CONCENTRIC MACLAURIN SPHEROID MODELS OF ROTATING LIQUID PLANETS

Journal Article · Wed May 01 00:00:00 EDT 2013 · Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637X/768/1/43· OSTI ID:22126833

Hubbard, W. B. ^[1]

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1. Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721 (United States)

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.

• OSTI ID: 22126833
• Journal Information: Astrophysical Journal, Vol. 768, Issue 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 0004-637X
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
ACCURACY
DENSITY
DISTRIBUTION
DISTURBANCES
EXPANSION
LIQUIDS
MASS
PERTURBATION THEORY
PLANETS
POTENTIALS
SATELLITES
SHAPE
SPACE
SPHEROIDS