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

  • V Dehant
  • M Folgueira
  • N Rambaux
  • S.B Lambert
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 133)

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 - σ_n)^2 where σ is the forcing frequency and σ_n 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

Keywords

Precession Nutation Poisson terms 

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References

  1. Bois, E., 2000. Connaissance de la libration lunaire à l’ère de la télémétrie laser-Lune, C. R. Acad. Sci. Paris, t. 1, Série IV, 809–823Google Scholar
  2. Bois, E., and D. Vokrouhlický, 1995. Relativistic spin effects in the Earth-Moon system, A & A 300, 559Google Scholar
  3. Bois, E., and N. Rambaux, 2007. On the oscillations in Mercury’s obliquity, Icarus, in pressGoogle Scholar
  4. Dehant, V., J. Hinderer, H. Legros, and M. Lefftz, 1993. Analytical approach to the computation of the Earth, the outer core and the inner core rotational motions, Phys. Earth Planet. Inter. 76, 259–282CrossRefGoogle Scholar
  5. Dehant, V., M. Feissel-Vernier, O. de Viron, C. Ma, M. Yseboodt, and C. Bizouard, 2003. Remaining error sources in the nutation at the submilliarcsecond level, J. Geophys. Res. 108(B5), 2275, DOI: 10.1029/2002JB001763Google Scholar
  6. Ferrándiz, J.M., J.F. Navarro, A. Escapa, and J. Getino, 2004. Precession of the nonrigid Earth: effect of the fluid outer core, Astron. J. 128, 1407–1411CrossRefGoogle Scholar
  7. Folgueira, M., V. Dehant, S.B. Lambert, and N. Rambaux, 2007. Impact of tidal Poisson terms to non-rigid Earth rotation, A & A 469(3), 1197–1202, DOI: 10.1051/0004-6361:20066822Google Scholar
  8. Greff-Lefftz, M., H. Legros, and V. Dehant, 2002. Effect of inner core viscosity on gravity changes and spatial nutations induced by luni-solar tides. Phys. Earth Planet. Inter. 129(1–2), 31–41CrossRefGoogle Scholar
  9. Hinderer, J., H. Legros, and M. Amalvict, 1987. Tidal motions within the earth’s fluid core: resonance process and possible variations, Phys. Earth Planet. Inter. 49(3–4), 213–221CrossRefGoogle Scholar
  10. Mathews, P. M., T. A. Herring, and B. A. Buffett, 2002. Modeling of nutation and precession: new nutation series for nonrigid Earth and insights into the Earth’s interior, J. Geophys. Res. 107(B4), DOI: 10.1029/2001JB000390Google Scholar
  11. McCarthy, D.D., and G. Petit (Eds.), 2004. Conventions 2003. IERS Technical Note 32, Publ. Frankfurt am Main: Verlag des Bundesamts für Kartographie und GeodäsieGoogle Scholar
  12. Moritz, H. and I.I. Mueller, 1987. Earth Rotation: Theory and Observation. The Ungar Publishing Company, New YorkGoogle Scholar
  13. Poincaré H., 1910. Sur la précession des corps déformables. Bulletin Astronomique, Serie I, 27, 321–356Google Scholar
  14. Rambaux, N., T. Van Hoolst, V. Dehant, and E. Bois, 2007. Inertial core-mantle coupling and libration of Mercury, A & A 468(2), 711–719Google Scholar
  15. Roosbeek, F., 1998. Analytical developments of rigid Mars nutation and tide generating potential series, Celest. Mech. Dynamical Astron. 75, 287–300CrossRefGoogle Scholar
  16. Roosbeek, F., and V. Dehant, 1998. RDAN97: An analytical development of rigid Earth nutations series using the torque approach, Celest. Mech. Dynamical Astron. 70, 215–253CrossRefGoogle Scholar
  17. Sasao, T., S. Okubo, and M. Saito, 1980. A simple theory on dynamical effects of stratified fluid core upon nutational motion of the Earth, Proc. IAU Symposium 78, ‘Nutation and the Earth’s Rotation’, Dordrecht, Holland, Boston, D. Reidel Pub. Co., 165–183Google Scholar
  18. Wahr, J.M., 1981. The forced nutations of an elliptical, rotating, elastic and oceanless earth, Geophys. J. R. Astron. Soc. 64, 705–727Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • V Dehant
    • 1
  • M Folgueira
    • 2
  • N Rambaux
    • 1
  • S.B Lambert
    • 1
  1. 1.Royal Observatory of BelgiumBelgium
  2. 2.Instituto de Astronomía y Geodesia (UCM-CSIC) Facultad de Ciencias MatemáticasUniversidad Complutense de MadridCiudad UniversitariaSpain

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