Contributions of Tidal Poisson Terms in the Theory of the Nutation of a Nonrigid Earth

Abstract

The tidal potential generated by bodies in the solar system contains Poisson terms, i.e., periodic terms with linearly time-dependent amplitudes. The influence of these terms in the Earth’s rotation, although expected to be small, could be of interest in the present context of high accuracy modelling. We have studied their contribution in the rotation of a non rigid Earth with elastic mantle and liquid core. Starting from the Liouville equations, we computed analytically the contribution in the wobble and showed that the presently-used transfer function must be supplemented by additional terms to be used in convolution with the amplitude of the Poisson terms of the potential and inversely proportional to (σ − σn)2 where σ is the forcing frequency and σn are the eigenfrequencies associated with the retrograde free core nutation and the Chandler wobble. These results have been detailed in a paper that we published in Astron. Astrophys. in 2007. In the present paper, we further examine the contribution from the core on the wobble and the nutation. In particular, we examine the contribution on extreme cases such as for wobble frequencies near the Free Core Nutation Frequency (FCN) or for long period nutations. In addition to the analytical computation, we used a time-domain approach through a numerical model to examine the core and mantle motions and discuss the analytical results.