Abstract

Extensive numerical experiments on the long-term dynamics of planetesimals near the orbits of planets around single stars with debris disks have been carried out. The radial sizes of planetesimal clusters and the planetary chaotic zone as a function of mass parameter \(\mu\) (planet–star mass ratio) have been determined numerically with a high accuracy separately for the outer and inner parts of the chaotic zone. The results obtained have been analyzed and interpreted in light of existing analytical theories (based on the planet–planetesimal mean motion resonance overlap criterion) and in comparison with previous numerical-experiment approaches to the problem. We show and explain how the stepwise dependence of the chaotic zone sizes on \(\mu\) is determined by the marginal resonances.

中文翻译：

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行星混沌区中小行星的长期动力学

摘要

已经对带有碎片盘的围绕单颗恒星的行星轨道附近的小行星的长期动力学进行了广泛的数值实验。根据质量参数\（\ mu \）（行星-恒星质量比）的函数，已分别以数字形式高精度确定了混沌区域的外部和内部的小行星簇和行星混沌区域的径向尺寸。根据现有的分析理论（基于行星－行星平均运动共振重叠准则）并与先前对该问题的数值实验方法进行了比较，对获得的结果进行了分析和解释。我们显示并解释了混沌区域大小对\（\ mu \）的逐步依赖性是如何由边际共振确定的。