Force on point mass vs extended mass Can anyone help me put some equations on this problem:
Some point mass A (mass mA) produces a gravitational field. Compare the force exerted on a point mass B (mass mB) to the force that would be exerted on a uniform density sphere centred on point mass B with the same total mass mB.
It's just a Newtonian gravity with volume integral problem. Cheers.
 A: The key to understanding your question is the Shell Theorem - that link gives you all the mathematics in great detail.
In summary, for an inverse square attraction, the net force due to a spherically symmetrical object is the same as if all the mass of the object were contained at its center.
The mathematical treatment considers the sphere to be made of of concentric shells, and then divides the shells into a set of rings. From the above article, this is the diagram:

All the mass in this shell is the same distance from $m$, so you can compute the contribution of force due to the mass $dM$. Then you integrate over all $\theta$ to obtain the force due to the entire shell - and find that it's as if the mass was at the center of the sphere.
And once you prove it for a single shell, the proof for a solid sphere is trivial.
A: Both the forces will be same.
Assuming that the point mass A is not inside the sphere B, the force exerted on each differential element of the sphere B will have a symmetry and the resultant will act like a point mass at the centre.
You should work out/look for the gravitational field of a spherical mass both inside and outside of it. Then you can figure it out.
