$A$ planet of mass $m$ moves around the Sun along an elliptical path with a period of revolution $T$. During the motion,the planet's maximum and minimum distance from the Sun is $R$ and $\frac{R}{3}$ respectively. If $T^2 = \alpha R^3$,then the magnitude of constant $\alpha$ will be

• A
  $\frac{10}{9} \cdot \frac{\pi^2}{GM}$
• B
  $\frac{20}{27} \cdot \frac{\pi^2}{GM}$
• C
  $\frac{32}{27} \cdot \frac{\pi^2}{GM}$
• D
  $\frac{1}{18} \cdot \frac{\pi^2}{GM}$