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 if 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 if the gravitational force of attraction between the planet and the star is proportional to r^(-5//2)
Answer» Solution :Here GRAVITATIONAL force PROVIDES centripetal force, `(mv^2)/( r) = (K)/(r^(5//2)) rArr V^2 = (K)/(MR^(3//2)) rArr T = (2pi r)/(v) = 2pi r sqrt((mr^(3//2))/(K)) rArr T^2 prop r^(7//2)`