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arXiv 1904.09342astro-ph.EPnlin.CD
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1 P/Halley彗星的动力学:李雅普诺夫和功率谱

On the dynamics of Comet 1P/Halley: Lyapunov and power spectra

Jorge A. Pérez-Hernández, Luis Benet

摘要:

使用纯牛顿模型的太阳系,我们调查的动力学彗星1 P/哈雷考虑特别是李雅普诺夫和功率谱的轨道,使用名义初始条件的喷气推进实验室的地平线系统。我们进行精确的数值积分的$(N+1)$限制的问题和第一变分方程,考虑的时间跨度为$2\times10^5$ ~yr。功率谱主要由宽带分量控制,峰值位于当前行星频率,包括来自木星、金星、地球和土星的贡献,以及哈雷和木星之间的$1:6$共振和更高的谐波。从最大李雅普诺夫指数的平均值,我们估计的彗星的名义轨道的李雅普诺夫时间,获得$τ_L \simeq 562$ ~年;其余的独立李雅普诺夫指数(不相关的时间反演对称性)渐近趋于零的$t^{-1/2}$。然而,我们的结果并没有显示最大李雅普诺夫指数的收敛性。我们认为,缺乏收敛的最大李雅普诺夫指数是一个签名的瞬态混沌,这将导致最终弹射彗星从太阳系。

英文摘要:

Using a purely Newtonian model for the Solar System, we investigate the dynamics of comet 1P/Halley considering in particular the Lyapunov and power spectra of its orbit, using the nominal initial conditions of JPL's Horizons system. We carry out precise numerical integrations of the $(N+1)$-restricted problem and the first variational equations, considering a time span of $2\times10^5$~yr. The power spectra are dominated by a broadband component, with peaks located at the current planetary frequencies, including contributions from Jupiter, Venus, the Earth and Saturn, as well as the $1:6$ resonance among Halley and Jupiter and higher harmonics. From the average value of the maximum Lyapunov exponent we estimate the Lyapunov time of the comet's nominal orbit, obtaining $τ_L \simeq 562$~yr; the remaining independent Lyapunov exponents (not related by time-reversal symmetry) tend asymptotically to zero as $t^{-1/2}$. Yet, our results do not display convergence of the maximum Lyapunov exponent. We argue that the lack of convergence of the maximum Lyapunov exponent is a signature of transient chaos which will lead to an eventual ejection of the comet from the Solar System.

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