Which of the following relations correctly estimates the mass of the Earth $M_E$ if $g$ is the accel

Question

Which of the following relations correctly estimates the mass of the Earth $M_E$ if $g$ is the acceleration due to gravity and $R_E$ is the radius of the Earth?

Professor PC Thomas Classes · Answer

The acceleration due to gravity on the surface of the Earth is given by $g = \frac{GM_E}{R_E^2}$. Rearranging this gives the mass of the Earth as $M_E = \frac{g R_E^2}{G}$.