, but looks different in each) i) Oblong bulge occupying the central part of the galaxy (has black hole near its center) ii) Contains stars spanning a large range in metallicity from about one-tenth to three times the value of our Sun. Unlike the halo, some star formation continues there today. The orbits of its stars are also elliptical, but less elliptical than those in the halo c) Thin ______ i) Inner, denser part of disk that runs from nuclear bulge to just short of the halo’s end ii) Contains the greater diversity of objects, including most of the stars in the Milky Way iii) We are in the thin disk, just a bit off the midplane, but between spiral arms d) __________ disk i) Outer, less dense disk that runs from the nuclear bulge to just short of the halo’s end ii) Is more puffed up with older, more metal-poor stars (relative to thin disk stars)
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Our Galactic Perspective is Better than Most: High Measurability (p. 146b-151) 1) Much of the introductory information about galaxies would be impossible to see and know from most positions within any galaxy. Where is our observation platform located now and how is it so special? 2) The Sun (and Earth) is heading away from the galaxy’s mid-plane, having just crossed it. 3) This roughly mid-plane position has very low gas and dust density compared to most other local regions in mid-plane (this gives us a clear view of our own and distant galaxies) 4) If we were located farther from the mid-plane, the Milky Way band would appear broader and thus obscure many distant galaxies from our view, though some of the previously hidden distant parts of our own galaxy would now come into view. The trade-off would not be good for cosmology; it is best to be where we are. 5) We are about half way between the center and outer edge (edge of halo) of our galaxy. If we were close to the densely packed galactic center, much of the universe would be obscured. 6) Comparing other galaxies types helps us understand our own home in the Milky Way galaxy a) Less flattened galaxies (irregulars and ellipticals) lack the simple rotational dynamics of disk galaxies b) Elliptical galaxies contain stars with a wide range of orbits, most with very eccentric and inclined orbits, which contain relatively less gas and dust (for observers inside this kind of system, no law relates the distance of a particular object to its observed radial velocity) c) Irregular galaxies: very irregular dynamics and patchy distributions of stars and nebulae (observers in such a galaxy would have a very difficult time seeing beyond their area) 7) In short, we occupy the best overall place in the Milky Way Galaxy, which is itself the best type of galaxy to learn about (1) stars, (2) galactic structure, and the (3) distant universe simultaneously; these are the three major branches of astrophysics. Galactic Habitable Zone (GHZ). (p. 151a-152) Main Point: Most other places in a galaxy (other than about where we are in ours) are less suited for life and scientific discovery for roughly the same reasons (correlation) • • • •
Galactic ______________ Zone (GHZ): part of a galaxy within which life can be maintained Not all parts of GHZ have life potential (must also be in _______________ Habitable Zone) CHZ has a lot to do with maintaining liquid water on the surface of an Earth-like planet GHZ boundaries, however, are set by different factors: o Needed planetary building blocks (see details in next section) o Galactic threats to complex life
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Building Blocks Needed for Planet Formation (p. 152b-159a) 1) Here is how the basic building blocks of a solar system are built a) Big Bang produced hydrogen and helium very early in the history of the universe b) Next 13 billion years: other elements produced within successive generations of stars and spread around; the abundance of metals relative to hydrogen in the local interstellar medium—that is, its “metallicity”—has gradually increased c) Today, _______ make up about 2% of mass of gas in Milky Way’s interstellar medium 2) A habitable solar system requires metallicity that is not too high or low in that part of galaxy a) Interstellar cloud (gas & dust) collapse produces new stars and their planets. A metal-rich cloud is more likely to fragment into smaller cloudlets to form relatively more low mass stars (the sort that are more likely to be form habitable solar systems). b) But if metallicity is too high, then too many planetesimals (the early asteroid-sized planetary building blocks) and planets will form in a solar system, produce orbital dynamics unfavorable to habitable planets (trouble comes primarily from migrating giant planets and too frequent bombardment from asteroids and comets) c) Earth-size terrestrial planets unlikely to form in a system condensing out of a more metalpoor cloud d) But if metallicity too _________: likely to get a chaotic traffic jam of uninhabitable planets e) Few stars with metallicities below the Sun’s have ________ planets (these bullies need to be in a solar system if a habitable terrestrial planet is to be possible). f) Metallicity of interstellar gas declines with increasing distance from Galactic _________. g) Earlier in history of Milky Way there was lower metallicity in any given part. Thus, given the previous point, habitable metallicity is only found closer to Galactic center as we go back in time. h) But inner part of galaxy is inhospitable to life for other reasons (e.g., lethal radiation). 3) Distribution of the chemical elements also must be fine-tuned if life is to be possible a) The Earth is mostly iron by mass. The cosmically abundant and life-essential volatile elements, hydrogen, carbon, and nitrogen, are very rare in the Earth. What really counts for habitability is their abundance in Earth’s crust, which was made possible by the asteroids and ________ that delivered most of them late in Earth’s formation. b) Most abundant elements in Earth were produced primarily in supernovae. Supernovae rate was ________ earlier in Milky Way history (and ratio of the two has changed): this narrows window of opportunity for production of habitable solar systems in the Milky Way because the rate of supernovae can’t be too high or low and there are limits to the acceptable ratio between the two kinds of supernovae. Galactic Threats to the Survival of Complex Life (p. 159b-161) Even if all the necessary building block elements are in the right place at the right time to build a terrestrial planet of the Earth’s mass and orbital characteristics, you can’t call it “habitable” until you can know that the planet is largely free of threats to complex life in the long run.
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Major long-range threats: (1) impacts by large asteroids/comets, (2) transient _________ events 1) Impacts by large asteroids or comets a) Example on Earth: Cretaceous/Tertiary extinction 65 million years ago (dinosaurs went extinct), was the result of an impact by a large extraterrestrial body (asteroid or comet) b) Source of comets in our Solar System: two reservoirs, the Kuiper Belt and the Oort cloud i) ________ Belt is just beyond Pluto’s orbit ii) _______ cloud: highly elliptical orbits (nearly parabolic); spend most of their time far from the Sun, typically at about twenty thousand AUs. Since comets in the Oort cloud are only weakly bound to the Sun, it doesn’t take much to perturb them (mainly Galactic-scale perturbations like encounters with Giant Molecular Clouds) and send them into possible collision course with Earth c) Asteroid threat in our Solar System depended i) Timing and details of Jupiter’s formation and orbit (see Chapter 4) ii) Galactic scale perturbations probably have little effect on the dynamics of asteroids. 2) High-energy radiation can also eliminate habitability (p. 161b) a) Earth’s __________ field and atmosphere shield its surface life from most dangerous radiation b) But certain extraterrestrial radiation bursts can damage the ozone layer in our upper atmosphere, resulting in more destructive radiation on the Earth’s surface c) We call such bursts energetic transient radiation events Optional: pages 162-166a The GHZ: An Exclusive Country Club within our Galaxy (p. 166b-167a) 1) Inner part of a galaxy suffers from greater radiation & comet collisions, thus Earth-size planet is less likely to form in a stable circular orbit. 2) Outer galactic regions are safer, but stars there will be accompanied by only relatively small terrestrial planets, planets too small to retain an atmosphere 3) GHZ is probably a fuzzy annulus (or ring) in the thin disk at roughly the Sun’s location, a ring whose habitability is itself compromised at several points where the spiral arms cross it 4) If proximity to the corotation circle is important for habitability, then this thin and often broken ring could be narrower still 5) GHZ offers best overall location for science 6) Based on recent scientific trends, the estimated size of the GHZ will continue to shrink
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Other Galaxies (p. 167b-168) 1) Most other galaxies are less likely to have significant habitable zones (GHZs) a) 99 percent of galaxies in the local universe are less __________. Thus in general, less metal rich, than the Milky Way Galaxy (since the average metallicity of a galaxy correlates with its luminosity). So entire galaxies could be devoid of Earth-size planets. b) Stars in elliptical galaxies have less ordered orbits, thus: i) More collisions ii) More likely to visit galaxy’s dangerous central regions iii) More likely to pass through interstellar clouds at disastrously high velocities c) In many ways, ours is the optimal galaxy for life i) Late-type spiral galaxy with orderly orbits ii) Comparatively little dangerous activity between spiral arms iii) High overall metallicity 2) Interactions between galaxies can also affect habitability. Andromeda galaxy: close encounter with our galaxy in about three billion years, which may: a) Dislodge most stars in the disks of both galaxies from their regular orbits b) Feed fresh fuel into our galaxy’s central ________ hole and bring it back to life, making that region of our galaxy even less desirable. c) Thus, the Milky Way Galaxy’s GHZ may only last another three billion years. Conclusion
Other regions of our galaxy & other regions of nearby cosmos: differ much from our part Precious few of those places appear as amenable to complex life as ours We occupy some of the best real estate in the Galaxy for doing astronomy
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Wednesday November 17 Chaisson, Hubble’s Law (p. 420-426a) Read the first part of this chapter and then answer these questions at the chapter’s end: P. 442: Self-Test, questions 1-3 P. 442: Review and Discussion, questions 1-4 P. 443: Problems, questions 1-2
Chaisson, Ch. 17: Cosmology Read the entire chapter and use all of the study helps provided by Chaisson.
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Monday November 22 (no lab this week) Optional Skywatch Lab Due Monday Extra Credit Skywatch: Found near the end of the Packet. Due today in class!
