Rotation of a rigid satellite with a fluid component. A new light onto Titan's obliquity

Abstract

We revisit the rotation dynamics of a rigid satellite with either a liquid core or a global sub-surface 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 Poincare-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 Poincare's "forme nouvelle des equations de la mecanique". 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.

arXiv comment39 pages, 6 figures, accepted in CeMDA

References in corpus (5)

• Reorientation of Sputnik Planitia implies a Subsurface Ocean on Pluto
• Titan's Obliquity as evidence for a subsurface ocean?
• Librational response of a deformed 3-layer Titan perturbed by non-keplerian orbit and atmospheric couplings
• Behavior of nearby synchronous rotation of a Poincaré-Hough satellite at low eccentricity
• The rotation of Io predicted by the Poincaré-Hough model

Cited by in corpus (5)

• Cassini states of a rigid body with a liquid core
• Homogeneous model for the TRAPPIST-1e planet with an icy layer
• Librations of a body composed of a deformable mantle and a fluid core
• Equivalence between simple multilayered and homogeneous laboratory-based rheological models in planetary science
• Tidal evolution of the Keplerian elements