Concentric maclaurin spheroid models of rotating liquid planets

W. B. Hubbard

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


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
Issue number1
StatePublished - May 1 2013


  • planets and satellites: interiors

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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