Privileged Planet, Ch. 9 & 10: Big Bang & Fine-Tuning (selected pages) Privileged Planet: Ch. 9: Our Place in Cosmic Time, p. 169-178a What Edwin Hubble discovered in the early 20th century 1) Measured distances to certain stars in nebulae (using methods beyond stellar parallax) 2) Concludes: many of these “nebulae” are separate galaxies, not star dust clouds in our galaxy 3) Observed redshift of these separate galaxies, thus all are moving away from us 4) Spectra of light from other galaxies shifted (stretched) toward _______ wavelength (red end) 5) Cause of red shift: acceleration of all galaxies away from us 6) Analogy: sound waves shift to longer (lower) tones when car drives by you 7) Spectra means the profile of colors, due to different wavelengths, that are inside a beam of light and that a prism or group of rainbow-producing raindrops in the sky reveal 8) Hubble was first to systematically compare: a) distance measurements b) redshift observations 9) The more distant a nebula (galaxy), the more strongly it was _____-shifted 10) Thus, the universe is expanding, he concluded (steps to this conclusion listed below) a) More distant galaxies show us the universe as it was further back in time, because light takes billions of years (long time) to travel billions of light years (long distance) b) More distant galaxies accelerating away from us faster than closer galaxies c) Thus very early in the history of the universe, the entire universe was expanding very rapidly, then it expanded less and less rapidly with the progress of time d) This is the sort of thing we observe in an explosion: very high acceleration at first, but that is quickly reduced
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11) Later this theory, developed by Hubble and others, came to be known as the Big Bang. The theory was opposed very early by atheists (and pantheists like Einstein) who disliked the idea of the universe having a beginning (the initial moment of the Big Bang) Einstein’s Theory of General Relativity fits with Hubble’s Discovery of Expanding Cosmos 1) General Relativity supported by bending star light as seen in solar eclipses (chapter 1) 2) General Relativity predicted that the universe was either expanding or contracting 3) Einstein introduced a “fudge factor,” a variable called the cosmological constant, invented just to keep the universe in a steady changeless condition (which his religion of pantheism suggested) 4) Einstein later admitted his “fudge factor” was “greatest blunder” of his career and agreed the universe must be expanding and must have had a beginning 5) Like Einstein, most astronomers of early 20th century believed in a static/eternal universe 6) Some scientists said it was anti-scientific to doubt eternity of universe; this view failed Discovering the Echoes of Creation: Triumph of Big Bang Theory (p. 174b-178a) 1) Steady state model (no Big Bang beginning): Fred Hoyle and others in 1940s 2) Matter spontaneously appears in the space between _________ as universe expands? 3) This would maintain a constant matter ___________ on large scales and accommodate the observations of an expanding universe, but avoid a beginning 4) For several decades, no direct evidence to decide between Big Bang and steady state 5) 1965, Penzias/Wilson, discover Cosmic _____________ Background Radiation (CMBR) 6) Detected radiation in microwave part of the electromagnetic spectrum, thus called CMBR 7) Light visible to humans comes from another part of the electromagnetic spectrum 8) CMBR: _____ degrees above absolute zero (utterly cold, almost absolutely cold) 9) Big Bang, not Steady State model, had predicted CMBR, thus death of steady state
Privileged Planet: Ch. 10: Tuned for Life/Discovery, pages 195-2 Universe Creating Machine: Story to Illustrate Universe “Fine-Tuned” for Life 304
1) Each knob (dial) on machine has countless numbered lines on it (countless settings) 2) Kinds of knobs (dials) include a) Gravitational Force Constant b) Electromagnetic Force Constant c) Strong Nuclear Force Constant d) Weak Nuclear Force Constant 3) All dials must be set precisely to get a habitable universe (fine-tuned universe). Example: Gravitational force dial must be set “just right”: a) If it had been slightly weaker, expansion after the Big Bang would have dispersed matter too rapidly, preventing the formation of galaxies and planets b) If it had been slightly stronger, universe would have collapsed in on itself 4) Ratio of various universal forces must be “just right” for possibility of life in a universe. Example: Ratio of gravitational force to electromagnetic force 5) Local vs. universal fine-tuning of the universe a) Local / universal (circle one) fine tuning: just-right features of some places in universe (e.g., CHZ in Ch. 7 or GHZ in Ch. 10) b) Local / universal (circle one) fine tuning: just-right features of cosmos as a whole (Ch.10) Optional: pages 197b-200a Fine-Tuning of Four Fundamental Forces (p. 200b-) 1) Strong nuclear force (study this one carefully using outline below) 2) Weak nuclear force (combined with weak nuclear force as “electroweak”) 3) Gravity The Strong Nuclear Force: Study this force more carefully than the others (notes below) 1) Summary Description: Holds protons and neutrons together in the ___________ of atoms. Overcomes (at short range) electromagnetic force and binds the otherwise repulsive, positively charged protons together. 2) If strong nuclear force were just slightly weaker than what it is, then … a) Universe would have fewer stable chemical elements and isotopes b) No element beyond ____________ could be produce in the universe c) Thus, life would not be possible d) But also measurability would be much lower: In a universe with a weaker strong nuclear force, each element would have fewer stable isotopes. The rich variety of chemical
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elements and stable isotopes significantly helps researchers measure and quantify Earthly and cosmic phenomena. 3) If strong nuclear force were slightly stronger than what it is, then … a) In early moments of Big Bang, all hydrogen would have become helium-2 b) Or other equally bad results that would eliminate the possibility of life Multi-Tuning (p. 205a-208a) 1) Description: In most analyses of the fine-tuning of the force strengths and constants of the universe, only one parameter is adjusted at a ________ (to make the problems easier to solve). This would correspond to changing one ________ at a time on our Universe Creating Machine, while leaving the other dials unchanged. Even taken individually, each of these examples of fine-tuning is impressive. But in the real universe the values of all the constants and force strengths must be satisfied simultaneously to have a universe hospitable to life. 2) Each physical parameter (dial on Universe Creating Machine) must be “just right” individually 3) To get all these parameters (dials) set “just right” simultaneously is even more unlikely 4) Many of these features also have to be “just right” to have a measurable universe (but we skip details of this correlation argument for US 311) Optional: pages 208b-210a Discoverability (p. 210b-212a) 1) Basic Description of Discoverability. In Chapter 1 we briefly distinguished among observability, measurability, and discoverability. Paul Davies, perhaps more clearly than any other writer, has pointed to the features of our universe that have facilitated the discovery of the laws of nature. Discovering a law has much to do with its simplicity. 2) Simple Mathematical Formula for Gravity. The simple inverse square law of gravity helped lead to the early discovery of the universal Law of Gravitation. The historical and conceptual path from Kepler to Newton to Einstein was facilitated, then, not only by the particular characteristics of our local environment but also by the mathematical simplicity of gravity. At the same time, the laws of physics are not so __________ that they prohibit the variety and complexity necessary for life. 3) Kepler’s Laws of Planetary Motion. Kepler’s formulation of his laws required that macroscopic bodies in our universe are well described by “classical” laws, that is, laws with distinct and measurable positions and motions. Davies argues that one should not just assume that any universe appearing from a quantum initial state would later exhibit classical properties.
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4) Stability of natural laws (not total chaos) is required for habitability: The properties of the most fundamental units of complexity we know of, quarks, must remain constant in order for them to form larger units, protons and neutrons, which then go into building larger units, atoms, and so on, all the way to stars, planets, and in some sense, people. The lower levels of complexity provide the structure and carry the information of life (e.g., DNA). 5) But our universe does not merely contain complex structures; it also contains elaborately nested layers of higher and higher complexity. a) Consider complex carbon atoms within still more complex sugars and nucleotides within more complex DNA molecules within complex nuclei within complex neurons within the complex human brain. b) Such “complexification” would be impossible in both a totally chaotic, unstable universe and an utterly simple, homogeneous universe of, say, hydrogen atoms or quarks. c) Surprisingly, our universe allows such higher order complexity alongside quantum indeterminacy and non-linear interactions (such as chaotic dynamics)—which tend to destabilize ordered complexity. 6) Why do such simple and elegant mathematical equations work so well in scientific theories? a) E. Wigner called it the “____________ effectiveness of mathematics in natural science.” b) It is only unreasonable if one assumes that the universe is not underwritten by reason Optional: 212b-215a Our Place in Cosmos: Are humans so tiny as to be virtually meaningless? No! (p. 215b-218) 1) Believers in naturalism (nature is all there is) routinely argue that because we are small compared to a vast universe, we as humans are therefore __________________ 2) Actually, we are near the ___________ of hierarchical set of scales within the cosmos: from quarks to the limits of the observable universe. Our middle size maximizes the total range of structures we can observe—both large and small. This suggests we are special. 3) If we were only about ________ orders of magnitude smaller (1/100th our current body size), the realm beyond the Earth’s surface might be largely unavailable for investigation 4) Maximum _______ resolution of an eye is a limiting factor; we are nicely placed in size now 5) Ironically, a tiny being would also have a more difficult time detecting the smallest particles because labs needed to detect them must be built by creatures about our size and dexterity 6) Science fiction to the rescue? Imagine some larger, more ethereal life form, such as the ghostly electromagnetic beings in Hoyle’s The Black Cloud or the giant floaters in Jupiter’s atmosphere, as Carl Sagan imagined in Cosmos. But even if such creatures could exist, they would be unlikely to be as _____________ of their environment as we are (probably a prerequisite for most of science).
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Wednesday November 24: Thanksgiving Enrichment Activity • Not Required • No Extra Credit Thanksgiving Project Invite some Muslims to your home for Thanksgiving. Read them the “Navigation by Fixed Stars” passage below (quoted from BCP, Unit 1, US 311 Course Packet). Talk about how Christians and Muslims looked to the stars God created for help in finding their way. Talk about how we need guidance in this life from something/someone bigger than ourselves. Affirm the monotheism of Islam, but then talk about the historic claims of Jesus Christ. Jesus clearly claimed to be God. You can’t just call Jesus a good man or a great prophet. When you clearly understand the claims of Christ, you realize that he was either Lord, a liar, or a lunatic (following a line of reasoning from C. S. Lewis). Share your testimony. Talk about the original idea of Thanksgiving: giving thanks to the one true God in a multicultural gathering. Navigation by Fixed Stars From a given location on Earth, a star rising above a particular reference point on the horizon on a given day will appear to rise at that same location every day. Sailors learned to guide their ships according to the rising and setting locations of fixed stars. This allowed them to determine their own position in latitude relative to their home or harbor. For example, the Pilgrims who landed in Plymouth Rock expected a relatively mild winter, comparable to that of England, for during their ocean journey they had maintained their ship’s direction on the same latitude. However, due to unanticipated effects of ocean currents, the New England winter is much harsher than that in the same latitude in England. Arabian nomads relied on the stars to navigate across trackless desert sands. The Quran affirms (6:95): “It is God who has appointed for you the stars, that by them you might be guided in the shadows of land and sea.”
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Monday November 29 Makeup Quizzes for Whole Semester Come to my office to take makeup quizzes if you properly reported your excused absences within the time frame specified in the syllabus. Do not come to my office if you forgot to follow the syllabus on this matter.
