First-order rotation solution of an oblate rigid body under the torque of a perturber in circular orbit

Real Observatorio de la Armada, 11 110 San Fernando, Spain e-mail: mlara@roa.es National Astronomical Observatory, Mitaka, 181-8588 Tokyo, Japan Departamento de Matemática Aplicada, Universidad de Murcia, 30 100 Murcia, Spain

Received: 15 December 2009
Accepted: 17 May 2010

Abstract

Aims. We discuss the rotational motion of an axisymmetric rigid body under the torque exerted by a massive point orbiting in a circular Keplerian orbit. The perturbation of the torque-free motion is modelled by applying MacCullagh's approximation.

Methods. Through successive approximations we use the unperturbed motion solution to get a first order solution for the Hamilton equations, which we apply to the complete problem.

Results. The solution of the perturbed problem is computed in closed form without the usual series expansions, and shows the main effects on the dynamics of the rigid body that are introduced by the perturbation. Remarkably, special configurations are discovered, for which the perturbation only introduces periodic oscillations in the torque-free motion. An application to the dwarf-planet Ceres shows the reliability of the analytical solution.