The 3:2 spin-orbit resonant motion of Mercury |
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Authors: | Anne Lemaitre Sandrine D’Hoedt Nicolas Rambaux |
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Institution: | (1) Département de mathématique, FUNDP, Rempart de la Vierge, 8, 5000 Namur, Belgium |
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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. |
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Keywords: | Mercury Resonance spin-orbit Hamiltonian formalism |
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