The range of validity of the two-body approximation in models of terrestrial planet accumulation: I. Gravitational perturbations
The range of validity of the two-body approximation in models of terrestrial planet accumulation: I. Gravitational perturbations
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类地行星堆积模型中二体近似的有效性范围：一、引力摄动
DOI：
10.1016/0019-1035(84)90137-4
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发表时间：
1984
期刊：
影响因子：
3.2
通讯作者：
L. Cox
中科院分区：
文献类型：
--
作者：
G. Wetherill;L. Cox
通过二维和三维数值积分计算了近距离接触（接近1 Au）至10 Tisser和影响球半径的微行星引起的半长轴、偏心率和倾角的引力扰动。这些比较的结果，治疗遇到一个两体问题，因为习惯在蒙特卡洛计算的轨道演化和行星积累的数值和分析研究。结果表明，当（V-Ve）=<$0.35（V =相对速度，Ve=最大物体逃逸速度）时，两体近似不能描述单个碰撞的结果。在这个低速区域，两体的“引力聚焦”截面不再有效;“反常引力聚焦”经常导致远距离未受扰动轨道上的物体成为近距离相遇，反之亦然。尽管存在这些差异，当VVe> 0.07时，由两体近似给出的平均扰动在2倍内是有效的。在这个相同的速度范围内，“阿诺德外推法”，即用几个非常近的遭遇来估计许多更远的遭遇的影响，被认为是一个有用的近似。
Gravitational perturbations in semimajor axis, eccentricity, and inclination resulting from close planetesimal encounters (near 1 AU) out to 10 Tisserand sphere of influence radii were calculated by two- and three-dimensional numerical integration. These are compared with the results of treating the encounter as a two-body problem, as is customary in Monte Carlo calculations of orbital evolution and in numerical and analytical studies of planetary accumulation. It is found that for values of ( V Ve) ⪅ 0.35 (V = relative velocity , Ve= escape velocity of largest body ) , the two-body body approximation fails to describe the outcome of individual encounters. In this low-velocity region, the two-body “gravitational focusing” cross section is no longer valid; “anomalous gravitational focusing” often leads to bodies on distant unperturbed trajectories becoming close encounters and vice versa. In spite of these differences, average perturbations given by the two-body approximation are valid within a factor of 2 when V Ve> 0.07 . In this same velocity range the “Arnold extrapolation,” whereby a few very close encounters are used to estimate the effect of many more distant encounters, is found to be a useful approximation.