On quasi-satellite periodic motion in asteroid and planetary dynamics

George Voyatzis, Kyriaki I. Antoniadou

Research output: Contribution to journalArticlepeer-review


Applying the method of analytical continuation of periodic orbits, we study quasi-satellite motion in the framework of the three-body problem. In the simplest, yet not trivial model, namely the planar circular restricted problem, it is known that quasi-satellite motion is associated with a family of periodic solutions, called family f, which consists of 1:1 resonant retrograde orbits. In our study, we determine the critical orbits of family f that are continued both in the elliptic and in the spatial models and compute the corresponding families that are generated and consist the backbone of the quasi-satellite regime in the restrictedmodel. Then, we show the continuation of these families in the general three-body problem, we verify and explain previous computations and show the existence of a new family of spatial orbits. The linear stability of periodic orbits is also studied. Stable periodic orbits unravel regimes of regular motion in phase space where 1:1 resonant angles librate. Such regimes, which exist even for high eccentricities and inclinations,may consist dynamical regions where long-lived asteroids or co-orbital exoplanets can be found.
Original languageEnglish
Article number59
Number of pages18
JournalCelestial Mechanics & Dynamical Astronomy
Issue number9
Publication statusPublished - 1 Sep 2018


  • 1:1 Resonance
  • Co-orbital motion
  • Periodic orbits
  • Quasi-satellites
  • Three-body problem


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