两颗行星在相互倾斜的轨道上运行的太阳系外系统的长期动力学

Rita Mastroianni, C. Efthymiopoulos
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引用次数: 0

摘要

摘要:我们重新讨论了两行星系统的长期动力学问题,其中行星轨道表现出较高的相互倾斜度。我们提出了一个长期动力学的“基本哈密顿模型”,以系统的角动量赤字(AMD)为参数化。世俗哈密顿量可以用行星间距离比幂的多极展开或通常的拉普拉斯-拉格朗日形式以封闭形式得到。相空间的主要特征(周期轨道的数量和稳定性、主要辅助共振的分岔、Kozai共振等)都可以通过选择“基本哈密顿量”中的相应项来恢复。应用包括使用哈密顿归一化技术对系统实际轨道状态的半解析测定。讨论了一个关于ν-仙女座星系最外层两颗行星系统的例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Secular dynamics in extrasolar systems with two planets in mutually inclined orbits
Abstract We revisit the problem of the secular dynamics in two-planet systems in which the planetary orbits exhibit a high value of the mutual inclination. We propose a ‘basic hamiltonian model’ for secular dynamics, parameterized in terms of the system’s Angular Momentum Deficit (AMD). The secular Hamiltonian can be obtained in closed form, using multipole expansions in powers of the distance ratio between the planets, or in the usual Laplace-Lagrange form. The main features of the phase space (number and stability of periodic orbits, bifurcations from the main apsidal corotation resonances, Kozai resonance etc.) can all be recovered by choosing the corresponding terms in the ‘basic Hamiltonian’. Applications include the semi-analytical determination of the actual orbital state of the system using Hamiltonian normalization techniques. An example is discussed referring to the system of two outermost planets of the ν-Andromedae system.
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