Chapter 16.5, Problem 75E

Gravitational field due to spherical shell A point mass m is a distance d from the center of a thin spherical shell of mass M and radius R. The magnitude of the gravitational force on the point mass is given by the integral

     ,

where G is the gravitational constant.

a.    Use the change of variable x = cos φ to evaluate the integral and show that if d > R, then , which means the force is the same as if the mass of the shell were concentrated at its center.

b.    Show that if d < R (the point mass is inside the shell), then F = 0.