Lab 11: Foucault Pendulum Introduction: This required do-it-yourself lab is due in class at the time indicated in the Schedule. Do not come to room 214 for this lab. Rather, go to the Foucault pendulum located just outside the planetarium and observe it for about 2 hours. To save time, when you first arrive at the pendulum to do the lab, notice which pegs are about to be knocked down and write down the times (on your watch) at which these pegs are knocked over while you are reading this lab and observing (this is critical data for the lab). Later in the lab you will be asked to label a drawing that shows where the pendulum was swinging when you first arrived. Each student must turn in his/her own lab report (it is okay to get help from others, but you must personally observe the events). Keep this lab description for final exam study purposes (don’t turn it in to me). To avoid getting a “0” on this lab (or only partial credit), be sure to completely answer each question with appropriate words and drawings. There are 60 equally-spaced peg positions in the pendulum setup and your job is to observe when pegs are knocked down as prescribed by the lab (2 pegs on one side of the circle; I suggest south, but the north side is okay too) and to think about the lab at other latitudes (as set up in thought experiments in the lab text). Remember to take things to study during the pendulum lab (this is a great time to study for the Nat Sci final in the presence of other students in your section and other sections). Turn in the pendulum lab at the beginning of class on the day of the final exam. Ask me questions at the beginning of class if you have any doubts about the lab. You will be tested on this lab too! Thought Experiments to Perform While You are Observing the OBU Pendulum (1) Thought Experiment #1: The Oscillating Yo-Yo Model Imagine that you have yo-yo (or a heavy object at one end of a length of string). We encourage you to actually try this, rather than just think about it (there should be a yo-yo hanging near the pendulum display--come see me if there is not). Swing the yo-yo to and fro to mimic the pendulum in the Wood Science Building (hold the end of the string in your fingers and cause the yo-yo to oscillate back and forth; don’t cause the yo-yo to climb up and down the string). While maintaining a constant rhythmic motion, twist the string in your fingers through about a 180° rotation and record what you see below. (An alternative method would be to walk around to the other side of the yo-yo, dodging the yo-yo as you cross over, until you are 180° from where you were at the start): 309
(a) Is the yo-yo still swinging in the same direction as initially? (b) Did the yo-yo twist around with the string (rotate on the string’s axis)?
(2) Thought Experiment #2: Apply the Yo-Yo Model to the Foucault Pendulum The inertia of the yo-yo kept it swinging in the same direction (the same plane of oscillation) despite the twisting effect from your fingers. In a similar manner, the inertia99 of the heavy pendulum bob keeps it swinging back and forth in the same plane, even while the Earth rotates and twists the pendulum’s point of attachment. This causes the pendulum bob to “give in to” the “twist” of its cable by slowly spinning on its axis, but this action does not alter the direction of the swing of the pendulum (plane of oscillation). (3) Thought Experiment #3: A Foucault Pendulum at the North Pole (a) Imagine an enormous Foucault pendulum at the north pole (b) Visualize the pendulum’s plane of swing remaining the same with respect to the fixed stars while Earth rotates counterclockwise beneath the pendulum. Pretend that a circle of huge pegs attached to Earth’s equator extend northward at a tangent to Earth so as to stick up all the way to the point that the swinging pendulum at the north pole can encounter that circle of pegs and knock them down. (c) As Earth silently rotates underneath the pendulum (without affecting the pendulum’s plane of swing), the imaginary circle of pegs that extend up around the pendulum from Earth’s equator rotates around the pendulum at the same rate as Earth itself rotates on its axis. The pegs in the circle are knocked down as they enter the path of the swinging pendulum. The pegs in this imaginary circle are analogous to the pegs around the Wood Science pendulum (particularly if our science building were located at the north pole). The room, along with its circle of pegs, rotates around the pendulum; eventually all of the pegs get in the way of the pendulum and are knocked down. (d) Although actually maintaining a constant direction of swing with respect to the fixed stars, the pendulum appears to change its direction with respect to the pegs. Actually the pegs share in the counterclockwise rotational motion of Earth and it is they that are moving around the pendulum, rather than the pendulum changing its plane of oscillation with respect to them. Apart from modern science, we believe ourselves to be standing still next to the pegs, instead of rotating with Earth. (i) How long will it take for our imaginary north pole pendulum to knock down all the pegs once? (ii) Why would the pendulum knock down all the pegs twice with every 360° of Earth’s rotation? (4) Thought Experiment #4: A Foucault Pendulum at the Equator (a) Imagine a Foucault pendulum at the equator. (b) The ground underneath this pendulum is moving eastward at thousands of miles per hour as the Earth rotates on its axis once daily. 99 The natural tendency to resist change in motion (Isaac Newton’s "first law of motion").
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(c) Although the ground moves eastward, it does not rotate underneath the pendulum. Thus the pendulum shares this continual eastward inertial motion with Earth. (i) Would a pendulum at the equator appear to undergo any change in its direction of swing at all? Why? (ii) Is a pendulum swinging in Shawnee going to behave like the one at the north pole, like the one on the equator, or will it have an intermediate behavior? First-Hand Examination of the OBU Pendulum (1) Answer these questions based on a reading of the explanatory poster displayed in the OBU pendulum exhibit area: (a) When and where did Jean Foucault first successfully (with decisive results) perform this experiment? (b) What did Foucault prove and how did he prove it? (c) What significance does this have for the acceptance of Copernican astronomy? (2) The Intermediate Rotational Period of a Foucault Pendulum in Shawnee. At a latitude intermediate between the north pole and equator, such as Shawnee, the ground beneath a Foucault pendulum (and the whole Wood Science building) undergoes a combination of motions, both eastward (as at the equator) and rotary counterclockwise (as at the north pole). A Foucault pendulum at the Earth’s north (or south) pole would appear to move through a complete rotation of its plane of oscillation in exactly 24 hours. As seen from Shawnee, will a complete rotation of the pendulum appear to take more or less than 24 hours? Explain your answer before doing any of the calculations below. (3) Discover the Period of a Complete Rotation of the OBU Pendulum. Observe our pendulum for about 2 hours (you have already observed it for part of this time if you followed our suggestion of reading the first part of the lab as you began your observations). Of course, you may read books or do whatever you please (sing, meditate, etc.) during the remainder of your 2 hours at the pendulum. The rest of the lab assumes that you are positioned north of the pendulum so that you are facing south (this puts east on your left and west on your right). All of the remaining questions pertain only to the south half of the circle of pegs (disregard pegs on north half of circle).100 Also, if the pendulum causes a peg to tip without falling (delaying that peg’s knockdown significantly; a rare event, but one that does happen), then count the first moment when it grazed and partially tipped the peg as the time of peg knock down. Below is a drawing of an ellipse the represents the circle of pegs as viewed from your sitting or standing position. Label and answer the questions on this drawing.
100 The north half of the circle of pegs represents that half of the apparent motion of celestial bodies (such as the Sun) that appears to go around and underneath the other side of Earth.
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South
East
West
North
Label as directed on the above drawing (1) Draw a line to show where the pendulum was swinging when you first arrived and label the line with your time of arrival. (2) Notice that there are 30 peg positions (whether pegs are standing upright in each position or not) on the south half of the circle (between due east and due west). Mark a visible dot on the drawing for each of these 30 peg positions. You should have 30 equally spaced dots on your drawing that run through a half circle. (3) Draw an “x” mark through each dot that represents a peg that has been knocked down (include pegs knocked down before your arrival). (4) Record the time beside each peg that is knocked down while you are present (minimum of 2 such events on ONE side of the circle personally observed and recorded). (5) As seen from above, which way does the pendulum appear to be changing its plane of oscillation? __________ clockwise; __________ counterclockwise (6) Draw a line to show where the pendulum is swing when you finish the lab. Having Troubles with Mathematics? Hints at how to do the Pendulum Lab •
The mathematical technique known as unit analysis helps you keep track of the units of each number in a problem in order that you may keep straight what to divide or multiply by in order to get a correct answer.
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For example, suppose you calculate that 1 peg is knocked down every 25 minutes (this will not happen in Shawnee; it is only an example of the mathematical technique):
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1 peg / 25 minutes
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Suppose you want to figure out how many pegs are knocked down per hour. Do it this way through unit analysis:
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1 peg / 25 minutes x 60 minutes / 1 hour = z
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The minutes units cancel out and you know to get out a calculator and punch in 60 divided by 25 to get 2.4 pegs per hour. I other words, you solved for “z” and found it be 2.4 pegs per hour.
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Suppose that you figure that the pendulum appears to change its orientation at a rate of 13° per hour and you want to figure out how many hours it will take to apparently change its orientation 360°. Here is how to set up the problem to solve for “z”:
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1 hour / 13° x 360° = z
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The degree units cancel out and you get an answer to “z” in hours. To solve for “z” you punch in 360 divided by 13. The answer is 27.69 hours. This is not the answer for Shawnee, but just an example to help you see how to work a real solution for the Shawnee Foucault pendulum.
Calculations (1) How much time elapses, on average, between peg knockdowns. ______ minutes (this must be the time between 2 pegs knocked down must be on the same--not opposite--side of the circle) (2) How many pegs are knocked down in an hour (include fraction of peg, for example 3.5 pegs per hour). __________ pegs/hour (3) Is this direction of the apparent change in “plane of oscillation” of the pendulum the same as or opposite to the direction of apparent motion of the Sun around Earth? __________ same; __________ opposite (4) Calculate the time when the first peg on the south side was knocked down when the pendulum was first started in the morning. __________ a.m. (5) Through what degree of rotation would the pendulum move in 1 hour? __________ degrees/hour. (6) Through what degree of rotation would the pendulum move in 24 hours? __________ degrees/day. (7) Calculate the total amount of time required for the pendulum to rotate through 360 degrees. __________ hours (period of the OBU Foucault pendulum)
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(8) Do you expect the answer to the previous question to be greater or less for Chicago? __________ greater; __________ less (9) Suppose you are kidnapped, taken to a distant unknown place, and kept indoors with no view of the sky. Would a Foucault pendulum be of any help to you to determine your location on Earth? ___ no; ___ yes .... by latitude ___ no; ___ yes ... by longitude ___ no; ___ yes. Notice that you should transfer your lab answers to the lab report. Save your original copy to study for the final exam. I do not plan to hand back your lab report.
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Foucault Pendulum Lab Report: Page 1 of 3 Name ______________________ Date & Time of Observations ______________ Others in Your Lab Group: (1) Thought Experiment #1: The Oscillating Yo-Yo Model (a) Is the yo-yo still swinging in the same direction as initially? (b) Did the yo-yo twist around with the string (rotate on the string’s axis)? (2) Thought Experiment #3: A Foucault Pendulum at the North Pole (a) How long will it take for our imaginary north pole pendulum to knock down all the pegs once? (b) Why would the pendulum knock down all the pegs twice with every 360° of Earth’s rotation? (3) Thought Experiment #4: A Foucault Pendulum at the Equator (a) Would a pendulum at the equator appear to undergo any change in its direction of swing at all? __________ Why? (b) Is a pendulum swinging in Shawnee going to behave like the one at the north pole, like the one on the equator, or will it have an intermediate behavior?
