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 |
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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 journal › Article
}
TY - JOUR
T1 - Concentric maclaurin spheroid models of rotating liquid planets
AU - Hubbard, William B.
PY - 2013/5/1
Y1 - 2013/5/1
N2 - 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.
AB - 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.
KW - planets and satellites: interiors
UR - http://www.scopus.com/inward/record.url?scp=84876796497&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84876796497&partnerID=8YFLogxK
U2 - 10.1088/0004-637X/768/1/43
DO - 10.1088/0004-637X/768/1/43
M3 - Article
AN - SCOPUS:84876796497
VL - 768
JO - Astrophysical Journal
JF - Astrophysical Journal
SN - 0004-637X
IS - 1
M1 - 43
ER -