Frozen Orbits at high eccentricity and inclination: Application to Mercury orbiter.

Nicolas Delsate, Philippe Robutel, Anne Lemaître, Timoteo Carletti

Research output: Contribution to journalArticlepeer-review


We hereby study the stability of a massless probe orbiting around an oblate central body (planet or planetary satellite) perturbed by a third body, assumed to lie in the equatorial plane (Sun or Jupiter for example) using an Hamiltonian formalism. We are able to determine, in the parameters space, the location of the frozen orbits, namely orbits whose orbital elements remain constant on average, to characterize their stability/unstability and to compute the periods of the equilibria. The proposed theory is general enough, to be applied to a wide range of probes around planet or natural planetary satellites. The BepiColombo mission is used to motivate our analysis and to provide specific numerical data to check our analytical results. Finally, we also bring to the light that the coefficient $J_2$ is able to protect against the increasing of the eccentricity due to the Kozai-Lidov effect.
Original languageEnglish
Pages (from-to)275-300
Number of pages26
JournalCelestial Mechanics & Dynamical Astronomy
Issue number3
Publication statusPublished - 2010


  • Methods: analytical study
  • Stability
  • Long-term evolution
  • Kozai resonances
  • Frozen Orbit equilibria


Dive into the research topics of 'Frozen Orbits at high eccentricity and inclination: Application to Mercury orbiter.'. Together they form a unique fingerprint.

Cite this