标题： 长期摄动理论与水星轨道 显示英文标题

标题： Theory of Secular Chaos and Mercury's Orbit

摘要： 我们研究行星系统的混沌轨道演化，重点关注长周期时间尺度上占主导地位的长期（即轨道平均）相互作用。 我们首先关注由多个大质量行星驱动的测试粒子的演化。 在偏心率和倾角的一阶近似下，其轨道以恒定频率进动。 但非线性效应可以将这些频率带入或移出与行星本征频率或这些频率的线性组合的长期共振中。 这些非线性长期共振的重叠导致了行星系统的长期混沌。 我们首次通过计算非线性长期共振的位置和宽度来量化这种动力学。 当来自解析计算和数值积分的结果同时显示在一个新开发的“平均动量图”（MMM）中时，结果非常一致。 这张图对于非共面行星系统尤其有启发性，并直观地展示了混沌来源于长期共振的重叠。 随后，我们将这种新的理解应用于水星。 之前的数值模拟已经确定水星的轨道是混沌的，并且水星甚至可能与金星或太阳相撞。 我们表明，水星的混沌主要是由四个模式的组合共振的重叠引起的，包括木星主导的偏心率模式、金星主导的倾角模式以及水星自身的自由偏心率和倾角。 太阳系的数值积分证实，这些共振角度交替地摆动和循环。 我们能够计算水星变得混沌的阈值：木星和金星必须具有几百分比的偏心率和倾角。 水星似乎正处于混沌的阈值上。 显示英文摘要

摘要： We study the chaotic orbital evolution of planetary systems, focusing on secular (i.e., orbit-averaged) interactions, because these often dominate on long timescales. We first focus on the evolution of a test particle that is forced by multiple massive planets. To linear order in eccentricity and inclination, its orbit precesses with constant frequencies. But nonlinearities can shift the frequencies into and out of secular resonance with the planets' eigenfrequencies, or with linear combinations of those frequencies. The overlap of these nonlinear secular resonances drive secular chaos in planetary systems. We quantify the resulting dynamics for the first time by calculating the locations and widths of nonlinear secular resonances. When results from both analytical calculations and numerical integrations are displayed together in a newly developed "map of the mean momenta" (MMM), the agreement is excellent. This map is particularly revealing for non-coplanar planetary systems and demonstrates graphically that chaos emerges from overlapping secular resonances. We then apply this newfound understanding to Mercury. Previous numerical simulations have established that Mercury's orbit is chaotic, and that Mercury might even collide with Venus or the Sun. We show that Mercury's chaos is primarily caused by the overlap between resonances that are combinations of four modes, the Jupiter-dominated eccentricity mode, the Venus-dominated inclination mode and Mercury's free eccentricity and inclination. Numerical integration of the Solar system confirms that a slew of these resonant angles alternately librate and circulate. We are able to calculate the threshold for Mercury to become chaotic: Jupiter and Venus must have eccentricity and inclination of a few percent. Mercury appears to be perched on the threshold for chaos.