LAUSR

Abstract We investigate analytically and numerically the variation of the obliquity (the axial tilt) of a hypothetical exo-Earth. A large number of exoplanets was discovered recently; since not much information is available about the masses and orbits of the stars and planets comprising a planetary exo-system, unlike for the planets of the Solar system, the problem is considered in a general setup. The exo-Earth is assumed to be rigid, axially symmetric and almost spherical, the difference between the largest and the smallest principal moments of inertia being a small parameter of the problem. Assuming the orbits of the celestial bodies to be quasiperiodic, we apply time averaging to study rotation of the exo-Earth at times large compared to the respective periods. In the present paper, we consider the case of non-resonant frequencies; we intend to study resonances in the future. In addition, we investigate numerically how the range of obliquity of the exo-Earth in a particular system comprised of a star and two planets varies on modifying the geometry of the orbits, the mass of the second planet and the initial obliquity.