Impact of tidal Poisson terms on nonrigid Earth rotation

Free access article

Issue		A&A Volume 469, Number 3, July III 2007


Page(s)		1197 - 1202
Section		Celestial mechanics and astrometry
DOI		http://dx.doi.org/10.1051/0004-6361:20066822

A&A 469, 1197-1202 (2007)
DOI: 10.1051/0004-6361:20066822

Impact of tidal Poisson terms on nonrigid Earth rotation

M. Folgueira^{1, 2}, V. Dehant³, S. B. Lambert³, and N. Rambaux^{3, 4}

¹ Instituto de Astronomía y Geodesia (UCM-CSIC), Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
    e-mail: martafl@mat.ucm.es
² Observatoire de Paris, SYRTE, CNRS/UMR8630, 75014 Paris, France
³ Royal Observatory of Belgium, 1180 Brussels, Belgium
    e-mail: v.dehant@oma.be,s.lambert@oma.be
⁴ Depart. of Mathematics, Facultés Univ. N. D. de la Paix, 5000 Namur, Belgium
    e-mail: Nicolas.Rambaux@fundp.ac.be

(Received 27 November 2006 / Accepted 3 April 2007)

Abstract
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 $(\sigma-\sigma_{\rm N})^2$ where $\sigma$ is the forcing frequency and $\sigma_{\rm N}$ 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.

Key words: reference systems -- Earth

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