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

作　　者：XU XingBo1,2 & FU YanNing1 1 Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, China 2 Graduate University of Chinese Academy of Sciences, Beijing 100039, China 

出　　处：《Science China(Physics,Mechanics & Astronomy)》2009年第9期1404-1413,共10页中国科学：物理学、力学、天文学（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 10833001)

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.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.

关 键 词：periodic ORBITS SPATIAL restricted THREE-BODY problem SYMMETRIC ORBITS AVERAGING 

分 类 号：P132.2[天文地球—天体力学]