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arXiv 1508.04518astro-ph.EP
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尽管太阳系行为混乱,但地球未来轨道仍高度稳定地演变

Highly stable evolution of Earth's future orbit despite chaotic behavior of the Solar System

Richard E. Zeebe

摘要:

由于太阳系的混沌性质,其动态长期稳定性的问题只能在统计意义上回答,例如基于附近轨道的数值系综积分。不稳定性,包括灾难性的遭遇和/或涉及地球的碰撞,被认为是通过水星离心率(eM)的大幅增加而引发的,估计概率约为1%。然而,最近的研究表明,数值太阳系积分的统计数据对数值算法的精度和类型很敏感。在这里,我报告了计算要求很高的系综积分(N=1,600,初始条件略有不同)的结果,这些结果是基于8颗行星和冥王星在5 Gyr以上的完整运动方程,包括广义相对论的贡献,以前所未有的精度进行的。标准辛算法在高偏心轨道和近距离相遇时产生虚假结果,因此将其与专门为这些情况设计的适当Bulirsch-Stoer算法相结合。目前的研究产生了水星偏心率大幅增加的可能性,比以前的估计要小。引人注目的是,在两种情况下,水星在与金星或太阳相撞之前,继续在高偏心率轨道上运行(在达到eM值>0.93之后)8千万到1亿年。最重要的是,1,600个解决方案中没有一个导致未来与地球近距离接触或地球轨道不稳定。我的结论是,尽管太阳系的行为混乱,但地球的轨道在数十亿年的时间里是动态高度稳定的。

英文摘要:

Due to the chaotic nature of the Solar System, the question of its dynamic long-term stability can only be answered in a statistical sense, e.g. based on numerical ensemble integrations of nearby orbits. Destabilization, including catastrophic encounters and/or collisions involving the Earth, has been suggested to be initiated through a large increase in Mercury's eccentricity (eM), with an estimated probability of ~1%. However, it has recently been shown that the statistics of numerical Solar System integrations are sensitive to the accuracy and type of numerical algorithm. Here I report results from computationally demanding ensemble integrations (N=1,600 with slightly different initial conditions) at unprecedented accuracy based on the full equations of motion of the eight planets and Pluto over 5Gyr, including contributions from general relativity. The standard symplectic algorithm produced spurious results for highly eccentric orbits and during close encounters, which were hence integrated with a suitable Bulirsch-Stoer algorithm, specifically designed for these situations. The present study yields odds for a large increase in Mercury's eccentricity that are less than previous estimates. Strikingly, in two solutions Mercury continued on highly eccentric orbits (after reaching eM values >0.93) for 80-100Myr before colliding with Venus or the Sun. Most importantly, none of the 1,600 solutions led to a close encounter involving the Earth or a destabilization of Earth's orbit in the future. I conclude that Earth's orbit is dynamically highly stable for billions of years, despite the chaotic behavior of the Solar System.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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