A new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem

被引：3

作者：

Xu XingBo ^{[1
]}

Fu YanNing ^{[1
,2
]}

机构：

[1] Chinese Acad Sci, Purple Mt Observ, Nanjing 210008, Peoples R China

[2] Chinese Acad Sci, Grad Univ, Beijing 100039, Peoples R China

来源：

SCIENCE IN CHINA SERIES G-PHYSICS MECHANICS & ASTRONOMY | 2009年 / 52卷 / 09期

基金：

中国国家自然科学基金;

关键词：

periodic orbits; spatial restricted three-body problem; symmetric orbits; averaging;

D O I：

10.1007/s11433-009-0191-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show that there exists a new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem. In such a solution, the infinitesimal body is confined to the vicinity of a primary and moves on a nearly circular orbit. This orbit is almost perpendicular to the orbital plane of the primaries, where the line of symmetry of the orbit lies. The existence is shown by applying a corollary of Arenstorf's fixed point theorem to a periodicity equation system of the problem. And this existence doesn't require any restriction on the mass ratio of the primaries, nor on the eccentricity of their relative elliptic orbit. Potential relevance of this new class of periodic solutions to real celestial body systems and the follow-up studies in this respect are also discussed.

引用

页码：1404 / 1413

页数：10