Impact of tidal Poisson terms on nonrigid Earth rotation

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Context. 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 on the Earth's rotation, although expected to be small, is of interest for high accuracy modeling. Aims. Therefore, we study their contribution to the rotation of a non-rigid Earth with an elastic mantle and liquid core. Methods. Starting from Liouville's equations, and following an analytical treatment, we obtain the relations accounting for Poisson terms in the forcing and providing the solution for the wobble. Results. We show that the transfer function between rigid and non rigid nutation amplitudes, as usually defined in the literature, must be supplemented by additional terms proportional to the amplitude of the Poisson term of the potential. These new terms are inversely proportional to (sigma - sigma(N))(2) where sigma is the forcing frequency and sigma(N) are the eigenfrequencies associated with the retrograde free core nutation and the Chandler wobble. The highest contribution to the nutation is 6 mu as (Delta psi) on the term 2l' - 2F + 2D - 2 Omega and remains below 1 mu as for the other terms. A contribution of 88 mu as/cy is found to the obliquity rate. We evaluate the variations of the third component of the wobble of the Earth and of the core in response to a zonal tidal potential, and show that there is no significant change.
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