The potential satisfies , and so for a radial function . Easily, , being the constant of universal attraction and being the total mass up to the radius . Now, graph for , considering the cases and .
And for the last part, use the fact that .
A spherical planet of radius (3/2)R is composed of two solid regions of different, but constant, mass distributions. The core is located at r<=R and has a uniform density p0 and total mass M. The outer region has mass distribution p1 and total mass (19/2)/M
Obtain a general expression for the gravitational field g(r), using poissons equation, at a general point r from the planets centre.
Also determine the gravitational field experienced by a satelite orbiting the planet at a general distance r>(3/2)R, express the answer in terms of the known mass of the planet core.
Any help greatly appreciated.