Write expressions for the gravitational force exerted by the earth on a point mass m located above, below and on the surface of the earth. Hence deduce expression for g on the earth’s surface.

Acceleration Due to Gravity of the Earth

The Earth is considered a sphere with radius R and uniform density rho. Its mass is proportional to its volume and density.

1. At Points Above the Earth’s Surface
For a point mass m located outside the Earth at a distance r from its center, the gravitational force follows the shell theorem. The force acts as if the entire mass of the Earth is concentrated at its center.

2. At Points Below the Earth’s Surface
At a point inside the Earth, at depth d below the surface, the point lies outside a smaller sphere of radius r and within an outer shell. The shell exerts no force on the point, and only the inner sphere contributes to the gravitational force.

3. At Points on the Earth’s Surface
For a point mass m on the surface, the distance from the Earth’s center is equal to its radius R .

The acceleration due to gravity, denoted by g , is defined as the acceleration experienced by a mass under the influence of Earth’s gravity. It depends on the Earth’s mass and radius.