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arXiv 1709.04845astro-ph.EP
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过去1亿年太阳系轨道运动的数值解:极限和新结果

Numerical Solutions for the orbital motion of the Solar System over the Past 100 Myr: Limits and new results

Richard E. Zeebe

摘要:

我报告的结果,从精确的数值积分的太阳系轨道在过去的1亿年的积分包HNBody。这些模拟使用了不同的积分算法、步长、初始条件,并包括了广义相对论、不同的月球模型、太阳的四极矩和多达16颗小行星的影响。我还使用一组可能的轨道要素来探索假设的行星9的潜在影响。最昂贵的积分(Bulirsch-Stoer)需要4个月的挂钟时间,最大相对能量误差<~3e{-13}。地球偏心率(DeE)的差异被用来跟踪两个解决方案之间的差异,当最大值|DeE|不可逆地超过平均eE(~0.028x0.1)的~10\%时,认为在时间τ处发散。结果表明,找到一个唯一的轨道解是有限的初始条件,从目前的星历和小行星摄动~ 54 Myr。奇怪的是,4个月的Bulirsch-Stoer积分和辛积分只需要5小时的挂钟时间(12天的时间步长,月球作为一个简单的四极摄动),同意约6300万年。在内部,这样的辛积分即使对于大的时间步长也是非常一致的,这表明时间步长和τ之间的关系不是辛积分的绝对精度的鲁棒指标。一颗假想的行星~9对DeE的影响在~ 6500万年时变得明显。使用τ作为标准,目前最先进的解决方案都不同于以前发表的结果超过5000万年。我还进行了本征模分析,这提供了一些洞察内部太阳系的混沌性质。目前的研究提供了新的轨道解决方案,在地质研究中的应用。

英文摘要:

I report results from accurate numerical integrations of Solar System orbits over the past 100Myr with the integrator package HNBody. The simulations used different integrator algorithms, step sizes, initial conditions, and included effects from general relativity, different models of the Moon, the Sun's quadrupole moment, and up to sixteen asteroids. I also probed the potential effect of a hypothetical Planet 9, using one set of possible orbital elements. The most expensive integration (Bulirsch-Stoer) required 4~months wall-clock time with a maximum relative energy error <~3e{-13}. The difference in Earth's eccentricity (DeE) was used to track the difference between two solutions, considered to diverge at time tau when max|DeE| irreversibly crossed ~10\% of mean eE (~0.028x0.1). The results indicate that finding a unique orbital solution is limited by initial conditions from current ephemerides and asteroid perturbations to ~54Myr. Bizarrely, the 4-month Bulirsch-Stoer integration and a symplectic integration that required only 5~hours wall-clock time (12-day time step, Moon as a simple quadrupole perturbation), agree to ~63Myr. Internally, such symplectic integrations are remarkably consistent even for large time steps, suggesting that the relationship between time step and tau is not a robust indicator for the absolute accuracy of symplectic integrations. The effect of a hypothetical Planet~9 on DeE becomes discernible at ~65Myr. Using tau as a criterion, the current state-of-the-art solutions all differ from previously published results beyond ~50Myr. I also conducted an eigenmode analysis, which provides some insight into the chaotic nature of the inner Solar System. The current study provides new orbital solutions for applications in geological studies.

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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