Obtain an expression for the acceleration due to gravity g in terms of mass of the earth M and gravitational constant G.

Acceleration Due to Gravity on the Earth’s Surface

The Earth is assumed to be a sphere with mass M and radius R . A body of mass m placed on the surface of the Earth experiences a gravitational force of attraction due to the Earth.

According to the law of gravitation, this force acts as if the entire mass of the Earth is concentrated at its center, as per the shell theorem. The gravitational force generates an acceleration g in the body, known as the acceleration due to gravity.

Using Newton’s second law of motion, the acceleration g depends only on the Earth’s mass and radius and is independent of the mass, size, or shape of the body falling under gravity.