Two planets $A$ and $B$ of equal mass have periods of revolution $T_{A}$ and $T_{B}$ such that $T_{A} = 2 T_{B}$. These planets are revolving in circular orbits of radii $r_{A}$ and $r_{B}$ respectively. Which of the following is the correct relationship between their orbital radii?

• A
  $2 r_{A}^{2} = r_{B}^{2}$
• B
  $r_{A}^{3} = 2 r_{B}^{3}$
• C
  $r_{A}^{3} = 4 r_{B}^{3}$
• D
  $T_{A}^{2} - T_{B}^{2} = \frac{\pi^{2}}{G M} (r_{B}^{3} - 4 r_{A}^{3})$