Concentric Maclaurin spheroid models of rotating liquid planets
Earth and Planetary Astrophysics
2013-05-06 v1
Abstract
I present exact expressions for the interior gravitational potential V of a system of N concentric constant-density (Maclaurin) spheroids. I demonstrate an iteration procedure to find a self-consistent solution for the shapes of the interfaces between spheroids, and for the interior gravitational potential. The external free-space potential, expressed as a multipole expansion, emerges as part of the self-consistent solution. The procedure is both simpler and more precise than perturbation methods. One can choose the distribution and mass densities of the concentric spheroids so as to reproduce a prescribed barotrope to a specified accuracy. I demonstrate the method's efficacy by comparing its results with several published test cases.
Cite
@article{arxiv.1305.0803,
title = {Concentric Maclaurin spheroid models of rotating liquid planets},
author = {W. B. Hubbard},
journal= {arXiv preprint arXiv:1305.0803},
year = {2013}
}