The Gravitational Compression of an Elastic Sphere

Abstract

On considering a sphere in hydrostatic gravitational equilibrium, composed of a homogeneous elastic material for which the variation of incompressibility x with pressure p is given by dx/dp=n, a constant, we find that there is an upper bound to the radius R of the sphere provided n=2, and that for all values of n there is a lower bound to the value of I/MR2, where I is the moment of inertia about a diameter and M is the mass of the sphere.