A MODEL SOLAR SYSTEM Teacher’s Guide – Getting Started
Purpose In this lesson, students will create several scale models of the solar system. Open with discussing the size of the universe and aim to steer the conversation towards the size of the astronomical bodies. Pose questions that make them think about how large one astronomical body is compared to another. How could they create a model, which factors in the scale of the bodies? Prerequisites An elementary understanding of the solar system, as well as familiarity with rates and conversion of units. Materials Below is a table of the values of diameters and true mean distance from the sun (source: http://solarsystem.nasa.gov/planets/index.cfm)
Astronomical Body
Diameter in miles
Sun Mercury Venus Earth Moon Mars Jupiter Saturn Uranus Neptune
864,337 3,032 7,521 7,918 2,159 4,212 86,881 72,367 31,518 30,599
True Mean Distance from the Sun (millions of miles) 36.0 67.2 93.0 N/A 141.6 483.6 886.5 1,783.7 2,795.2
Required: Some of the actual everyday items listed in the table on the second student and rulers to measure these objects. Suggested: Access to the internet or other reference source for finding diameters and mean distances and modeling clay comes in handy for creating spheres with small diameters. Optional: Spreadsheet software such as Excel, logarithmic graphing paper.
Worksheet 1 Guide The first three sheets comprise the first day’s lesson and focus on gathering measurements and the first attempt at scaling a model. Worksheet 2 Guide The final two sheets comprise the second day’s lesson and has students try two more scales, and then extends the lesson to mean distance from the sun.
A MODEL SOLAR SYSTEM Hayden Planetarium, part of the Rose Center for Earth and Space of the American Museum of Natural History in New York City was redesigned in 2000 to include the Scales of the Solar System exhibit, which shows the vast array of sizes of the planets and the sun. The exhibit demonstrates the massive size of the solar system by modeling the astronomical bodies as spheres, with the sun being the extremely large sphere visible in the top left corner of the photo below. The model Earth (pictured above with the other terrestrial planets) is 10 inches in diameter. How large is the model Sun in the Hayden Planetarium? How large are the other modeled planets? How might you calculate these things? If you were to build your own model of the solar system, the first piece of information that you would need to gather would be sizes of the astronomical bodies. One of the easier ways to think about the sizes of the bodies is in terms of diameter. What are the approximate diameters of the sun, planets and moon in our solar system? Use the Internet or another reference tool to find these diameters. Astronomical Body Sun Mercury Venus Earth Moon Mars Jupiter Saturn Uranus Neptune
Diameter in miles
Now that you have the approximate diameters of the bodies in the solar systems, determine how to model the solar system physically in the classroom. What objects found in everyday life might be most helpful in your model? The table on the following page provides objects and approximate diameters, along with their approximate diameters to help create your model. What object would you choose to represent the Earth? Jupiter? The Sun? Are there other objects that you might add?
Everyday Objects with Approximate Diameters Possible Objects to Use
Marble Tolley Marble Black Grape Gnocchi Golf Ball Racketball Ball Bouncy Ball Tennis Ball Baseball
Approximate Diameter 0.1 inch 0.2 inch 0.3 inch 0.4 inch 0.5 inch 0.6 inch 0.75 inch 0.8 inch 1 inch 2.5 inches
Orange Bocce Ball
4 inches
Possible Objects to Use Plasma Ball Hamster Ball Crystal Ball Volleyball Honeydew melon
6 inches
7.5 inches 8 inches 10 inches 12 inches
Basketball Beach Ball Bean Bag Chair Wrecking Ball Water Walking Ball Times Square New Year’s Eve Ball Tempietto of San Pietro in Rome Large Cannonball Concretion
5 inches Medium Medicine Ball
Approximate Diameter
20 inches 4 feet 6 feet 6.5 feet 15 feet 18 feet 40 feet
Epcot Geosphere 1939 New York World’s Fair Perisphere
165 feet 180 feet
1. If the Sun were to be represented by something with a 40-foot diameter, what is the model’s scale? Show your work.
2. With the scale found in #1, what everyday object would represent the Earth? The remaining 7 planets? The moon? Show your work.
Planet Sun Mercury Venus Earth Moon Mars Jupiter Saturn Uranus Neptune
Model Scale #1: ________________________________________ True Diameter Scale Diameter Everyday Object 864,327 miles
Diameter 40 feet
3. What flaws does this particular scale have? Is this possible to create in your classroom? Why or why not? If not, how might you alter your scale so you could use things you can represent in the classroom?
Recall from the last class what problems your scale might have had. What might you do differently so that your scale uses objects that you can use in the classroom? Planet Sun Mercury Venus Earth Moon Mars Jupiter Saturn Uranus Neptune
Model Scale:#2: ________________________________________ True Diameter Scale Diameter Everyday Object
Diameter
4. How does your new model compare to the first one? Is it smaller or larger in scale? Which aspects of the first model are better than the second? Which aspects of the second are better than the first?
