Rotating planets in newtonian gravity

Abstract

Variational techniques have been used in applications of hydrodynamics in special cases. What is needed is an action that is general enough to deal with potential flows, as well as vortex flows, with rotating fluids, in Nature, and in the laboratory; it has become available only recently. Of special note is a new theory of the sounds of He II. This paper is one of several that aim to test and develop the Action Principle for hydrodynamics in diverse contexts. We study models of rotating planets, compressible fluid bodies in a stationary state of motion, under the influence of a fixed gravitational field. The hope is to account for the shape and the flow velocities, given the size of the equatorial bulges, the angular velocity at the equator, and the density profiles. The theory is applied to the principal objects in the solar system, from Earth and Mars to Saturn with its famous hexagonal flow and its characteristic ring system. Planetary rings are an unforeseen but, as it turns out, a natural and inevitable feature of the dynamics; past cataclysmic events are not needed to explain their existence. This paper is prepared for a systematic application of a new action principle to a detailed study of the planets. The present invention is to test the versatility of the theory in astrophysical applications while raising some objections against traditional methods.