Analytical Study of the Co-orbital Motion in the Circular Restricted Three-body Problem  

作　　者：Xinhe Shen Tao Liu Xinhao Liao 

机构地区：[1]Shanghai Astronomical Observatory,Chinese Academy of Sciences,Shanghai 200030,China [2]Key Laboratory of Planetary Sciences,Chinese Academy of Sciences,Shanghai 200030,China [3]University of Chinese Academy of Sciences,Beijing 100049,China [4]School of Physical Science and Technology,ShanghaiTech University,Shanghai 201210,China

出　　处：《Research in Astronomy and Astrophysics》2023年第4期121-132,共12页天文和天体物理学研究（英文版）

基　　金：supported by the National Natural Science Foundation of China (NSFC) (grant No.11973010)。

摘　　要：In the restricted three-body problem(RTBP), if a small body and a planet stably orbit around a central star with almost exactly the same semimajor axis, and thus almost the same mean motion, this phenomenon is called the coorbital motion, or equivalently, the 1:1 mean motion resonance. The classical expansion of the disturbing function is divergent when the semimajor axis ratio of the small body to the planet is close to unity. Thus, most of the previous studies on the co-orbital dynamics were carried out through numerical integrations or semi-analytical approaches. In this work, we construct an analytical averaged model for the co-orbital motion in the framework of the circular RTBP. This model is valid in the entire coorbital region except in the vicinity of the collision singularity. The results of the analytical averaged model are in good agreement with the numerical averaged model even for moderate eccentricities and inclinations. The analytical model can reproduce the tadpole, horseshoe and quasi-satellite orbits common in the planar problem. Furthermore, the asymmetry of 1:1 resonance and the compound orbits(Icarus 137:293–314) in the general spatial problem can also be obtained from the analytical model.

关 键 词：celestial mechanics-methods analytical-minor planets-asteroids GENERAL 

分 类 号：P132.2[天文地球—天体力学]