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arXiv · 1510.06521

Effective stability around the Cassini state in the spin-orbit problem

Marco Sansottera·Christoph Lhotka·Anne Lemaître
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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, $\dotΩ$, and the polar moment of inertia, $C$.

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Marco Sansottera, Christoph Lhotka, Anne Lemaître. 2015-10-22. Effective stability around the Cassini state in the spin-orbit problem. https://doi.org/10.1007/s10569-014-9547-6

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