The dynamical evolution of nearly half of the known extrasolar planets in multiple-planet systems may be dominated by secular perturbations. The commonly high eccentricities of the planetary orbits calls into question the utility of the traditional Laplace-Lagrange (LL) secular theory in analyses of the motion. We analytically generalize this theory to fourth-order in the eccentricities, compare the result with the second-order theory and octupole-level theory, and apply these theories to the likely secularly-dominated HD 12661, HD 168443, HD 38529 and Ups And multi-planet systems. The fourth-order scheme yields a multiply-branched criterion for maintaining apsidal libration, and implies that the apsidal rate of a small body is a function of its initial eccentricity, dependencies which are absent from the traditional theory. Numerical results indicate that the primary difference the second and fourth-order theories reveal is an alteration in secular periodicities, and to a smaller extent amplitudes of the planetary eccentricity variation. Comparison with numerical integrations indicates that the improvement afforded by the fourth-order theory over the second-order theory sometimes dwarfs the improvement needed to reproduce the actual dynamical evolution. We conclude that LL secular theory, to any order, generally represents a poor barometer for predicting secular dynamics in extrasolar planetary systems, but does embody a useful tool for extracting an accurate long-term dynamical description of systems with small bodies and/or near-circular orbits.
展开▼
机译:在多行星系统中,将近一半的已知太阳系外行星的动力学演化可能受到长期扰动的支配。行星轨道的普遍偏心率使人们质疑传统拉普拉斯-拉格朗日(LL)世俗理论在运动分析中的实用性。我们将这种理论分析性地推广到偏心率的四阶,将结果与二阶理论和八极级理论进行比较,并将这些理论应用于可能世俗支配的HD 12661,HD 168443,HD 38529和Ups And multi -行星系统。四阶方案产生了维持分支自由度的多分支准则,并暗示了小物体的分支速度是其初始偏心率的函数,这是传统理论所缺乏的。数值结果表明,二阶和四阶理论揭示的主要差异是世俗周期性的变化,并且行星偏心距变化的幅度较小。与数值积分的比较表明,相对于二阶理论,四阶理论提供的改进有时使再现实际动力演化所需的改进相形见war。我们得出的结论是,LL世俗理论,无论以任何顺序,通常都无法预测太阳系外行星系统的长期动力学,但它确实体现了一个有用的工具,可用于提取具有小物体和/或近于圆形轨道。
展开▼