Everything is Attracted to Everything Else Newton's Law of Universal Gravitation Name: Date: Period: Data

Analysis

Extra Credit

Total

/8

/20

/4

/28

Background As we found out the force of gravity between two objects is given by the following formula: Where F is the force (N), m1 and m2 are the two masses (kg), r is the distance between the center of the two masses, and G is the gravitational constant ( ). The units for G are the way they are so that the equation for the force of gravity produces a number with units in Newtons. Also note, G is an incredibly small number. Hypothesis The acceleration an object experiences is

so the the acceleration of mass 1 from

the gravity of mass 2 will be:

Where G is the gravitational constant, m1 is the mass of the planet (kg), m2 is the mass 30 of the Sun (1.99x10 kg), and r is the distance between m1 and m2 (meters). Procedure Setting up Data Collection 1. Go to http://astro.unl.edu/naap/pos/animations/kepler.html 2. On the upper right hand side, under 'orbit settings' click on 'set parameters for' Mercury. 3. On the bottom left hand side click on 'Newtonian Features'. This will display the acceleration from gravity for the planet towards the Sun. 4. On the graph click on 'vector' and 'line' for acceleration. This will display the acceleration vector on the planet. 5. Go back to 'orbit settings' and click 'go' to start running the clock. 6. To speed up or slow down time go to 'animation controls' on the mid-right of the page and move the slider. Measuring Acceleration 1. On the 'Newtonian Features' graph on the bottom of the page record the acceleration of the planet towards the Sun by first recording its largest and smallest acceleration. The largest acceleration will be recorded as a1 and the smallest acceleration will be recorded as a2 2. Take the average of these two numbers. This value will be recorded as a. Measuring the Distance to the Sun (r) 1. The value of r is listed approximately as the semi-major axis in 'Orbit Settings' in the upper right part of the page. 2. The value of r is listed in units of AU (Otherwise known as Astronomical Units). This is the average distance between the Earth and the Sun. To convert from AU to meters multiply your distance in AU by 150, 000, 000.

Data Planet Mercury Venus Mars Jupiter Saturn Uranus Neptune Pluto

m1 (kg)

r (meters)

3.30x10

23

4.87x10

24

6.42x10

23

1.90x10

27

5.68x10

26

8.68x10

25

1.02x10

26

1.31x10

22

2

a1 (m/s )

2

a2 (m/s )

2

a(m/s )

2

(m/s )

Analysis 1. What appears to be the relationship between the mass of the planet and its acceleration towards the Sun?

2. From our equation in the hypothesis what would we predict the relationship would be between a planet's mass and its acceleration towards the Sun?

3. What is the relationship between the measured acceleration a and the value

?

Does this support our hypothesis or not?

4. If the mass of the Sun were to increase the acceleration of the planets towards it would do what? Similarly, the force of gravity on the planets would do what?

5. If the distance between the planets and the Sun were to increase the acceleration of the planets towards it would do what? Similarly, the force of gravity on the planets would do what?