Suppose we drill a hole through the Earth along its diameter and drop a small mass m down the hole. Assume that the Earth is not rotating and has a uniform density throughout its volume. The Earth’s mass is ME and its radius is RE. Let r be the distance from the falling object to the center of the Earth. Derive an expression for the gravitational force on the small mass as a function of r when it is moving inside the Earth. Derive an expression for the gravitational force on the small mass as a function of r when it is outside the Earth. On the graph below, plot the gravitational force on the small mass as a function of its distance r from the center of the Earth.

Suppose we drill a hole through the Earth along its diameter and drop a small mass m down the hole. Assume that the Earth is not rotating and has a uniform density throughout its volume. The Earth’s mass is ME and its radius is RE. Let r be the distance from the falling object to the center of the Earth. Derive an expression for the gravitational force on the small mass as a function of r when it is moving inside the Earth. Derive an expression for the gravitational force on the small mass as a function of r when it is outside the Earth. On the graph below, plot the gravitational force on the small mass as a function of its distance r from the center of the Earth.