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arXiv · 1305.0803

Concentric Maclaurin spheroid models of rotating liquid planets

W. B. Hubbard
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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.

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W. B. Hubbard. 2013-05-03. Concentric Maclaurin spheroid models of rotating liquid planets. https://doi.org/10.1088/0004-637x/768/1/43

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