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^-5/2, then T² is proportional to:

R^7/2

$m R \omega^2=F_{g r}$

$\Rightarrow m R \omega^2=\frac{k}{R^{5 / 2}}$

$\omega^2=\frac{k}{m R^{7 / 2}} \quad \Rightarrow \quad \omega \propto \frac{1}{R^{7 / 4}}$

$\Rightarrow T \propto R^{7 / 4} \quad \Rightarrow \quad T^2 \propto R^{7 / 2}$