密排五行星系统的偏心率与稳定性
Eccentricities and the Stability of Closely-Spaced Five-Planet Systems
摘要：
对系外行星的观测表明，行星在近距离轨道上的系统很常见，这引发了一个问题：“行星之间的轨道距离有多近，并且在很长一段时间内仍然保持动力学稳定？”".为了解决这个问题，我们研究了由五颗行星组成的理想化行星系的稳定性，每颗行星的质量与地球相等，绕一颗太阳质量的恒星运行。所有的行星都在同一个平面上，并在同一个方向上运行，行星之间的间距以希尔球半径为单位。我们所整合的大多数系统都是从一个或多个偏心轨道上的行星开始的，考虑的偏心率$e$与$e= 0.05$一样大。对于给定的初始轨道间隔，单个行星的较大初始偏心率通常会导致较短的系统寿命，而系统对初始偏心轨道上的行星的依赖性很小。不稳定时间的近似趋势增加指数与初始轨道分离的行星发现以前的行星与最初的圆形轨道的系统也存在与最初的偏心轨道。平均运动共振也倾向于破坏这些系统的稳定性，尽管系统寿命的减少没有最初的圆形轨道那么大。所有行星都具有初始$e= 0.05$和对齐的近顶角的系统通常比初始半长轴间距相同且只有一颗行星具有$e= 0.05$的系统存活得更长，但它们的寿命略短于行星最初在圆形轨道上的系统。
英文摘要：
Observations of exoplanets have revealed that systems with planets on closely-spaced orbits are common, which motivates the question "How closely can planets orbit to one another and still be dynamically-stable for very long times?". To address this question, we investigate the stability of idealized planetary systems consisting of five planets, each equal in mass to the Earth, orbiting a one solar mass star. All planets orbit in the same plane and in the same direction, and the planets are uniformly spaced in units of mutual Hill Sphere radii. Most of the systems that we integrate begin with one or more planets on eccentric orbits, with eccentricities $e$ as large as $e= 0.05$ being considered. For a given initial orbital separation, larger initial eccentricity of a single planet generally leads to shorter system lifetime, with little systematic dependence of which planet is initially on an eccentric orbit. The approximate trend of instability times increasing exponentially with initial orbital separation of the planets found previously for planets with initially circular orbits is also present for systems with initially eccentric orbits. Mean motion resonances also tend to destabilize these systems, although the reductions in system lifetimes are not as large as for initially circular orbits. Systems with all planets having initial $e= 0.05$ and aligned periapse angles typically survive far longer than systems with the same spacing in initial semi-major axis and one planet with $e= 0.05$, but they have slightly shorter lifetimes than those with planets initially on circular orbits.
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