Stellar and planetary Cassini states

¹ CIDMA, Departamento de Física, Universidade de Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal
e-mail: correia@ua.pt
² ASD, IMCCE-CNRS UMR 8028, Observatoire de Paris, 77 Av. Denfert-Rochereau, 75014 Paris, France

Received: 21 February 2015
Accepted: 15 June 2015

Abstract

Cassini states correspond to equilibria of the spin axis of a body when its orbit is perturbed. They were initially described for satellites, but the spin axis of stars and planets undergoing strong dissipation can also evolve into some equilibria. For small satellites, the rotational angular momentum is usually much smaller than the total angular momentum, so classical methods for finding Cassini states rely on this approximation. Here we present a more general approach, which is valid for the secular quadrupolar non-restricted problem with spin. Our method is still valid when the precession rate and the mutual inclination of the orbits are not constant. Therefore, it can be used to study stars with close-in companions, or planets with heavy satellites, like the Earth-Moon system.