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 will depend if the gravitational force of attraction between the planet and the star is proportional to `r^(-5//2)`.

Explanation

As gravitation provides centripetal force
`(m v^(2))/(r ) = (K)/(r^(5//2))`,
i.e., `v^(2) = (K)/(m r^(3//2))`
So that `T = (2pi r)/(v) = 2pi r sqrt((m r^(3//2))/(K))`
or `T^(2) = (4pi^(2)m)/(K)r^(7//2)` , so `T^(2) prop r^(7//2)`