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Deriviation of why mass can be thought of as to act at the centre

The last equations where Feynman explains why the mass of an object can be taken to be acting at the centre i.e where he has a hollow spheres, in the section ‘Gravitational field of large objects’. I cant understand the following:If we call xx the distance of a certain plane section from the center, then all the mass that is in a slice dxdx is at the same distance rr from PP, and the potential energy due to this ring is −Gm′dm/r..

Also, why are the limits taken as such i.e R-a and R+a. And the part where he explains how the potential is the same inside the sphere.

ASKED  Osaid

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