The Physics of Rotational Flattening and the Point Core Model

Abstract

The effect of rotation on the shape (figure) and gravitational quadrupole of astronomical bodies is calculated by using an approximate point core model: A point mass at the center of an ellipsoidal homogeneous fluid. Maclaurin’s analytical result for homogenous bodies generalizes to this model and leads to very accurate analytical results connecting the three observables: oblateness (ò), gravitational quadrupole ( J 2 ), and angular velocity parameter ( q ). The analytical results are compared to observational data for the planets and a good agreement is found. Oscillations near equilibrium are studied within the model.