## Exploration 12.2: Set Both xo and vo for Planetary Orbits

x0 = | v0y =

This Exploration shows a planet orbiting a star. The initial position in the x direction and the initial velocity in the y direction of the planet can be set at t = 0 time units when the planet is on the x axis. The difference in orbital trajectory, therefore, is due to the planet's initial position and velocity (in this animation GM = 1000). Restart.

1. As you vary the initial velocity of the planets, how do the orbital trajectories change?
2. What happens to the orbit when x0 gets really small (keep v0y = 10)?
3. What happens to the orbit when x0 gets really large (keep v0y = 10)?
4. What happens to the orbit when v0y gets really small (keep x0 = 5)?
5. What happens to the orbit when v0y gets really large (keep x0 = 5)?
6. Find the condition for circular motion.
7. For circular motion, what is the period?
8. During each of your investigations, what was happening to the angular momentum as time passed? Why?
9. Make x0 = 10. Then for small v0, what type of orbit occurs?
10. For x0 = 10, what v0 makes the orbit circular?
11. As you increase v0 (x0 = 10), the orbit changes shape. What shape does it have just beyond the speed required for circular orbit?
12. As you increase v0 (x0 = 10) even further, you eventually reach a condition of "escape." Use energy considerations to predict what this escape velocity should be.
13. For any circular orbit, predict (and then check on the graphs) how the magnitude of potential energy compares to kinetic. Likewise for escape velocity.
14. For a given orbit, you should note that the angular momentum remains constant. How does this relate to the other quantities in the table (under the simulation window), and discuss what is meant by the angle "theta."

When you get a good-looking graph, right-click on it to clone the graph and resize it for a better view.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.