Effective stability around the Cassini state in the spin-orbit problem |
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Authors: | Marco Sansottera Christoph Lhotka Anne Lemaître |
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Institution: | 1. naXys, Department of Mathematics, University of Namur, Rempart de la Vierge, 8, 5000?, Namur, Belgium
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Abstract: | We investigate the long-time stability in the neighborhood of the Cassini state in the conservative spin-orbit problem. Starting with an expansion of the Hamiltonian in the canonical Andoyer-Delaunay variables, we construct a high-order Birkhoff normal form and give an estimate of the effective stability time in the Nekhoroshev sense. By extensively using algebraic manipulations on a computer, we explicitly apply our method to the rotation of Titan. We obtain physical bounds of Titan’s latitudinal and longitudinal librations, finding a stability time greatly exceeding the estimated age of the Universe. In addition, we study the dependence of the effective stability time on three relevant physical parameters: the orbital inclination, $i$ , the mean precession of the ascending node of Titan orbit, $\dot{\varOmega }$ , and the polar moment of inertia, $C$ . |
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