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

TL;DR

This paper models the rotation dynamics of satellites with fluid layers, like Titan, using a Hamiltonian approach, providing insights into their obliquity and internal structure.

Contribution

It introduces a unified approximation for modeling rigid satellites with fluid components, applying a Hamiltonian formalism to analyze Titan's obliquity.

Findings

Titan's obliquity can be explained by a slight departure from hydrostatic equilibrium.

The model supports the Cassini state as an explanation for Titan's current orientation.

The fluid layer significantly influences the satellite's rotational dynamics.

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.