The 3:2 spin-orbit resonant motion of Mercury

  • Anne Lemaitre
  • Sandrine D’Hoedt
  • Nicolas Rambaux
Review Article


Our purpose is to build a model of rotation for a rigid Mercury, involving the planetary perturbations and the non-spherical shape of the planet. The approach is purely analytical, based on Hamiltonian formalism; we start with a first-order basic averaged resonant potential (including J 2 and C 22, and the first powers of the eccentricity and the inclination of Mercury). With this kernel model, we identify the present equilibrium of Mercury; we introduce local canonical variables, describing the motion around this 3:2 resonance. We perform a canonical untangling transformation, to generate three sets of action-angle variables, and identify the three basic frequencies associated to this motion. We show how to reintroduce the short-periodic terms, lost in the averaging process, thanks to the Lie generator; we also comment about the damping effects and the planetary perturbations. At any point of the development, we use the model SONYR to compare and check our calculations.


Mercury Resonance spin-orbit Hamiltonian formalism 


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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • Anne Lemaitre
    • 1
  • Sandrine D’Hoedt
    • 1
  • Nicolas Rambaux
    • 1
  1. 1.Département de mathématiqueFUNDPNamurBelgium

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