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, Ω, and the polar moment of inertia, C. © 2014 Springer Science+Business Media Dordrecht.
CITATION STYLE
Sansottera, M., Lhotka, C., & Lemaître, A. (2014). Effective stability around the Cassini state in the spin-orbit problem. Celestial Mechanics and Dynamical Astronomy, 119(1), 75–89. https://doi.org/10.1007/s10569-014-9547-6
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