A light planet is revolving around a massive star in a circular...

Let the gravitational force of attraction be $F = \dfrac{GMm}{{R}^{3 / 2}}$.

Now, this gravitational force will provide the required centripetal force. Therefore, 

$\dfrac{GMm}{{R}^{3 / 2}} = m{\omega}^{2}R$

$⇒ {\omega}^{2} ∝ \dfrac{1}{{R}^{5 / 2}} ∵ T = \dfrac{2\pi}{\omega}$

$⇒ {T}^{2} ∝ {R}^{5 / 2}$