The radius of a planet is $R_1$ and a satellite revolves round it in a circle of radius $R_2$. The t

Question

The radius of a planet is $R_1$ and a satellite revolves round it in a circle of radius $R_2$. The time period of revolution is $T$. Find the acceleration due to the gravitation of the planet at its surface.

Professor PC Thomas Classes · Answer

From Kepler's third law, $T^2 = \frac{4\pi^2 R_2^3}{GM} \implies GM = \frac{4\pi^2 R_2^3}{T^2}$. Acceleration due to gravity at surface is $g = \frac{GM}{R_1^2} = \frac{4\pi^2 R_2^3}{T^2 R_1^2}$.