5. Can you try and create a model that incorporates the best qualities of the first and the best qualities of the second model? Compare with your classmates, and see if you can find the best possible scale. What qualities do the best scales possess? Planet Sun Mercury Venus Earth Moon Mars Jupiter Saturn Uranus Neptune
Model Scale #3: ________________________________________ True Diameter Scale Diameter Everyday Object
Diameter
Consider now the mean distance of each planet from the sun (exclude the moon now). Search for the values of the average distance between the planets and the sun, and see if you can incorporate
this into your model. Is the scale also appropriate for your ideal model decided in the last question?
Planet
Model Scale #4: ____________________________________________ True Mean Distance Scaled Mean Scaled Mean from the Sun (millions Distance (in Distance (in of miles) miles) feet)
Scaled Mean Distance (in inches)
Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune 6. Using this model scale, would we be able to see Neptune if we were standing at the Sun? Can you think of a place where we could actually demonstrate this model?
7. Since the model Earth at the Hayden Planetarium is 10 inches in diameter, what is the scale that the designers used? How large are the remaining planets and the Sun?
A MODEL SOLAR SYSTEM
Teacher’s Guide – Possible Solutions Below are just three possible scales that your students might use: Scale 1: (1/10^8):1 Scale 2: (1/10^9):1
Scale 3: [1/(2.5x10^7)]:1
Celestial Body Sun
Object
Diameter
Object
Diameter
Object
Diameter
Hot Air Balloon
40 feet
Bean Bag Chair
4 feet
World’s Fair Perisphere
180 feet
Mercury
Golf Ball
1.7 inches
English Pea
0.2 inches
Hamster Ball 7.5 inches
Venus
Bocce Ball
4 inches
Raisin
0.4 inches
Basketball
18 inches
Earth
Grapefruit
5 inches
Marble
0.5 inches
Beach Ball
20 inches
Moon
Gnocchi
1 inch
0.1 inches
Grapefruit
5 inches
Mars
Bouncy Ball
2.5 inches
Nerds candy Pea
0.3 inches
Small Sugar Pumpkin
10 inches
Jupiter
Wrecking Ball Beanbag Chair
6 feet
Grapefruit
5 inches
18 feet
4 feet
Bocce Ball
4 inches
Large Cannonball Tempiette of San Pietro
Uranus
Beach Ball
20 inches
Racketball
2.25 inches Water Walking ball
6.5 feet
Neptune
Basketball
18 inches
Golf Ball
1.7 inches
6 feet
Saturn
Wrecking Ball
15 feet
Listed below are objects and diameters that fill the missing table on the second student page Possible Objects Approximate Possible Objects Approximate to Use Diameter to Use Diameter Nerds Candy 0.1 inch Grapefruit 5 inches English pea 0.2 inch Plasma Ball 7 inches Pinhead 0.3 inch Volleyball 8.5 inches Raisin 0.4 inch Honeydew melon 9 inches Acorn 0.6 inch Small Sugar Pumpkin 10 inches Golf Ball 1.7 inches Watermelon 12 inches Racketball Ball 2.25 inches Basketball 18 inches Tennis Ball 2.7 inches Times Square New Year’s 12 feet Eve Ball Baseball 2.8 inches First Modern Hot Air 40 feet Balloon Orange 3 inches Epcot Geosphere 165 feet CCSS Addressed N-Q.1, N-Q.2, N-Q.3, F-LE.1
A MODEL SOLAR SYSTEM
Teacher’s Guide – Extending the Model Visualizing the geometry of the planets is a very nice accomplishment but for further work, you may also be interested in looking at, and plotting, the numbers and seeing how various properties of the planets might be related. The geometry so far has warned us that this will be difficult, since the diameters of the four smallest planets and the diameters of the four largest form two clusters that are relatively far apart. The mean distances from the Sun also span quite a large range, and seeing any patterns on a regular piece of graph paper will be tough. A mathematical device that makes it easier to see the behavior of numbers spread that widely is to plot logarithms of the numbers rather than the numbers themselves. For any set of data that varies over many orders of magnitude—be it the planets, or the energies of earthquakes or the annual incomes of families—plots of the logarithms of the data tend to be very helpful. When you look at the diameters and the mean distance from the Sun of the various planets and plot them on log-log paper, no pattern becomes immediately evident. There would be a purpose in doing this primarily in preparation for yet another set of data about the planets—the time it takes each planet to complete one revolution about the Sun. The unit in which this is typically measured is the time it takes the Earth to do this, namely one Earth year. Let us take the data for the mean time of revolution of each planet, and list them next to the mean distances from the Sun. Again, the sensible thing to do is to plot these on log-log paper, as may be seen on the figure. You’re able to see one phenomenon right away: the two sets of data move up together. A closer look at the log-log plot shows that the numbers seem to fall very close to a straight line. This means that for each planet, the logarithm of y, the period of revolution, is linearly related to x, the mean distance from the Sun. The form of the mathematical equation that this data seems to tell you is where a and b are numbers we can read off the graph. If you measure the difference in x and y between Mercury and Pluto you should get about 8.2 cm and about 12.3 cm respectively. So the slope of the line is very nearly 1.5 (or 3/2). This says that or which gives you with
.
What this data shows is Kepler’s Third Law, that the square of the period of revolution is proportional to the cube of the mean radius of the orbit. If students have come to like logarithmic plots, they may want to investigate the Richter Scale for earthquakes – or the loudness of sounds.
