The Spin-Orbit Resonant Rotation of Mercury: A Two Degree of Freedom Hamiltonian Model |
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| Authors: | Sandrine D'hoedt Anne Lemaitre |
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| Institution: | (1) Département de mathématique, FUNDP, 8, Rempart de la Vierge, B-5000 Namur, Belgium;(2) Département de mathématique, FUNDP, 8, Rempart de la Vierge, B-5000 Namur, Belgium |
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| Abstract: | The paper develops a hamiltonian formulation describing the coupled orbital and spin motions of a rigid Mercury rotation about
its axis of maximum moment of inertia in the frame of a 3:2 spin orbit resonance; the (ecliptic) obliquity is not constant,
the gravitational potential of mercury is developed up to the second degree terms (the only ones for which an approximate
numerical value can be given) and is reduced to a two degree of freedom model in the absence of planetary perturbations. Four
equilibria can be calculated, corresponding to four different values of the (ecliptic) obliquity. The present situation of
Mercury corresponds to one of them, which is proved to be stable. We introduce action-angle variables in the neighborhood
of this stable equilibrium, by several successive canonical transformations, so to get two constant frequencies, the first
one for the free spin-orbit libration, the other one for the 1:1 resonant precession of both nodes (orbital and rotational)
on the ecliptic plane. The numerical values obtained by this simplified model are in perfect agreement with those obtained
by Rambaux and Bois Astron. Astrophys. 413, 381–393].
This revised version was published online in July 2006 with corrections to the Cover Date. |
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| Keywords: | Cassini laws Hamiltonian formalism Mercury planetary rotation resonance spin-orbit |
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