Planetary Motion with Different Force Laws
Force Law: force = Gr^n
For example, n = 1 to give an ellipse centered at the origin (simple harmonic motion, force proportional to distance)
And n = -2, the inverse square law, will give elliptic orbit with the Sun at one focus (inverse square law, force proportional to (distance)^(-2))
Important because it shows precession of orbit if force not exactly inverse square,
this for Mercury confirmed Einstein's theory of General Relativity