Imagine a light planet revolving around a very massive star in a circular orbit of radius .r. with a period of revolution T On what power of .r. will the square of time period depend on the gravitational force of attraction between the planet and the star is proportional to r^(-5//2)

Imagine a light planet revolving around a very massive star in a circu

1.	Imagine a light planet revolving around a very massive star in a circular orbit of radius .r. with a period of revolution T On what power of .r. will the square of time period depend on the gravitational force of attraction between the planet and the star is proportional to r^(-5//2)
Answer» Solution :The RESULTANT gravitational force PROVIDES NECESSARY centripetal force `(mV^2)/R=(K)/(r^(5//2))impliesV^(2)=K/(mr^(3//2))` So that `T = (2pir)/V=2pirsqrt(("mr"^(3//2))/K)` So `T^(2) prop r^(7//2)`