Body tides in the Earth-Moon system and the Earth's rotation

G. A. Krasinsky

Proceedings of the Journées 2003 "Systèmes de Référence Spatio-Temporels", A. Finkelstein & N. Capitaine (eds.), Institute of Applied Astronomy, St. Petersburg, 107-113 (2004)

Abstract

Differential equations of rotation of the Earth with the viscous fluid core are presented and applied to explanation of a number of observed effects in the Earth's rotation. The equations take into account some important effects ignored in the adopted theory of the Earth's rotation, namely the effects from the perturbing torques caused by interaction of the potentials, induced by the tidal deformations of the Earth and its uid core, with the tide arousing bodies (including the dissipative cross interaction of the lunar tides with the Sun and the solar tides with the Moon). Perturbations of this kind could not be accounted in the adopted theory in which only those obtainable by the method of the transfer function are considered. The derived equations explicitly depend on two parameters characterizing the dissipation of energy of the Earth's rotation. These parameters are the effective tidal phase lag  due to the dissipation by rotation of the Earth as a whole, and the tidal phase lag c due to the dissipationby the differential rotation of the fluid core. The preliminary analysis has shown that the most noticeable of the dissipative effects - the excess of the observed secular obliquity rate compared with predictions of the rigid body model, and the large out-phase amplitudes of the 18.6-year and semi-annual nutations indeed may be explained as the combined effect of these two types of dissipative perturbations.