First-Hand Examination of the OBU Pendulum (1) Answer these questions based on a reading of the explanatory poster displayed in the OBU pendulum exhibit area: (a) When and where did Jean Foucault first successfully (with decisive results) perform this experiment? (b) What did Foucault prove and how did he prove it? (c) What significance does this have for the acceptance of Copernican astronomy? (2) The Intermediate Rotational Period of a Foucault Pendulum in Shawnee. As seen from Shawnee, will a complete rotation of the pendulum appear to take more or less than 24 hours? Explain your answer.
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PENDULUM LAB REPORT PAGE 2 OF 3 (3) Discover the Period of a Complete Rotation of the OBU Pendulum. Below is a drawing of an ellipse the represents the circle of pegs as viewed from your sitting or standing position. Label and answer the questions on this drawing.
South
East
West
North
Label as directed on the above drawing (a) Draw a line to show where the pendulum was swinging when you first arrived and label the line with your time of arrival. (b) Count the total number of pegs on the south half of the circle (between due east and due west). __________ pegs. (c) Mark a visible dot on the drawing for each of these counted pegs. (d) Draw an “x” mark through each dot that represents a peg that has been knocked down (include pegs knocked down before your arrival). (e) Record the time beside each peg that is knocked down while you are present (minimum of two such events personally observed and recorded). (f) As seen from above, which way does the pendulum appear to be changing its plane of oscillation? __________ clockwise; __________ counterclockwise (g) Draw a line to show where the pendulum is swing when you finish the lab. 317
PENDULUM LAB REPORT PAGE 3 OF 3 Calculations and Conclusions (1) How much time elapses, on average, between peg knockdowns. ______ minutes (2) How many pegs are knocked down in an hour (include fraction of peg, for example 3.5 pegs per hour). __________ pegs/hour (3) Is this direction of the apparent change in “plane of oscillation” of the pendulum the same as or opposite to the direction of apparent motion of the Sun around Earth? __________ same; __________ opposite (4) Calculate the time when the first peg on the south side was knocked down when the pendulum was first started in the morning. __________ a.m. (5) Through what degree of rotation would the pendulum move in 1 hour? __________ degrees/hour. (6) Through what degree of rotation would the pendulum move in 24 hours? __________ degrees/day. (7) Calculate the total amount of time required for the pendulum to rotate through 360 degrees. __________ hours (period of the OBU Foucault pendulum) (8) Do you expect the answer to the previous question to be greater or less for Chicago? __________ greater; __________ less (9) Suppose you are kidnapped, taken to a distant unknown place, and kept indoors with no view of the sky. Would a Foucault pendulum be of any help to you to determine your location on Earth? ___ no; ___ yes .... by latitude ___ no; ___ yes ... by longitude ___ no; ___ yes.
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Chaisson, Ch. 18: Life in the Universe Read the entire chapter and use all of the study helps provided by Chaisson.
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Wednesday December 1 Privileged Planet, Copernican & Anthropic Principles, p. 247-274 Main Idea: Because the Copernican Principle has fallen on hard times, the Anthropic Principle and Many World Hypotheses have been called in to help. What help do these new approaches actually offer and with what consequences? Metaphysical Pretensions 1. Cosmology is the most comprehensive natural science: the study of the entire cosmos. Because of its grand scope, many of its guiding rules exceed what we can directly observe and must be evaluated indirectly by explanatory power, aesthetic appeal, intuition, etc. We may have doubts about these rules because they are speculative. The Copernican Principle (CP) is one such rule. 2. It is legitimate to begin cosmological investigation assuming the CP as long as one … ______________________________________________________ [complete this sentence] Hint: what is the role of “evidence”? 3. Every scientist has a worldview that guides his choice of research problems and approach to solving them. But worldviews sometimes distort evidence. Has rigid adherence to the CP harmed science? 4. What’s wrong with saying “no evidence could count against the CP because the CP is part of the very definition of science itself”? See hints below: • This is trying to acquire by definition what must be won by evidence and argument • We can’t determine reality by imposing a definition of science that restricts the questions we ask Testing Eight Copernican Principle Predictions Some scientists treat this as a CP prediction: “The same natural laws rule heaven and Earth.” This approach to science had a long history prior to Copernicus, motivated in large part by the Christian doctrine of creation. In fact the universality of natural laws is the hallmark of modern science. Medieval science slowly led in this direction away from its pagan Greek heritage. Copernicus didn’t prove this. Rather his theory appeared physically impossible until this assertion could be established (which Newton did). We will not treat the universality of natural laws as a CP prediction because it is too general. The CP entails specific predictions listed and tested below. 1. Earth isn’t exceptionally suited for life in our Solar System. Other planets in the Solar System probably harbor life as well. 321
The failure of this prediction has only reinforced how narrow are the conditions for habitability, even for planets in an ______ solar system. Some of the planets once said to diminish the Earth’s status now seem to be the __________ of her habitability. 2. Our Sun is a typical star. Prediction fails! Our Sun has a number of important, and unusual, life-permitting properties that simultaneously contribute to its measurability. These include its age, luminosity, metallicity and galactic orbit. 3. Our Solar System is typical; we should expect many others like it. Not enough data to be sure. What data we do have counts somewhat against this prediction. Up to this time the method of data collection has been biased toward disconfirmation. A fair sample of data will be available by about the year 2007. 4. Even if our Solar System is not typical, there are lots of planetary configurations that are consistent with the presence of biological organisms. Variables like the number and types of planets and moons are mainly contingencies that have little to do with the existence of life in a solar system. Evidence from Chapters 1-6 weighs heavily against this prediction. For example, the following are profoundly important for the existence of complex life on Earth: The existence of a large, well placed moon, of virtually circular planetary orbits, of a properly placed asteroid belt with certain properties, the early bombardment of these asteroids on the Earth, the outlying gas giants to sweep the Solar System of sterilizing comets and asteroids later on. 5. Our Solar System’s location in the Milky Way is relatively unimportant. How might predictions #4 & #5 have retarded science? How does recent evidence for a galactic habitable zone contradict prediction #5? 6. Our Galaxy is not particularly exceptional or important. Life could just as easily exist in old, small, elliptical, & irregular galaxies. Prediction fails! All galaxies in the early history of the universe, and low mass galaxies forming now, have a low metallicity that makes them unlikely habitats for life. Similar problems for habitability attach to globular clusters and irregular galaxies. Large, spiral galaxies like the Milky Way formed at about the same time, and are much more habitable than galaxies of different ages and types. 7. The universe is infinite in space and matter and eternal in time. One the greatest scientific discoveries was that the universe had a beginning and that it has a finite amount of matter and space. An infinite universe would have almost required the CP. Why? 322
Why did Newton, who had a largely Christian worldview, favor an infinite universe? It explained why gravity did not cause all the matter of the universe to collapse He viewed the universe as the “divine sensorium”--the medium through which God acted in the world. To be adequate to this task, it needed to be infinite. Anything that begins to exist (Big Bang) must have some “_________” cause to bring it into existence. Two prominent attempts to avoid this conclusion have been: 1. _______ State Model: attempt at beginningless universe. The universe has been expanding (Hubble showed), but new matter must have been continually coming into existence. This reconciles the observation of an expanding universe with the cherished idea of a beginningless universe. But this model is now dead. 2. __________ Universe Model: our universe is one in eternal cycle of Big Bangs, expansions, & collapses. This model has failed due to:
Energy available to do the work would decrease with each expansion & collapse Universe has only a fraction of the mass required for collapse Evidence of re-acceleration of the cosmic expansion reinforces last point
8. The laws of physics are not specially arranged for the existence of complex or intelligent life. Prediction fails: see Chapter 10. Recall the universe creating machine analogy; mess with the dials just a bit and life is impossible. The evidence that points to the failure of Copernican Principle predictions #1-#6 constitutes local fine-tuning for the possibility of life. In the case of #8 we see universal fine-tuning for life. Hawking’s hope: rid ourselves of the design implications of universal fine-tuning by proving it the result of some grand unified natural law. While this might resolve the appearance of fine-tuning between independent variables (different dials on the universe creating machine), it would created a larger problem. Instead of multiple variables, there would be a single, grand one, from which the array of sublaws would produce our habitable universe. It would be like a billiard play on a table with a countless number of balls that sinks every ball in one shot. This is an even higher order of intelligence than required for one ball at a time. Two Forms of the Anthropic Principle: WAP and SAP 1. Weak Anthropic Principle (WAP): We can expect to observe local conditions necessary for our existence as observers (local fine tuning). 2. Strong Anthropic Principle (SAP): We can expect to find ourselves in a universe compatible with our existence. The SAP applies the same reasoning if the WAP, but extends it to the laws, constants, and initial conditions of the universe as a whole (universal fine tuning)
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Objection to the use of WAP & SAP: Neither are sufficient explanations for fine-tuning 1. WAP & SAP simply state necessary conditions for our existence. But conditions are not full explanations. What is surprising is not that we observe a habitable universe, but that a habitable universe is, so far as we know, the only one that exists. 2. How does the Firing Squad story attempt (and fail) to explain away the “surprise” of finetuning? Many Worlds (Multiverse) Hypothesis 1. How does a multiverse eliminate the “surprise” of fine-tuning and what role does the “selection effect” play in this strategy? 2. If, under the command of the multiverse hypothesis, no amount of evidence for finetuning could ever threaten the CP and its anti-design implications, then does it make this strategy sound more like science or philosophy? Why? 3. Problems with the multiverse approach include: a. Inflation of available universe “tries” without evidence b. Destroys our ability to make practical judgments based on probabilities 4. If science is a search for the best explanation, based on the actual evidence from the physical world, rather than merely a search for the best naturalistic explanations of the physical world, how responsible is it to adopt an approach to science (multiverse) that makes one incapable of seeing evidence of design (regardless of how strong it might be)? The Failure of the Copernican Principle (p. 271b-274) 1. What does this mean? “In a sense, we are nestled snuggly in the “center” of the universe, not in a trivial spatial sense, but along the parameters of habitability and measurability. This fact stands in stark contrast to expectations nurtured by the CP.” 2. The universe is unimaginably large compared to the size of humans a. Is this a huge waste of space unless there is life beyond our solar system as the movie “Contact” maintains (in keeping with the CP) b. How does the correlation between habitability and measurability reverse the implication of a large universe and make it point away from the CP and toward intelligent design?
