Concentric Maclaurin spheroid models of rotating liquid planets

TL;DR

This paper introduces an exact, iterative method for modeling the interior gravitational potential of rotating liquid planets using concentric Maclaurin spheroids, improving accuracy over perturbation techniques.

Contribution

It provides a new, precise iterative approach to determine spheroid shapes and gravitational potential, matching prescribed barotropes for planetary interior modeling.

Findings

Method accurately reproduces prescribed barotropes.

Self-consistent solutions for spheroid shapes and potentials are achievable.

Comparison with test cases confirms high precision.

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.