The Spin-Orbit Resonant Rotation of Mercury: A Two Degree of Freedom Hamiltonian Model

摘要: The paper develops a hamiltonian formulation describing the coupled orbital and spin motions of rigid Mercury rotation about its axis maximum moment inertia in frame 3:2 orbit resonance; (ecliptic) obliquity is not constant, gravitational potential mercury developed up to second degree terms (the only ones for which an approximate numerical value can be given) reduced two freedom model absence planetary perturbations. Four equilibria calculated, corresponding four different values obliquity. present situation corresponds one them, proved stable. We introduce action-angle variables neighborhood this stable equilibrium, by several successive canonical transformations, so get constant frequencies, first free spin-orbit libration, other 1:1 resonant precession both nodes (orbital rotational) on ecliptic plane. obtained simplified are perfect agreement with those Rambaux Bois [Astron. Astrophys. 413, 381–393].