Periodic orbits of the elliptic restricted problem for the Sun-Jupiter-Saturn system

Kwok, Johnny H.; Nacozy, P. E.

doi:10.1007/bf01228948

Cited by 7 publications

(2 citation statements)

References 4 publications

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“…Detailed bifurcation and stability properties of the families can be found in . Furthermore, periodic orbits near the 2:5 resonance, typically corresponding to the Sun-Jupiter-Saturn system are investigated by Kwok & Nacozy (1982, Michtchenko & Ferraz-Mello (2001).…”

Section: Other Higher Order Resonancesmentioning

confidence: 99%

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Review Article: Resonant Families of Periodic Orbits in the Restricted Three-body Problem*

Pan¹,

Hou²

2022

Res. Astron. Astrophys.

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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).

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Section: Other Higher Order Resonancesmentioning

confidence: 99%

“…Bifurcation points and stability of the generated families are vividly shown. Besides, research on periodic orbits of the ERTBP model for the Sun-Jupiter-Saturn system (2:5 resonance) has been conducted by many researchers (Kwok & Nacozy 1982Michtchenko & Ferraz-Mello 2001).…”

Section: Other Higher Order Resonancesmentioning

confidence: 99%