Making use of the result obtained in the question 3 , determine the gravitational potential \(\mathcal{V}_{G}\) in the case of a homogeneous solid sphere of radius \(R\) as a function of \(r \leq R\).

Question 3

Show that if you have a mass \(M\) distributed of on a spherical shell, that is, on a sphere of radius \(R\) hollow inside, and a point mass \(m\) at a distance \(h\) from the sphere, the gravitational potential energy is \(V=-G \frac{m M}{(R+h)}\). This again is equivalent to the fact that all the mass of the spherical shell can be considered to be concentrated in the center of the sphere.