Concentric maclaurin spheroid models of rotating liquid planets

Research output: Contribution to journalArticle

44 Citations (Scopus)

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.

Original languageEnglish (US)
Article number43
JournalAstrophysical Journal
Volume768
Issue number1
DOIs
StatePublished - May 1 2013

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rotating liquids
spheroids
planets
planet
gravitational fields
liquid
perturbation
multipoles
iteration
expansion
method

Keywords

  • planets and satellites: interiors

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

Concentric maclaurin spheroid models of rotating liquid planets. / Hubbard, William B.

In: Astrophysical Journal, Vol. 768, No. 1, 43, 01.05.2013.

Research output: Contribution to journalArticle

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