Run the simulation by double-clicking the green arrow; do not press the Run button yet. This simulation shows circular orbits around a central mass. The simulation uses Newtonian mechanics to show the motion of objects in orbit about a central mass where we work in units such that GM = 1. You can drag particles to a new position. You can also double-click the particle or click on the U(r) check-box and see the effective potential that it experiences. Along with the plot of the effective potential, you can see the values of the parameters describing the motion: position, energy, angular momentum, radial and angular speeds. The time, t, is given and clicking in the simulation gives you radial and azimuthal coordinates, respectively.
1. Initialize, but do not play (the Run button) the simulation. Now play the animation and note the radial position and period of one of the orbiters.
2. Record the period and radial distance from the central mass for each orbiter
3. According to Kepler's laws, you should get a linear relationship between the period squared and the radius raised to some power. What is that power? Plot your data and check your answer.