Given a spherically symmetric mass distribution with density , explain how to obtain the gravitational field , where the potential satisfies Poisson's equation
The remarkable planet Geometria has radius 1 and is composed of an infinite number of stratified spherical shells labelled by integers . The shell has uniform density , where is a constant, and occupies the volume between radius and .
Obtain a closed form expression for the mass of Geometria.
Obtain a closed form expression for the gravitational field due to Geometria at a distance from its centre of mass, for each positive integer . What is the potential due to Geometria for ?