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The 3:2 spin-orbit resonant motion of Mercury

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

Abstract

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.

Keywords

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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