On the Dynamical Stability of the Solar System
On the Dynamical Stability of the Solar System
复制标题
论太阳系的动态稳定性
DOI：
10.1086/589232
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
G. Laughlin
中科院分区：
文献类型：
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作者：
K. Batygin;G. Laughlin
对整个太阳系（太阳+八颗行星）的行星轨道运动进行了经典牛顿近似的长期数值积分，跨度为20 Gyr。结果表明，在这段时间内没有出现严重的不稳定性。随后，利用雅克·拉斯卡（Jacques Laskar）描述的分叉方法，进行了两个数值实验，目的是确定太阳系中行星轨道变得不稳定的动态允许演化。实验产生了一个演变，其中水星福尔斯落在太阳上的时间为1.261 Gyr，另一个演变是水星和金星在8.62亿年碰撞。在后一种解决方案中，由于水星的不稳定行为，火星在8.22亿年时被逐出太阳系。我们已经进行了一些数值测试，确认这些结果，并表明它们不是数值工件。使用合成的长期扰动理论，我们发现，水星是不稳定的，通过一个入口到一个线性的长期共振与木星在其相应的本征频率的经验延长周期的可伸缩性。讨论了广义相对论对系统动力学稳定性的影响。应用分叉方法的外太阳系（木星，土星，天王星和海王星）没有表现出不稳定的迹象，在24 Gyr的整合过程中，与预期的天王星动力学寿命为1018年。
A long-term numerical integration of the classical Newtonian approximation to the planetary orbital motions of the full solar system (Sun + eight planets), spanning 20 Gyr, was performed. The results showed no severe instability arising over this time interval. Subsequently, utilizing a bifurcation method described by Jacques Laskar, two numerical experiments were performed with the goal of determining dynamically allowed evolutions for the solar system in which the planetary orbits become unstable. The experiments yielded one evolution in which Mercury falls onto the Sun at ~1.261 Gyr from now, and another in which Mercury and Venus collide in ~862 Myr. In the latter solution, as a result of Mercury’s unstable behavior, Mars was ejected from the solar system at 822 Myr. We have performed a number of numerical tests that confirm these results and indicate that they are not numerical artifacts. Using synthetic secular perturbation theory, we find that Mercury is destabilized via an entrance into a linear secular resonance with Jupiter in which their corresponding eigenfrequencies experience extended periods of commensurability. The effects of general relativity on the dynamical stability are discussed. An application of the bifurcation method to the outer solar system (Jupiter, Saturn, Uranus, and Neptune) showed no sign of instability during the course of 24 Gyr of integrations, in keeping with an expected Uranian dynamical lifetime of 1018 yr.