Imagine a light planet revoling around a very massiv star in a circular orbit of radius R with a period of revolution T. if the gravitatinal force of attraction between the planet and the star is proportional to `R-(5//2)`

Explanation

The gravitational force is proportional to `R^(-5//2)`
`rArr F = K . R^(-5//2)` , where K is a constant. This is the force that provides the centripetal force for the planet.s revolution around the star
` rArr K . R^(-5//2)= m omega^2 . R " but " omega = (2pi)/(T)`, so
`K.R^(-5//2) = m ((2pi)/(T))^2 . R rArr T^2 = ((4pi^2. m)/(K)) R^(7//2)`
Hence , `T^2 prop R^(7//2)`