Question

Conceptual Question about gravitational field intensity:
Why is it that "a field at any point outside of a spherical mass is the same as it would be if the mass was concentrated at a point at the centre of the sphere?"

Answer 1

The center of the sphere is the center of mass of the sphere (assuming a uniform density). By definition, the center of mass is the point where all the mass of a body would have to be located if it were concentrated at only one point so as to have the same effect on the outside world that the body would have. So the answer is in two parts:

1. The center of mass yields the same field as the mass for point outside the mass *by definition*.

2. The center of the sphere, assuming uniform density, is the center of mass of the sphere.

Answer 2

If you know enough mathematics you can prove this thing. You can find this in any college book of mechanics. Even in Klepner