Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to R−52, and T2 is proportional to
R7/2
Centripetal force ∝R−52
or mRω2∝R−52
or ω2∝R−52−1
or ω∝R−72
or (2πT)2∝R−72
or T2∝R72