Titan's rotation: A 3-dimensional theory

TL;DR

This paper develops a comprehensive 3D analytical and numerical theory of Titan's rotation, focusing on its equilibrium Cassini state, libration frequencies, and the influence of inclination, revealing potential resonances.

Contribution

It provides the first combined analytical and numerical model of Titan's 3D rotation, including libration frequencies and the role of inclination.

Findings

Mean obliquity of 2.2 arcmin

Libration frequencies approximately 2.1, 167.5, and 306.3 years

Inclination significantly influences Titan's rotation and potential wobble resonance

Abstract

We study the forced rotation of Titan seen as a rigid body at the equilibrium Cassini state, involving the spin-orbit synchronization. We used both the analytical and the numerical ways. We analytically determined the equilibrium positions and the frequencies of the 3 free librations around it, while a numerical integration associated to frequency analysis gave us a more synthetic, complete theory, where the free solution split from the forced one. We find a mean obliquity of 2.2 arcmin and the fundamental frequencies of the free librations of about 2.0977, 167.4883, and 306.3360 years. Moreover, we bring out the main role played by Titan's inclination on its rotation, and we suspect a likely resonance involving Titan's wobble.