Non-rigid Contributions to the Precession Rate of a Two-layers Earth Model

The Earth's internal structure contributes to the precession rate in a non-negligible way considering current accuracies. These contributions come from a variety of sources, the most important being associated to the crossing effects of nutational terms and to the departures of the Earth rheology with respect to a perfect elastic model. To compute them we work out this problem in a unified way within the Hamiltonian framework developed in Getino and Ferrándiz (2001). It allows a consistent treatment of these effects, since all the perturbations are derived from the same tide generating expansion and the crossing effects are rigorously obtained through Hori's canonical perturbation method. These analytical expressions are constructed by considering a two layer Earth model made up of an anelastic mantle and a fluid core, perturbed by the gravitational action of the Moon and the Sun. We discuss the origin and the magnitude of the different terms and determine their influence in the value of the Earth's dynamical ellipticity, as well as the related indirect effects on the nutation series.