Orbital Stability of Planetary Quasi-Satellites

  • Seppo Mikkola
  • Kimmo Innanen


An object having the same mean motion and mean longitude, but different eccentricity than a planet, appears to circle the planet like a retrograde moon. If the distance is large enough such that the object is not gravitationally bound to the planet, this type of motion is another kind of 1:1 resonant trajectory, in addition to the Trojan-type orbits. We have studied the stability of such a motion both numerically and analytically, and have found adiabatic invariants which govern this type of motion. As long as the orbits are almost coplanar, stability seems to persist in the restricted problem. This applies both to the circular and eccentric restricted three-body problems. Numerical computations in the actual Solar System suggest that at least the Earth and Venus could have such satellites at roughly the distance of 0.1 AU. In the case of Mars, the motions are unstable and lead to escape from such an orbit in a time-scale of few million years.

Key words

stability satellites asteroids 


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Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Seppo Mikkola
    • 1
  • Kimmo Innanen
    • 2
  1. 1.Department of Physics and AstronomyYork UniversityNorth YorkCanada
  2. 2.Turku University ObservatoryPiikkiöFinland

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