State Newton’s shell theorem for the gravitational force.

This theorem explains the gravitational force exerted by a spherical shell or a solid sphere on a point mass. It can be summarized as follows:

1. Point Mass Outside a Uniform Spherical Shell
If a point mass lies outside a spherical shell with a uniform mass distribution, the shell attracts the mass as though its entire mass is concentrated at its center.

– Explanation: The gravitational forces from different parts of the shell have components both along and perpendicular to the line joining the mass to the center. The perpendicular components cancel out, leaving a net force directed towards the center of the shell.

2. Point Mass Inside a Uniform Spherical Shell
If a point mass lies inside a spherical shell, the net gravitational force on it is zero.

– Explanation: The forces exerted by different regions of the shell cancel each other out completely, resulting in no net gravitational force inside the shell.

3. Point Mass Inside a Homogeneous Solid Sphere
If a point mass lies inside a solid sphere, it experiences a gravitational force directed towards the center of the sphere. This force is proportional to the distance from the center.

– Explanation: Only the mass of the sphere that is inside the radius of the point mass contributes to the gravitational force. The mass outside the radius does not exert any net force on the point mass.