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Rotation of a rigid satellite with a fluid component: a new light onto Titan’s obliquity

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Abstract

We revisit the rotation dynamics of a rigid satellite with either a liquid core or a global subsurface ocean. In both problems, the flow of the fluid component is assumed inviscid. The study of a hollow satellite with a liquid core is based on the Poincaré–Hough model which provides exact equations of motion. We introduce an approximation when the ellipticity of the cavity is low. This simplification allows to model both types of satellite in the same manner. The analysis of their rotation is done in a non-canonical Hamiltonian formalism closely related to Poincaré’s “forme nouvelle des équations de la mécanique”. In the case of a satellite with a global ocean, we obtain a seven-degree-of-freedom system. Six of them account for the motion of the two rigid components, and the last one is associated with the fluid layer. We apply our model to Titan for which the origin of the obliquity is still a debated question. We show that the observed value is compatible with Titan slightly departing from the hydrostatic equilibrium and being in a Cassini equilibrium state.

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Notes

  1. Dumberry and Wieczorek (2016) could only highlight 5 degrees of freedom because their model of the Moon is axisymmetric and not triaxial.

  2. Here and throughout the paper, we follow the IAU recommendations which state that the symbol for a Julian year is “a”. Hence, radian per year is written “rad/a”.

  3. Here, we define Titan’s Laplace plane as the plane whose orientation is given by the constant part of the inclination solution of TASS1.6. (Vienne and Duriez 1995).

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Acknowledgements

We thank Benoît Noyelles and the anonymous referee for their constructive comments. G.B. also thanks Philippe Robutel for the useful conversations on the theoretical parts of this work and Rose-Marie Baland and Marie Yseboodt for our instructive discussion on this problem during the 2017 DDA meeting in London. Funding was provided by Université Pierre et Marie Curie and Observatoire de Paris.

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Authors and Affiliations

  1. IMCCE, Observatoire de Paris, UPMC Univ. Paris 6, PSL Research University, Paris, France

    Gwenaël Boué, Nicolas Rambaux & Andy Richard

  2. Universcience, Palais de la découverte, Paris, France

    Andy Richard

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  1. Gwenaël Boué
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  2. Nicolas Rambaux
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  3. Andy Richard
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Correspondence to Gwenaël Boué.

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Boué, G., Rambaux, N. & Richard, A. Rotation of a rigid satellite with a fluid component: a new light onto Titan’s obliquity. Celest Mech Dyn Astr 129, 449–485 (2017). https://doi.org/10.1007/s10569-017-9790-8

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