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 language | English (US) |
---|---|
Article number | 43 |
Journal | Astrophysical Journal |
Volume | 768 |
Issue number | 1 |
DOIs | |
State | Published - May 1 2013 |
Keywords
- planets and satellites: interiors
ASJC Scopus subject areas
- Astronomy and Astrophysics
- Space and Planetary Science