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Planetary Motion

In this exercise you are to use Interactive Physics to explore planetary motion and the universal law of gravitation.

1. Set up a miniature planetary system in Interactive Physics. Go to the World menu and choose universal gravity. Place a ‘Sun’ (a circle) on the screen with a mass of 10¹² kg and a ‘planet’ with a mass of 0.1 kg (don't make the circles very large!). Place the planet 3 meters away from the sun in the x direction; you can read the x-y positions of the sun and planet at the bottom of the screen.

2. By giving the planet an appropriate initial velocity, you want to establish a circular orbit. Knowing the mass of the sun, the radius of the orbit (3 meters), and the universal gravitational constant G, calculate the velocity the planet must have in order to be in a circular orbit.

3. Now enter this value into the “properties” window for the planet, click on “Run,” and see if you do in fact get a circular orbit.

4. Change the mass of the planet; is the orbit changed?

5. What if the planet is given a mass of 10¹² kg (the same as the sun)? Do you then see a different orbit? Can you explain this?

6. Go back to the original mass for the planet. Now try changing its initial velocity. Describe what the orbit looks like if the velocity is increased a little over what you used to get a circular orbit.

7. What happens if the initial velocity is less than for a circular orbit?

8. For this last orbit, at which point(s) in the orbit is the planet moving the fastest? the slowest? Can you explain this in terms of the force exerted by the sun on the planet?

9. At which point(s) in the orbit is the gravitational force the greatest? the least?

10. Turn on tracking for the planet (select the planet, then click on the World menu: choose every 2 or 4 frames). Display the velocity and acceleration vectors for the orbiting planet (select the planet and then click on Define, then Vectors, then velocity and acceleration). Now run the simulation for one complete orbit. Describe what you observe, and compare this to the answers you gave in the last two sections.

11. Place a second planet in an orbit beyond the first planet. You want to give the new planet an initial velocity so it goes in a circle; will its velocity be less than or greater than the original planet?

Give both planets initial velocities so that they move in circular orbits. Which planet has the greater period? Which planet moves at a greater speed?