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Exploration 12.1: Different xo or vo for Planetary Orbits



choose x0 =

Please wait for the animation to completely load.

This Exploration shows 10 identical planets orbiting a star. The initial position of the planets can be set at t = 0 time units when the planets are on the x axis. The difference in orbital trajectory, therefore, is due to the planets' initial velocities (in this animation GM = 1000). Restart.

  1. As you vary the initial positions of the planets, how do the orbital trajectories change?
  2. Find a planet with circular motion. What is the period for this motion?
  3. What happens to the orbit when x gets really small?
  4. What happens to the orbit when x gets really large?


choose v0y =

Please wait for the animation to completely load.

This part of the Exploration shows 10 identical planets orbiting a star. The initial velocity of the planets can be set at t = 0 time units when the planets are on the x axis.

  1. As you vary the initial velocities of the planets, how do the orbital trajectories change?
  2. Find a planet with circular motion. What is the period for this motion?
  3. What happens to the orbit when v gets really small?
  4. What happens to the orbit when v gets really large?

Download PDF Worksheet

Exploration authored by Mario Belloni and modified by Emmy Belloni.

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