The ellipticity of a slowly rotating configuration

Abstract

The second-order virial theorem is used to set upper and lower bounds for m/ε_R for a slowly rotating configuration, where m is the ratio of the centrifugal acceleration at the equator to the (average) gravitational acceleration on its surface and ε_R is the ellipticity of its slightly oblate figure of equilibrium. The bounds obtained are explicitly evaluated for the poly tropes, for a model consisting of a core and a mantle of constant densities, and for a particular model for the earth.