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Monday December 6 Lab 12: Galileo Film Introduction to the 2002 NOVA film: “Galileo’s Battle for the Heavens” This film reviews some of the principal themes of the course and prepares you to answer a few new questions on the final exam. This film will also help you prepare for the optional final exam about the three chief systems of the world available in 1615 (I may choose this essay for your class section; see the final exam study guide.) Judged relative to past films and popular books about Galileo, this film is far more accurate and interesting. The actor Simon Callow plays Galileo in dramatic reenactments of key moments from his life in which he often speaks directly from the actual writings of Galileo. This film is based on Dava Sobel’s excellent best–selling book, Galileo’s Daughter: A Historical Memoir of Science, Faith, and Love (Walker, 1999). Second only to Dava Sobel, the Christian astronomer/ historian Owen Gingerich appears more than any other scholar in this film. Answer These Questions While You Watch the Film: Transfer Answers to the Lab Report 1. Galileo thought nature was written in the language of _______________ (something humans share with God, most scientists thought). This, plus precise observations, formed the foundation of Galileo’s science. 2. While working at the University of Padua, Galileo began a relationship with a woman living in the city of _______________. This resulted in three illegitimate children. The first child, Virginia, was born in 1600. 3. Galileo taught himself how to grind _______________ and thereby increased their ability to magnify 10 times. Thus came the first telescope suitable for astronomical discovery. 4. In 1609, when Virginia was 9 years old he spent many sleepless nights looking through his _________. 5. Galileo saw four “planets” of Jupiter. These were the four ______ of Jupiter (we now know there are more). 6. Why did Galileo want to leave the University of Padua and join the Medici court in Tuscany (capital: Florence)?
7. Describe the difficulties and advantages of Virginia’s life as a nun living in a convent?
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8. One of Galileo’s followers asked him to consider the phases of Venus as evidence for the Copernican system. With what other system of the world were these new observations consistent (not mentioned in the film)? Answer: The ___________ system. The Jesuits (Society of Jesus) had embraced this alternative theory that was neither Ptolemaic, nor Copernican. The Jesuits were fervent Roman Catholic participants in the CounterReformation.101 9. Only some priests in Florence opposed Galileo. What were they inappropriately teaching from their pulpits?
10. The Grand Duchess Christina was concerned with how Copernicanism could be harmonized with the Bible. How did Galileo deal with this concern? Answer: The Bible was not intended to teach _______. 11. The inquisition put Bruno to death primarily for what? Denial of Christ’s divinity, or teaching that Earth moves? (Circle One) The historical chapter in the Privileged Planet book reinforces this point most clearly. 12. Cardinal Bellarmine, a leading figure of the inquisition in Rome, heard of Galileo from the lower clergy in Florence. Galileo decided to go to Rome in 1616 to head off misperceptions and to try to convince his own church of the truth of Copernicanism. What was the outcome of this attempt?
13. Dava Sobel, the author of the book upon which this film is primarily based, has an explanation for why Galileo’s daughter choose her name Celeste (meaning, heavens) as a new nun. What is the explanation?
14. Leading church officials (especially Cardinal Bellarmine) said they would interpret the Bible in Copernican style if Galileo could prove Copernicanism scientifically. Is this an appropriate Christian strategy for thinking about new scientific ideas? In any case, rightly or wrongly,
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Many Ptolemaicists, including Christoph Clavius, accepted the Capellan system (a popular variant of the Ptolemaic system) in which Venus and Mercury revolve around the Sun. The inability to put debates to rest about the order or center of motions of Venus and Mercury is part of the monstrous character of the Ptolemaic system, according to Copernicus. 326
Galileo took up the challenge. Did Galileo actually succeed in proving Copernicanism? Yes/ No (circle one)
15. What thought experiment did Galileo devise to defend a moving Earth?
16. Did this thought experiment prove Earth moves? Yes/ No (circle one) 17. Maria Celeste’s convent was, by the standards of that day, quite wealthy/ poor (circle one). 18. Does the film claim that the Catholic Church taught that the heavens are incorruptible? Yes/ No (circle one). We know from primary historical documents that Cardinal Bellarmine and most Jesuits believed the heavens to be corruptible, based in part on their interpretations of Genesis 1, and confirmed by observations of a “new star” (supernova). Why was this issue so important in Galileo’s day? What did Galileo think about this and why?102
19. For what does sunspot motion provide evidence?
20. Why was Galileo particularly happy with the election of the Pope Urban VIII?
21. Galileo shared with his daughter Maria Celeste a letter written to him by Pope Urban VIII. Judging from how Galileo’s daughter describes this letter, what can we conclude about the tone and intent of the letter?
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Bellarmine accepted corruptibility before 1572, on the basis of his hexameral lectures. 327
22. Galileo received permission from Pope Urban VIII to write about Copernicanism, but only if treated as _______________. 23. Based upon correspondence between father and daughter over five years, it is likely that Maria Celeste functioned as ______________ of Galileo’s book Dialogue on the Two Chief World Systems. 24. In this book, Galileo put the words of Pope Urban VIII into the mouth of the simple-minded character Simplicio. This was unfortunate because the Pope never __________ to Galileo again because he was so angry with Galileo. 25. The verdict of Galileo’s trial: Galileo was placed under _________ arrest and his book was banned. 26. Why did Pope Urban VIII intend for Galileo to receive such harsh sentence? The Pope felt ________ by his old friend Galileo and the Pope was under pressure to more fully advance the Counter Reformation. 27. What do we know about the relationship between Galileo and his daughter based on the evidence existing today?
28. Forced to abandon astronomy, to what subject did Galileo turn with success (hidden blessing of inquisition; God turns even evil to our good)?
29. Galileo’s work in this area was foundation to the grand synthesis of what great scientist? ___________ 30. What did Pope John Paul II declare in 1992 regarding the Galileo affair?
Deeply entrenched myths about the Galileo affair that the film does not perpetuate. (good job NOVA) • • • •
Galileo proved the Copernican theory through observations of the phases of Venus, etc. Christian theologians and priests refused to look through Galileo’s telescope The Catholic Church uniformly opposed Galileo The Galileo affair was mostly a war between science vs. religion 328
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Lab 12: Lab Report from Galileo Film
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Galileo thought nature was written in the language of _______________ Galileo began a relationship with a woman living in the city of _______________ Galileo taught himself how to grind _______________ In 1609 (Virginia was 9) he spent many sleepless nights looking through his _________ Galileo saw 4 “planets” of Jupiter (4 __________ of Jupiter; we now know there are more) One of Galileo’s followers asked him to consider the phases of Venus as evidence for the Copernican system. With what other system of the world were these new observations consistent (not mentioned in the film)? Answer: The ___________________ system. The Grand Duchess Christian was concerned with how Copernicanism could be harmonized with the Bible. How did Galileo deal with this concern? Answer: The Bible was not intended to teach _________________. The inquisition put Bruno to death primarily for what? Denial of Christ’s divinity, or teaching that Earth moves? (circle one) Leading church officials (especially Cardinal Bellarmine) said they would interpret the Bible in Copernican style if Galileo could prove Copernicanism scientifically. Did Galileo actually accomplish this? Yes/ No (circle one) What thought experiment did Galileo devise to defend a moving Earth?
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Why was Galileo particularly happy with the election of the Pope Urban VIII?
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Galileo shared with his daughter Maria Celeste a letter written to him by Pope Urban VIII. Judging from how Galileo’s daughter describes this letter, what can we conclude about the tone and intent of the letter?
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Galileo received permission from Pope Urban VIII to write about Copernicanism, but only if treated as _______________. Based upon correspondence between father and daughter over five years, it is likely that Maria Celeste functioned as ______________ of Galileo’s book Dialogue on the Two Chief World Systems. In this book, Galileo put the words of Pope Urban VIII into the mouth of the simple-minded character Simplicio. This was unfortunate because the Pope never ____________ to Galileo again because he was so angry with Galileo. Why did Pope Urban VIII intend for Galileo to receive such harsh sentence? The Pope felt _______________ by his old friend Galileo and the Pope was under pressure to more fully advance the Counter Reformation. Forced to abandon astronomy, to what subject did Galileo turn with success (a hidden blessing of the inquisition)? Galileo’s work in this area was foundational to the grand synthesis of what great scientist? ___________________ What did Pope John Paul II declare in 1992 regarding the Galileo affair?
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Privileged Planet, Ch. 15: Universe Designed for Discovery Discerning Design Describe how the modern study of Stonehenge is an example of a scientific investigation in which an uncontroversial design inference is made in archaeology. Is the method for making a design inference in SETI any different? Is inferring intelligent design from the fine-tuning of the universe any different? How? (The next questions will help you answer the “how” question in more detail) Chance, Necessity and Design How can we reliably distinguish among these causes: “Chance, Necessity and Design”? In 1967 Jocelyn Bell mistook signals from a neutron star for intelligent communication. How we can avoid her mistake? Hint: how do we recognize necessity (e.g., natural laws that govern neutron stars) in contrast to contingency (something that could have been otherwise)? Note that “necessity” in this question is not “ultimate” necessity, but only “proximate” necessity. Christians see natural laws as proximate necessity, even though they know God did not ultimately have to create a universe with such laws. It is easy distinguish necessity from contingency. It is difficult to separate out the two kinds of contingency: chance and design. Why is the argument for design not merely a matter of calculating probabilities or complexities? Hint: Flip a coin a thousand times, and you’ve just participated in an enormously improbable event. Explain why one should or should not infer design from this event [hint: the “event” is the outcome of a particular series of heads and tails]. Specification: A Suitable Pattern High improbability is often a necessary condition, even if it’s not a sufficient one for inferring design. How did the sequence of prime numbers beamed to Earth in the movie Contact allow the scientists to infer design? Hint: the sequence was not only high improbable (a necessary condition), but it also exhibited another condition that made the design inference reliable. What was it? The 2 conditions for a good design inference, taken together, are called “specified complexity.” Why? Illustrate with Mount Rushmore. For a pattern to reliably indicate design, it will also need to be relevantly independent of the event or structure in question. The SETI researchers in Contact would not have recognized that the prime number sequence was from aliens if they were ignorant of prime numbers. How is this prime number pattern “independent” of the transmission of space signals so as to make it tightly “specified”?
