旋转液体行星的同心Maclaurin球体模型
Concentric Maclaurin spheroid models of rotating liquid planets
摘要：
我提出了一个系统的N同心等密度（麦克劳林）球体的内部引力势V的精确表达式。我演示了一个迭代过程，找到一个自洽的解决方案的形状之间的接口球体，和内部的引力势。外部自由空间的潜力，表示为多极展开，出现作为自洽解决方案的一部分。该方法比微扰法更简单、更精确。人们可以选择同心球体的分布和质量密度，以便按照规定的精度再现规定的正压面。我证明了该方法的有效性，通过比较其结果与几个已发表的测试案例。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
