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 (CRTBP) and the elliptic restricted three-body problem (ERTBP).
Resonance transition periodic orbits exist in the chaotic regions where the 1:1 resonance overlaps with nearby interior or exterior resonances in the circular restricted three-body problem (CRTBP). The resonance transition periodic orbits have important applications for tour missions between the interior and the exterior regions of the system. In this work, following the increase of the mass parameter μ in the CRTBP model, we investigate the breakup of the first-order resonant periodic families and their recombination with the resonance transition periodic families. In this process, we can describe in detail how the 1:1 resonance gradually overlaps with nearby first-order resonances with increasing strength of the secondary’s perturbation. Utilizing the continuation method, features of the resonance transition periodic families are discussed and characterized. Finally, an efficient approach to finding these orbits is proposed and some example resonance transition periodic orbits in the Sun–Jupiter system are presented.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.