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Living organisms clearly exhibit an “independent pattern” that specifies their existence. We recognize the value of “being alive” as opposed to being dead. The fine-tuning of the universe for life is another “independent pattern” that we know is valuable. How does this analogy illustrate the meaning of a valuable independent pattern: “Art and music have a value that trash and mere noise lack.”? A Cosmic Design What is the difference between logical and natural “necessity”? Is the law of gravity logically necessary? How does this distinction help us to recognize real design as oppose to merely apparent design in fine-tuning? Hint: The actual vs. possible universes. A common complaint about the book’s thesis is this: “no matter how improbable the existence of our actual universe, it’s no more improbable than the other possible ones.” What is a good answer to this and what value judgment is involved? The Correlation as a Meaningful Pattern Does the habitability-measurability correlation provide a meaningful pattern that is independent of the fine tuned features themselves (and move us to infer design)? Hint: is there a logical or natural necessity for the habitability-measurability correlation? If we hypothesize that the universe is designed at least in part to allow intelligent observers to make discoveries, the habitability-measurability correlation we observe is what we would expect. But if the cosmos exists by chance and if intelligent observers like human beings are simply a rare accident, we would not expect this correlation. How does the Star Trek story illustrate this contrast? Conclusion: Study this Summary of the Book [with my comments] We live in a universe with laws and initial conditions finely tuned for the existence of complex life. Although narrowly constrained, they do not _____________ give rise to such life. They are necessary but not nearly ___________ for it. In extremely _____ pockets of that universe, conditions are congenial to the existence of beings who can observe the starry heavens above and ponder the meaning of their existence. In at least one of these places [i.e., Earth], despite struggle and adversity [which Christians know comes from “the Fall” from God’s grace], some came to believe that the world around them was a rational, orderly universe, accessible not only to rational thought but also to careful investigation. Centuries of study, amplified by technological tools and innovation, have given rise to an unparalleled knowledge of the world around us. The combination of those preliminary discoveries now gives rise to another: The same rare conditions that have sustained our existence also make possible a stunning array of discoveries about the universe [this is the book’s main habitability-measurability “correlation” thesis].
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There is a purposeful value in this. Because of it, and only because of it, our aspirations for scientific knowledge and discovery can be ___________. Careful investigation, study, and observation of the natural world ultimately succeed. With enough persistence, the natural world discloses itself to us in ways that we do not, and sometimes cannot, anticipate. Once perceived, the thought creeps up quietly but insistently: The universe, whatever else it is, is designed for _________. What better mandate could there be for the scientific pursuit of truth? Scientific discovery enjoys a sort of cosmic prestige, but a prestige apparent and available only to those open to the possibility that the cosmos exists for a _________.
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Wednesday December 8 Privileged Planet, Ch. 16 & Conclusion, p. 313-335 Two Preliminary Complaints about Design in Natural Science 1. Naturalistic science has been overwhelmingly successful in the long run. Let’s stick with it! Response: Naturalism is severely challenged by a universe with a beginning and a universe with fine-tuned natural laws. The correlation between habitability and measurability also challenges naturalism (so don’t assume naturalism before the correlation argument has had a chance of persuading us to give up naturalism). 2. Intelligent design is unscientific because it infers supernatural, not natural, intelligent agency. Response: The issue is whether the action of an intelligence, whatever its source, is detectable. Don’t attempt to win an argument with definition rather than evidence. If we want science to give us knowledge about nature, it will have to be open-minded and not simply applied naturalistic philosophy. There are a variety of scientific methods and thus science is not easily defined in one way. Nine Objections to a Designed Correlation of Habitability & Measurability (& Responses) I’ve broken down the first objection into two and have skipped over the more marginal or speculative objections. I will only test over the objections and responses listed here. 1. It’s impossible to falsify the “correlation by design” argument Recent philosophy of science scholarship shows that high level theories (such as the correlation thesis) resist simple refutation; nevertheless, it’s valuable to be able to specify what evidence would count against such a theory. How might the following count against the correlation thesis? Discover a distant and very different environment, which, while quite hostile to life, nevertheless offers a superior platform for making as many diverse scientific discoveries as does our local environment. 2. There are too many counterexamples (exceptions) to the “correlation by design” argument Why is it inconsistent for critics to advocate both objections 1 and 2? In response to objection #2: Why doesn’t the correlation thesis predict perfect agreement between habitability and measurability in every case? (Hint: If one considers conditions for measurability in isolation, is it easy to come up with exceptions? How does the design of laptop computers help illustrate a response to objection #2?) 335
3. Whatever environment we found ourselves in, we would find examples conducive to its measurability. We are simply under the illusion of this selection effect. How does the George and Laura Valentine story respond to this objection? Hint: How does the comparison of “her route” with other locations in the city establish that the placement of Valentines is specified by a meaningful pattern? Are we able to compare the habitability and measurability of our environment with others (in regard to local or universal fine tuning--or both)? Murky vs. clear atmosphere: what affect does this have on habitability and measurability? We can compare our local setting with other settings only because of the high capacity for discovery that our setting provides. As we learn to make more and more comparisons, and comparisons that would have been impossible to make from these other environments, this selection effect objection grows less and less tenable. 4. You’re cherry picking. You have used a biased sample to argue for the correlation. How can answers to the following questions help us respond to this objection? Have the authors chosen broadly important examples from many scientific disciplines? Have other scientists noticed evidence of the correlation (despite lacking a full formulation as here)? Could future research uncover evidence against the correlation? Is it good to risk being wrong? How does “correlation by design” spur research, while the “multiverse by chance” theory does not? Which of the two seems intended primarily to avoid certain unwelcome metaphysical possibilities? Why? 5. Complexity is a necessary condition for both complex life and high measurability. Thus, the greater the complexity, the greater the chance for a correlation between habitability and measurability. So the correlation is inevitable and thus trivial. Complexity often linked to low/high (circle one) habitability and low/high measurability. Example: Jupiter’s complex _______ atmosphere hinders life and scientific measurements, but Earth’s simple ____________ atmosphere supports life and scientific measurements. Other examples: complex orbits within _________ systems and galaxies usually hinder life and measurability. 6. The correlation isn’t mystical or supernatural, because it’s the result of natural processes. 336
The correlation forms a meaningful pattern, which, while quite ____________ with the laws of physics, nevertheless gives us very good reason to suppose that those _______ and ________ conditions, which allow for a variety of types of such entities like planetary systems, point to purpose and intelligent design in the cosmos. Our argument doesn’t rest on the notion that Earth is ________ or that its environment has been ________ fine-tuned, but on a particular ________—the correlation between habitability and measurability—of which our environment is an exemplar. 7. You haven’t really challenged naturalism. You’ve just challenged the idea that nature doesn’t exhibit purpose or design. True, for example, ancient pagan scientists often combined naturalism with design by conceiving of the cosmos as a self-causing, eternal, intelligent being (pantheism). Today’s new age movement has revived this combination. But Big Bang theory counts heavily against this combination in that a causal agent that somehow transcends the cosmos is a much more fitting explanation for the Big Bang and the resulting physical universe. 8. You haven’t shown that ETs don’t exist. In fact, design seems to improve this possibility. Which worldview, when combined with evidence for life’s rarity, renders ETs most likely: a supernatural form of intelligent design or a non-design form of naturalism? Why? 9. “God wouldn’t do it that way.” (God would not have made the cosmos we observe) Detecting “design” scientifically need not address theology of the designer (his purposes and character). Last sentence: “Specifically theological objections deserve specifically ___________ responses.”
Conclusion: Reading the Book of Nature Two worldviews: (1) cosmos exists for no purpose. (2) cosmos finds it proper interpretation in terms of purpose, design, and intention. Most begin with one view or the other, but all should evaluate the evidence, especially the evidence for the correlation between habitability and measurability, which defies #1 (and defies naturalism altogether when combined with a theory that points to a universe that had a beginning and is not self-caused, e.g., the Big Bang theory). Since the nineteenth century, an increasingly influential definition of science has forbidden design detection in science: “Science is the search for the best naturalistic explanation of nature.” The more open-minded definition of science is: “Science is the search for the best explanation of nature,” which opens up the possibility of detecting design through evidence for the combination of improbability and a meaningful pattern. Such an approach to science stimulates new research: “Herein lies a virtue in seeing the correlation between habitability and 337
measurability as the result of purposive design rather than mere coincidence: we should expect to find it elsewhere, and we should expect to continue making discoveries because of it.” Viewing it as a coincidence is theoretically and aesthetically sterile. A designed cosmos may make the possibility of extra-terrestrial life ______ rather than less likely. But the fact is, given the evidence we have considered, there’s no reason to assume that a designed universe, if large, must also be widely inhabited. After all, its size and age serve at least one other purpose. We stand gazing at the heavens beyond our little oasis, not into a meaningless abyss, but into a wondrous arena commensurate with our capacity for _______—indeed, one so skillfully and astonishingly ____-tuned for life and observation that it seems to beg discovery of an extra-terrestrial intelligence immeasurably more vast, more ancient, and more amazing than anything we have been willing to expect or imagine. Today’s Three Most Popular Worldviews for Reading the Book of Nature 1. Purposeless chance cosmos (multiverse): Leap of faith that undermines human rationality 2. Purposeful designed cosmos: Self-designed intelligent cosmos (new age approach) (Big Bang opposes this pantheistic view) 3. Purposeful designed cosmos: Caused by intelligence beyond the cosmos (Big Bang highly suggests this theistic view) Correlation of habitability and measurability: an independent pattern that cries out “intelligent design”!
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Final Exam Study Guide 1.
There will be 80 questions on the final. 40 of the 80 questions will be from exams 1 and 2 from this semester (but this time you cannot use notes/books). The other 40 questions will be from material covered since exam 2. Only this part of the test will be partly open and partly closed note/book as usual. You may use your planisphere on any part of the final.
2.
You may attend any of the three final exam times listed at the bottom of the last page of the reading schedule. There is no need for prior approval. Just show up for the final. But only switch exam times if you have a good reason, such as far too many finals on one day.
3.
Use the posted answer keys to correct your own exams 1 and 2 to prepare for the final.
4.
Study the new material (since exam 2) in the same way you found most effective for studying for exams 1 and 2. There are no sample questions for the new material other than recent quizzes. Review the kinds of questions you missed on previous exams and quizzes and identify patterns in your misconceptions regarding the course. Outline your lecture notes and highlight the important ideas (following the study guides).
