CONCENTRIC MACLAURIN SPHEROID MODELS OF ROTATING LIQUID PLANETS
CONCENTRIC MACLAURIN SPHEROID MODELS OF ROTATING LIQUID PLANETS
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DOI：
10.1088/0004-637x/768/1/43
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发表时间：
2013-04
期刊：
影响因子：
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通讯作者：
W. Hubbard
中科院分区：
文献类型：
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作者：
W. Hubbard
给出了N个同心等密度(Maclaurin)球体系统的内部引力势V的精确表达式。我演示了一个迭代程序，为球体之间的界面形状和内部引力势找到一个自洽的解。表示为多极展开的外部自由空间势作为自洽解的一部分出现。该方法比摄动法更简单、更精确。人们可以选择同心球体的分布和质量密度，以便以指定的精度重现规定的正压差。通过与几个已发表的测试用例进行比较，证明了该方法的有效性。
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.