标题： 双星系统中行星的长期稳定性 显示英文标题

标题： Long-Term Stability of Planets in Binary Systems

摘要： 一个简单的天体力学问题被研究：在双星系统附近的相空间哪些区域中，行星可以长时间存在？ 行星被视为在偏心双星系统场中运动的测试粒子。 研究了一组双星偏心率和质量比的值，并检查了行星围绕其中一颗恒星近距离运行的情况，以及行星在双星轨道之外围绕系统的质心运行的情况。 根据结果，推导出两种经验表达式：1）围绕每颗恒星的最大轨道，以及2）整个双星系统最小的轨道，在这些轨道中测试粒子能够存活整个积分时间（10^4个双星周期）。 所推导的经验表达式在双星偏心率e为0.0 ≤ e ≤ 0.7-0.8，质量比mu为0.1 ≤ mu ≤ 0.9的两个区域内大致与质量比mu和双星偏心率e成线性关系，可用于指导在双星系统中寻找行星。 在考虑了双星系统中单一低质量行星的情况后，还检查了围绕双星系统中一颗恒星运行的相互作用行星系统的稳定性，尽管细节较少。 显示英文摘要

摘要： A simple question of celestial mechanics is investigated: in what regions of phase space near a binary system can planets persist for long times? The planets are taken to be test particles moving in the field of an eccentric binary system. A range of values of the binary eccentricity and mass ratio is studied, and both the case of planets orbiting close to one of the stars, and that of planets outside the binary orbiting the system's center of mass, are examined. From the results, empirical expressions are developed for both 1) the largest orbit around each of the stars, and 2) the smallest orbit around the binary system as a whole, in which test particles survive the length of the integration (10^4 binary periods). The empirical expressions developed, which are roughly linear in both the mass ratio mu and the binary eccentricity e, are determined for the range 0.0 <= e <= 0.7-0.8 and 0.1 <= mu <= 0.9 in both regions, and can be used to guide searches for planets in binary systems. After considering the case of a single low-mass planet in binary systems, the stability of a mutually-interacting system of planets orbiting one star of a binary system is examined, though in less detail.