Optional Extra Credit Final Exam Essay This could only help you; it can’t hurt to try. There is no 2nd chance to write this after the final exam. If you write a good essay and are within about 2 percentage points of the next course grade up (after your final exam score has been figured into your grade), then I will bump you up to the next course grade. You may write out this essay in advance and get my opinion of it, but you will need to write it again (without notes) on the paper I provide on the final exam day. These essays provide you with a chance to reflect back on some of the big themes of the course and to consolidate your understanding of them in light of the course as a whole. There is no required length on these essays. Write as much as needed to prove to me that you have a firm grasp of the material. Give details, not just generalities. You need not go beyond the sources assigned in this class. I will choose one of the following essays for you to write, so study both of them: 1. Given the evidence available in 1615, which system of the world had at that time the strongest claim for acceptance? This question will entail writing about the following 3 systems of the world: Ptolemaic, Copernican, and Tychonic. Cite specific observational evidence and other arguments that would be used to decide which of the 3 could be considered superior and why. 2. What is the thesis of the book The Privileged Planet? Give three examples of evidence that supports the thesis. Identify two major objections to the thesis. How do the authors respond to these objections?
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How can I calculate the final exam grade necessary to get a certain grade? Suppose your class average going into the final were 78%. You could calculate the final exam grade you would need to get a “B” by setting up the following algebraic equation to solve for the unknown “X” (final exam grade). Put 78 multiplied by (.65) (65% of class grade already determined) and with 79.5 on the other side of the equation (which is the lowest “B” grade): 78(.65) + x(.35) = 79.5. To solve this equation, we could go through these steps: x(.35) = 79.5 78(.65)... x(.35) = 79.5 - 50.7... x = 28.8/.35 = 82.3. Thus, you would need to get an 82.3% on the final to get a “B” in the class. The only other way to get lower than an 82.3 on the final and still get a “B” in the class would be to write an optional essay on the final and write it well (see packet instructions). These calculations assume you did not do the extra credit skywatch. When I post the final grades, the final essay grade will be marked as one of the following • • •
“?” (question mark) if you were not close enough to next grade up to have your essay graded “0” if you were close to next grade up, but I found your essay insufficient (no grade change) “100” if you were close to next grade up and I found your essay sufficient to raise your grade
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Extra Lab Activities Makeup Labs: Video Reports Guidelines for Making Up Labs that You Missed 1. Makeup video lab assignments are available only as a means to make up lab absences that are for valid reasons (such as illness; see the syllabus for details). If you missed a lab that happened to be a video lab, then you will make up that lab by watching the videos that were shown to the other students in lab (there is only 1 lab in the fall and 2 in the spring that are like this; all the other labs are hands-on labs). If you are making up a lab that was originally a video lab, then you will turn in the original lab report for that lab, not a new one as described in point 5 below. 2. Such reasons must be presented in advance (by phone, if necessary) to the lab coordinator and then later turned into the same lab coordinator. 3. Currently, all the videos on this list are in the Audio-Visual Room in the Learning Center basement. There are viewing rooms available for students there. 4. You must view at least 50 minutes of science videos from the approved list below (always watch complete videos, even if it takes you over the 50 minute minimum). 5. Makeup video lab report. Write a 2-3 page summary and analysis (type-written, doublespaced, normal-sized font, 1-inch margins) to be turned in within a week of the date of the lab period that was missed. 6. Although completion of an alternative writing assignment may prevent a student from getting a “no pass” grade for a lab session, it does not take away that student’s responsibility to know the materials covered in that lab. Students must get notes for any labs they miss and study these for any upcoming tests. 7. The minimum requirement of 50 minutes of science videos means that you must watch one or more videos that amount to at least 50 minutes of viewing time. For example, if the first video you watch is 40 minutes, then you must watch a complete second video that puts your total over 50 minutes. 8. Indicate your excuse for missing a lab and the date of the lab you missed. Type or write this on the top of the first page of your report. 9. Indicate the time length of each video you watched as well as the total viewing time.
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Video List Key 1. 2. 3. 4. 5.
Name: Author (or narrator) or organization who did the filming. Title: Title of given video followed by title of series if it is part of a series, or name of series. Publisher: “Publisher” = who sells this video (the publisher is also often the producer). Place: Indicates video location (AV = Audio-Visual Room in Learning Center basement) Series. If an entry is a series (e.g., Earth Revealed), all videos in the series follow with numbers.
Video List Name: Annenberg/CPB Collection. Title: Earth Revealed Series. Publisher: S. Burlington VT: The Annenberg/CPB Collection, Place: AV (All parts of this series are in AV room) Each episode below is approximately 1 hour in length. 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 24: 25: 26:
Down to Earth Earth Becoming Alive Earth’s Interior The Sea Floor The Birth of a Theory Plate Dynamics Mountain Building Earth’s Structures Earthquakes Geologic Time Evolution Through Time Minerals: The Materials of Earth Volcanism Intrusive Igneous Rocks Weathering and Soils Mass Wasting Sedimentary Rocks: The Key to Past Environments Metamorphic Rocks Running Water 1: Rivers, Erosion, and Deposition Running Water 2: Landform Evolution Ground Water Glaciers Waves, Beaches and Coasts Living With Earth, Part 1 Living With Earth, Part 2
Name: Hawking, Stephen. 342
Title: Universe Within, The. Publisher: Burlington: Carolina Biological Supply Co., Place: AV 28 Minutes Name: Morrison, Philip. Title: From Atoms to Asteroids: A Life of Philip Morrison. Publisher: Burlington: Carolina Biological Supply Co., Place: AV 28 Minutes *Name: A. E. Wilder-Smith Title: Origins: The Origin of the Universe Publisher: Films for Christ Place: AV 30 Minutes *Name: A. E. Wilder-Smith Title: Origins: The Earth, A Young Planet? Publisher: Films for Christ Place: AV 30 Minutes
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Extra Credit Lab: Skywatch Make a Protractor Quadrant 1. Purchase the protractor sold in the bookstore as an optional supply item for this course 2. Use a 3x5 note card (or equivalent stiff paper product) that has been cut into a long rectangular shape and then bent lengthwise by 90˚. It functions as a sighting device. 3. To construct the bent-card sighting device mentioned in the previously, do the following: a. Cut card material into about a 1/2 x 3 1/2 inch rectangle. b. Fold it in half lengthwise and work with it until it retains a 90˚ bend c. Tape this card to the rotating arm as illustrated below: place the bent card lengthwise along the arm of the protractor, and align the creased edge of the card with the bottom edge of the protractor arm.
Rotating arm Stiff card attaches here so that it runs most of the length of the rotating arm
Zero mark (also labelled as 180°) Wasted space: I will fix this in the 2005 edition.
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How to Use a Protractor Quadrant in the Optional Outdoor Skywatch Lab Object-to-Object Protractor Quadrant Measurement 1. Set the protractor rotating arm at zero degrees by the following means: 2. Slide your thumb’s fingernail on the top surface of the protractor until it runs into the raised zero mark (you should be able to feel it in the dark). 3. Move the arm of the protractor until it hits your fingernail and thus lines up with zero. 4. Look along the length of the card and move the whole protractor until the card is lined up directly with the 1st celestial object. 5. Without moving the protractor as a whole, rotate the protractor arm until it is roughly pointed toward the 2nd celestial object. 6. Move your head (without moving the protractor) so that you can sight the 2nd celestial object alongside the card on the arm. 7. Once you are satisfied with this 2nd alignment, you can relax, turn on your flashlight, and read off the angular measurement indicated by the arm of the protractor. This measurement constitutes the angular distance between two celestial bodies, such as between two stars. Altitude-of-Object Protractor Quadrant Measurement 1. Hold the protractor as level as possible so that your true horizon (not tree or hill tops) will be at zero degrees (this is equivalent to making your “1st sighting” in the other method). 2. Without moving the protractor as a whole, rotate the protractor arm until it is roughly pointed toward the celestial object whose altitude is in question. 3. Carefully move your head (without moving the protractor) so that you can sight the celestial object alongside the card on the arm. 4. Once you are satisfied with this alignment, you can relax, turn on your flashlight, and read off the angular measurement indicated by the arm of the protractor. This angular measurement is the altitude of the celestial object (i.e., how many degrees that object appears above one’s horizon). 5. Note: You have no way of determining the linear height of or the distance to a celestial object with this instrument. The altitude measurement is a calculation of the angular separation between a level line of sight to your horizon and the line of sight to the particular object. If you are asked to determine the altitude of a constellation, consider the midpoint of the constellation to constitute its “location” relative to the horizon. Do this BEFORE you go Outdoors into the Night: Steps in Arming Yourself for Star Wars (1) Latitude of Shawnee (look on a map if you don’t know yet).
Record here: ________ ° N
(2) Refer to the Basic Celestial Phenomena (BCP) Guide in your Packet for help if needed. (3) Some activities will require observations separated by about two hours on the same night. Read the Skywatch lab all the way through before you go out and plan your schedule. (4) Getting Your Team and Timetable Established
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Decide with whom you will work to complete as many of the Skywatch labs as you can do during good weather. We suggest that you work in small groups, but only use group information if you were physically present when it was collected. All students must hand in complete lab reports with drawing in order to get individual credit for this lab. Be sure to record on your lab report the members of your group and where and when you did this lab. (5) Becoming Familiar with Your Miller Planisphere Rotate the two moving parts of your planisphere in opposite directions and notice how the hourly time indicator wheel passes by today’s date. Move the two moving parts of your planisphere again, but this time make sure that the time indicator is moving in the right direction, in the direction of forward time past the mark for today’s date. Run through an entire 24 hour sequence to get a feel for the stars that appear during each time frame at this time of year (the stars that appear in the clear oval window are the ones you will be able to see (assuming city light pollution does not mess you up). Does this exercise have any bearing on how and when you will complete different parts of this lab (in other words, how can you use the planisphere to determine when to observe certain constellations in the sky)? Just think about this now. By the way, don’t forget that while we are on daylight savings time, 9 p.m. on the planisphere is really 10 p.m. in Shawnee (add 1 hour to planisphere time to get the time on your wristwatch). When you rotate the two moving parts of your planisphere in opposite directions, what are you simulating? What is moving relative to what? From the perspective of an Earthling who thinks that he is not in motion, how might one interpret the motion that you are now simulating on your planisphere (assume that you are an ancient Babylonian for a moment)? Just think about this now; we will come back to this idea later. (6) Decide on a suitable location for this lab. Try going far east on MacArthur, for example. You must be able to position yourself so that sources of artificial light are distant or at least blocked by trees (but sometimes you will have to move to see stars behind certain trees). (7) Collect the following items you will need for the Skywatch labs. (a) Protractor quadrant (you made one following Lab 1 instructions) (b) Miller Planisphere (available in bookstore; write your name on it) (c) Clipboard or notebook with observing plan (including this lab) (d) Flashlight with red cellophane covering (cellophane given out in lab)103 (e) Drawing paper (unlined, such as typing or cheap Xerox paper) (f) Two or more pencils (or one mechanical pencil) and an eraser (g) A watch (h) Clothes for easy movement and for sitting/reclining on the ground (j) Plan where you will go potty (especially if you go to a remote location) (k) Dedication, devotion and determination!
