Series expansions for encounter-type solutions of Hill's problem
Series expansions for encounter-type solutions of Hill's problem
复制标题
希尔问题的遭遇型解的级数展开
DOI：
10.1007/bf01234287
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
J. Petit
中科院分区：
文献类型：
--
作者：
M. Hénon;J. Petit
希尔问题被定义为当两个质量很小时，平面三体问题的极限情况。本文介绍了分析的发展，在这两个小机构接近对方从一个最初的大距离，互动了一段时间，和分离的双头型的解决方案。首先指出，与普遍的看法相反，希尔的问题是不是一个特殊的情况下的限制问题，而是一个不同的问题，具有相同程度的普遍性。然后，我们开发了一系列的扩展，允许一个准确的表示的渐近运动的两个小机构的方法和出发阶段。对于小的影响距离，我们表明，整个轨道有一个绝热不变量，这是明确计算的一系列的形式。对于大的碰撞距离，运动可以近似地用扰动理论来描述，该理论最初是由Goldreich和特里梅因提出的，并在希尔问题的背景下重新推导。
Hill's problem is defined as the limiting case of the planar three-body problem when two of the masses are very small. This paper describes analytic developments for encounter-type solutions, in which the two small bodies approach each other from an initially large distance, interact for a while, and separate. It is first pointed out that, contrary to prevalent belief, Hill's problem is not a particular case of the restricted problem, but rather a different problem with the same degree of generality. Then we develop series expansions which allow an accurate representation of the asymptotic motion of the two small bodies in the approach and departure phases. For small impact distances, we show that the whole orbit has an adiabatic invariant, which is explicitly computed in the form of a series. For large impact distances, the motion can be approximately described by a perturbation theory, originally due to Goldreich and Tremaine and rederived here in the context of Hill's problem.