Question

[Advance Problem]

Assume that the force of gravitation $F \propto \frac{1}{r^{n} }$. Then show that the orbital speed in a circular path of radius r is proportional to $\frac{1}{r^{(n-1)/2}}$ while its time period T is proportional to $r^{(n+1)/2}$.

Answer 1

The answer is 1/r*(n-1)/2