Suppose two planets (spherical in shape) of radii R and 2 R, but mass M and 9 M respectively have a centre to centre separation 8 R as shown in the…

Suppose two planets (spherical in shape) of radii $\displaystyle R$ and $\displaystyle 2 R$, but mass $\displaystyle M$ and $\displaystyle 9$ M respectively have a centre to centre separation $\displaystyle 8$ R as shown in the figure. A satellite of mass ' m ' is projected from the surface of the planet of mass ' M ' directly towards the centre of the second planet. The minimum speed ' $\displaystyle v$ ' required for the satellite to reach the surface of the second planet is $\displaystyle \sqrt{\frac{\mathrm{a}}{7} \frac{\mathrm{GM}}{\mathrm{R}}}$ then the value of ' a ' is \_\_\_\_. [Given : The two planets are fixed in their position]