103 Red light will not inhibit night vision.
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Skywatch Lab: Night Sky Activities Constellations Use your planisphere to help you identify the following constellations in the night sky. Indicate the date and exact time when you observe each item; some items must be seen early in the morning before sunlight obscures your vision of the stars; be sure to include “a.m.” or “p.m.” in the time column. The “ALT.” column refers to “altitude” or the angular measurement from the nearest horizon to roughly the midpoint of a constellation. Use your protractor quadrant to measure each altitude (see Pre-Lab instructions). Your altitude measurements and time records must correspond in such a way as to be in the ballpark of reality in order to get credit for this part of the lab. Date
time
Alt.
Constellation LEO SAGITTARIUS Gemini Taurus Orion URSA MAJOR URSA Minor Cassiopeia Cephus
Comments Lion; 6 stars form backward question mark; important to Babylonian astronomers Archer; teapot shape; associated with a centaur known as an expert marksman Twins; together form one vertex of Winter Hexagon; many stars, form candy bar shape Bull; charging Orion; V-shaped head is in line with the three stars of Orion’s belt Hunter; with belt of three stars that are within larger rectangular shape of stars Big Bear; (known in part as the Big Dipper, Drinking Gourd, etc.; ignore rest of bear) Little Bear; (Little Dipper; includes Polaris as end of little dipper’s handle) Queen; constellation shaped like a “W”; between L. Dipper & Andromeda King; 6 stars shaped like a house (is it upside down, on its side, or upright?)
Refer to your planisphere, and circle the names of any of the above constellations that contain a section of the ecliptic. Such constellations are zodiac constellations, and may contain a planet. If you see a bright “star” in any of these constellations that does not correspond to your planisphere, it is probably a planet. When visible, planets usually outshine neighboring stars. Measure the altitude of Polaris with your protractor quadrant. Altitude of Polaris: _________ Time: _________ 347
At the time you observed, how much water would the Big Dipper hold (circle a or b)? (a) more than half of the bowl area, (b) none or less than half of the bowl area Orientation and Navigation. How does your latitude in degrees (recorded above in the Pre-Lab) compare with the altitude of Polaris (AP)? Check the one option below that best fits (“AP” stands for “Altitude of Polaris” and “L” stands for the “Latitude” of a person observing Polaris). AP = L ___
90 - L = AP ___
AP - 90 = L ___
AP = 90 regardless of L ___
Diurnal Motion If you observe the stars over a period of several hours, they will appear to move in a certain pattern. One way to monitor apparent stellar motion is to use the Big Dipper as a “star clock.” (1) Identify the two “pointer stars” in the bowl of the Big Dipper (on the side of the bowl opposite the handle). If you draw a line through the two “pointer stars” in the Big Dipper, this line will run approximately through Polaris (the North Star). Thus, these two stars “point” the way to Polaris. (2) Imagine that the line connecting the two pointers with Polaris is a hand of a giant clock. The center of the clock is Polaris itself. On a picture of a clock below, draw in the position of this “pointer clock-hand” accurately if “12 o’clock” represents straight overhead, and if the clock is perpendicular to your line of sight, facing due north, so that the center represents Polaris. Be accurate to at least “half-hour” positions or intervals on the clock face.
• = Polaris 12
9
•
3
6
Time observed: _______ a.m./p.m. (circle one)
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(3) A second time, about 2 hours or more later, repeat step 2. If necessary, this may be done on a subsequent evening, but should be completed within a week.
• = Polaris 12
9
•
3
6
Time observed: _______ a.m./p.m. (circle one) Star Landscape Drawing (1) Label a piece of drawing or typing paper “Star Landscape Drawing” (2) Go to a location at which streetlights are at least absent toward the northern horizon. Indicate on your paper where you are (by street or area of land). (3) At this location draw the Big Dipper (not the whole “Big Bear,” but only the “Dipper” part of the constellation). Also draw the Little Dipper, Cassiopeia, and Cephus. Use large dots to represent bright stars and small dots for faint stars; then connect the appropriate dots with lines to form each constellation. Draw all 4 constellations on one piece of paper in their proper orientation with respect to each other and with respect to the horizon and any other landmarks such as trees and buildings (draw whatever you see as a landscape beneath the stars, but you don’t have to be Michelangelo). If all 4 constellations are not visible for whatever reason, draw as many as you see. Label each constellation and earthly landmark. Also label Polaris.
Skywatch Post-Lab (do this AFTER you FINISH your night lab) When at home in a lighted room, reflect on your experiences under the starry skies... The answers to the questions in this Post-Lab will be included in your lab report. Diurnal Motion
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Calculate the apparent diurnal motion as follows from the data recorded above, in the “diurnal motion” section of the night lab. Through how many “clock-face-hours” did the “pointer-clock-hand” move? __________ clock-face hours We used a clock-face to sketch the observed positions of the big dipper only because clockintervals are more familiar, and more easily estimable, to most people than are angular degrees. The clock-face had nothing to do with the time of a particular observation, or the elapsed time between your observations. If your first drawing showed the hand at 11:00 and the second drawing showed it at 1:30, then the distance of arc it moved through would be 2.5 “clock-facehours.” Be accurate to at least half-hour intervals. Convert the number of “clock-face-hours” to angular degrees. Through how many angular degrees did the “pointer-clock-hand” or Big Dipper move? __________ angular degrees
• = Polaris
1 hr. = 30° 30 min = 15°
12 90° 9
•
3
6
How to convert the clock-face arc to angular degrees: Consider the diagram above. In terms of angular degrees it should be obvious that the arc from 12 to 3 on the clock-face is equal to a right angle, or 90°, and therefore an arc that reaches between any two hours on a clock-face (e.g., the distance between 12 and 1) is equivalent to 30° (90° ÷ 3 hours = 30 degrees). For the example above, 2.5 “clock-face-hours” would equal 2.5 hrs x 30°/hr = 75°. What was the actual elapsed time during which the motion of the Big Dipper was observed? Elapsed time: __________ hours & __________ minutes Subtract the first “Time Observed p.m.” from the second “Time Observed p.m.” Elapsed time has nothing to do with the “clock-face” diagrams in steps 1–2.
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Convert the elapsed time from the previous step into hours. Total elapsed time: __________ hours For example, if the elapsed time is 2 hours and 15 minutes, then express the time in terms of hours only, as 2.25 hours. To do this, divide the number of minutes into 60 minutes per hour, and then add the result to the number of hours: 1) 15 min. ÷ 60 min./hr = 0.25 hr 2) 0.25 hr + 2 hr = 2.25 hours Calculate the diurnal motion in angular degrees per hour. Observed rate of diurnal motion: __________°/hr For example, if the Big Dipper moved through 75° during 2.25 hours , then the rate of diurnal motion would be 75° ÷ 2.25 hrs = 33.33°/hr. Calculate the actual rate of diurnal motion, given a complete rotation of the Earth every 24-hour day. Theoretical rate of diurnal motion: __________°/hr Calculate your percentage error: __________ % Percentage error = (Observed value – Theoretical Value) ÷ (Theoretical Value) x %100. Disregard any negative sign. Final Instructions Transfer your Skywatch answers to the lab report Staple to the lab report: Star-landscape drawing Turn in the lab report on the due date announced in class
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Skywatch Lab Report (TURN THIS IN FOR CREDIT FOR LAB): PAGE 1 of 3 Name: _________________ Members of Skywatch Group
Locations
Dates and Times
The latitude of Shawnee (from a map) is: __________° N Transfer your data to this table (circle constellations containing the ecliptic): Time: Include AM/PM. “Altitude” means measuring to the middle of a constellation. Date
Time
Altitude
Constellation LEO SAGITTARIUS Gemini Taurus Orion URSA MAJOR URSA Minor Cassiopeia Cephus
How much water would the Big Dipper hold when you observed it? Time: __________ (a) more than half of the bowl area (b) none or less than half of the bowl area (circle one) Altitude of Polaris measured by protractor quadrant. Polaris Altitude : __________ How does your latitude in degrees (recorded above in the Pre-Lab) compare with the altitude of Polaris (AP)? Check the one option below that best fits (“AP” stands for “Altitude of Polaris” and “L” stands for the “Latitude” of a person observing Polaris). AP = L ___
90 - L = AP ___
AP - 90 = L ___ 353
AP = 90 regardless of L ___
SKYWATCH LAB REPORT: PAGE 2 OF 3 Draw Big Dipper “pointer clock-hand” at 1st observation. Time observed: __________
• = Polaris 12
9
•
3
6
Draw Big Dipper “pointer clock-hand” at 2nd observation. Time observed: __________
• = Polaris 12
9
•
3
6
Staple your “Star-Landscape Drawing” to the back of this lab report. Through how many “clock-face-hours” did the “pointer-clock-hand” move? __________ clock-face hours Convert the number of “clock-face-hours” to angular degrees. Through how many angular degrees did the “pointer-clock-hand” or Big Dipper move? __________ angular degrees
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SKYWATCH LAB REPORT: PAGE 3 OF 3 What was the actual elapsed time during which the motion of the Big Dipper was observed? Elapsed time: __________ hours and __________ minutes Convert the elapsed time from the previous step into hours. Total elapsed time: __________ hours Calculate the diurnal motion in angular degrees per hour. Observed rate of diurnal motion: __________°/hr Calculate the actual rate of diurnal motion, given a complete rotation of Earth every 24-hour day Theoretical rate of diurnal motion: __________°/hr Calculate your percentage error: __________%
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Old Exam Copies Acknowledgments We thank Ezra Shahn and Hunter College for some of the basic ideas (and some specific wording) for three of our labs: Distances of Celestial Objects, Archimedes’ Principle, and Galileo’s Inclined Plane. Old Exams This final course packet material is not consistently paginated due to its varied origins.
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