Abstract

In a restricted circular three-body problem, the concept of the minimum velocity surface \(\mathscr{S}\) is introduced, which is a modification of the zero-velocity surface (Hill surface). The existence of the Hill surface requires the occurrence of the Jacobi integral. The minimum velocity surface, apart from the Jacobi integral, requires conservation of the sector velocity of a zero-mass body in the projection on the plane of motion of the main bodies. In other words, there must exist one of the three angular momentum integrals. It is shown that this integral exists for a dynamic system obtained after a single averaging of the original system over the longitude of the main bodies. The properties of \(\mathscr{S}\) are investigated. We highlight the most significant issues. The set of possible motions of the zero-mass body bounded by surface \(\mathscr{S}\) is compact. As an example, surfaces \(\mathscr{S}\) for four small moons of Pluto are considered within the averaged Pluto–Charon–small satellite problem. In all four cases, \(\mathscr{S}\) is a topological torus with a small cross section, having a circumference in the plane of motion of the main bodies as the center line.

中文翻译：

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受限圆形三体问题中的最小速度面

摘要

在一个受限的圆三体问题中，引入了最小速度曲面\（\ mathscr {S} \）的概念，该概念是对零速度曲面（希尔曲面）的一种修改。希尔表面的存在要求雅可比积分的出现。除Jacobi积分外，最小速度表面要求在主体运动平面上的投影中保留零质量物体的扇形速度。换句话说，必须存在三个角动量积分之一。结果表明，对于原始系统在主体经度上进行一次平均后获得的动态系统，该积分存在。\（\ mathscr {S} \）的属性被调查。我们重点介绍最重要的问题。由表面\（\ mathscr {S} \）界定的零质量物体的可能运动的集合很紧凑。例如，在平均的冥王星-夏隆-小卫星问题内，考虑了冥王星的四个小卫星的表面\（\ mathscr {S} \）。在所有四种情况下，\（\ mathscr {S} \）是具有较小横截面的拓扑圆环，其在主体运动平面中的圆周为中心线。