The restricted three-body problem (RTBP) is a fundamental model in celestial mechanics. Periodic orbits in the synodic frame play a very important role in understanding the dynamics of the RTBP model. Most of these periodic orbits, when interpreted in the sidereal frame, are actually resonant periodic orbits. As a result, numerical computation of the periodic orbits is also one approach for researchers to understand the orbital resonances of the three-body problem. Extensive studies have been carried out on this topic, concerning either the circular case or the elliptic case of this model. In this paper, we make a brief review of the history and current status of the studies on resonant periodic orbits in the RTBP model. Starting from the unperturbed two-body problem, we organize the review paper by the two cases of this model—the circular restricted three-body problem and the elliptic restricted three-body problem.

Shanshan Pan;Xiyun Hou

School of Astronomy and Space Science,Nanjing University,Nanjing 210023,China;Institute of Space Environment and Astrodynamics,Nanjing University,Nanjing 210093,China;Key Laboratory of Modern Astronomy and Astrophysics,Ministry of Education,Nanjing 210023,China

天文和天体物理学研究

[1]Shanshan Pan;Xiyun Hou-.Review Article:Resonant Families of Periodic Orbits in the Restricted Three-body Problem)[J].天文和天体物理学研究,2022(07):14-31

RTBP,synodic,sidereal

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