Titan's rotation

A 3-dimensional theory

¹ University of Namur, Department of Mathematics, Rempart de la Vierge 8, 5000 Namur, Belgium
² IMCCE, Paris Observatory, UPMC, Univ. Lille 1, CNRS UMR 8028, 77 avenue Denfert Rochereau, 75014 Paris, France e-mail: noyelles@imcce.fr
³ LAL/University of Lille, 1 impasse de l'Observatoire, 59000 Lille, France

Received: 1 June 2007
Accepted: 24 October 2007

Abstract

Aims.We study the forced rotation of Titan seen as a rigid body at the equilibrium Cassini state, involving the spin-orbit synchronization.

Methods.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.

Results.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.