Dehant, V. and Folgueira, Marta and Rambaux, N. and Lambert, S.B.
(2009)
*Contributions of Tidal Poisson Terms in the Theory of the Nutation of a Nonrigid Earth.*
In
Observing our changing earth.
Springer, Berlín, pp. 455-462.
ISBN 978-3-540-85425-8

PDF
Restringido a Repository staff only hasta 2020. 414kB |

Official URL: http://www.springerlink.com/content/q527541907427303/

## 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 (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. 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.

Item Type: | Book Section |
---|---|

Additional Information: | General Assembly of the International Association of Geodesy/24th General Assembly of the International Union of Geodesy and Geophysics |

Uncontrolled Keywords: | Precession - Nutation - Poisson terms |

Subjects: | Sciences > Physics > Astronomy |

ID Code: | 15265 |

References: | Bois, E., 2000. Connaissance de la libration lunaire `a l’`ere de la t´el´em´etrie laser-Lune, C. R. Acad. Sci. Paris, t. 1, S´erie IV, 809–823. Bois, E., and D. Vokrouhlick`y, 1995. Relativistic spin effects inthe Earth-Moon system, A & A 300, 559. Bois, E., and N. Rambaux, 2007. On the oscillations in Mercury’s obliquity, Icarus, in press. 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, 259–282. 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: 10.1029/2002JB001763. Ferr´andiz, 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, 1407–1411. 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: 10.1051/0004-6361:20066822. 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), 31–41. 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), 213–221. 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: 10.1029/2001JB000390. McCarthy, D.D., and G. Petit (Eds.), 2004. Conventions 2003. IERS Technical Note 32, Publ. Frankfurt am Main: Verlag des Bundesamts f¨ur Kartographie und Geod¨asie. Moritz, H. and I.I. Mueller, 1987. Earth Rotation: Theory and Observation. The Ungar Publishing Company, New York. Poincar´e H., 1910. Sur la pr´ecession des corps d´eformables. Bulletin Astronomique, Serie I, 27, 321–356. Rambaux, N., T. Van Hoolst, V. Dehant, and E. Bois, 2007. Inertial core-mantle coupling and libration of Mercury, A & A 468(2), 711–719. Roosbeek, F., 1998. Analytical developments of rigid Mars nutation and tide generating potential series, Celest. Mech. Dynamical Astron. 75, 287–300. Roosbeek, F., and V. Dehant, 1998. RDAN97: An analytical development of rigid Earth nutations series using the torque approach, Celest. Mech. Dynamical Astron. 70, 215–253. 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., 165–183. Wahr, J.M., 1981. The forced nutations of an elliptical, rotating, elastic and oceanless earth, Geophys. J. R. Astron. Soc. 64, 705–727. |

Deposited On: | 18 May 2012 09:10 |

Last Modified: | 06 Feb 2014 10:20 |

Repository Staff Only: item control page