Celestial Mechanics and Dynamical Astronomy

, Volume 120, Issue 2, pp 131–162 | Cite as

Quasi-satellite orbits in the general context of dynamics in the 1:1 mean motion resonance: perturbative treatment

  • Vladislav V. SidorenkoEmail author
  • Anatoly I. Neishtadt
  • Anton V. Artemyev
  • Lev M. Zelenyi
Original Article


Our investigation is motivated by the recent discovery of asteroids orbiting the Sun and simultaneously staying near one of the Solar System planets for a long time. This regime of motion is usually called the quasi-satellite regime, since even at the times of the closest approaches the distance between the asteroid and the planet is significantly larger than the region of space (the Hill’s sphere) in which the planet can hold its satellites. We explore the properties of the quasi-satellite regimes in the context of the spatial restricted circular three-body problem “Sun–planet–asteroid”. Via double numerical averaging, we construct evolutionary equations which describe the long-term behaviour of the orbital elements of an asteroid. Special attention is paid to possible transitions between the motion in a quasi-satellite orbit and the one in another type of orbits available in the 1:1 resonance. A rough classification of the corresponding evolutionary paths is given for an asteroid’s motion with a sufficiently small eccentricity and inclination.


Asteroids 1:1 mean-motion resonance Quasi-satellite orbits Double averaging Retrograde satellite orbits 



The work was supported in part by the Russian Foundation for Basic Research (projects 13-01-00251 and NSh-2519.2012.1) and by the Presidium of the Russian Academy of Sciences under the scope of the Program 22 “Fundamental problems of Solar System investigations”. We are grateful to M.A.Vashkovyak and M.Efroimsky for reading the manuscript and useful discussions. We thank also anonymous referees for all their corrections and suggestions.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Vladislav V. Sidorenko
    • 1
    • 2
    Email author
  • Anatoly I. Neishtadt
    • 3
    • 4
  • Anton V. Artemyev
    • 4
  • Lev M. Zelenyi
    • 4
  1. 1.Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  3. 3.Loughborough UniversityLoughboroughUK
  4. 4.Space Research InstituteRussian Academy of SciencesMoscowRussia

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