Analytical versus semi-analytical determinations of the Oppolzer terms for a non-rigid Earth |
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Authors: | V Frede V Dehant |
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Institution: | (1) Observatoire de Paris, URA 1125, 61, avenue de l'Observatoire, F-75014 Paris, France e-mail: fred@hpvlbi.obspm.fr, FR;(2) Observatoire royal de Belgique, 3, avenue circulaire, B-1180 Bruxelles, Belgique, XX |
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Abstract: | Estimations of the Oppolzer terms for the angular momentum and rotation axes of a non-rigid Earth are obtained from two different
approaches and compared. The first approach is an analytical method which relies on the solutions of the Liouville equations
for a two-layer Earth model. The Oppolzer terms are evaluated from analytical expressions. The results are then compared to
those calculated from Wahr's theory of nutation for a non-rigid Earth, which is the second approach used. Results are obtained
for the main nutation frequencies and for the precession case. The differences between the two solutions are generally quite
small (the relative error is most of the time under 8%) and are, for a large part, due to successive approximations and truncation
effects during their determination. Departures of the results from the two methods are significantly larger for frequencies
near the Free Core Nutation (FCN) resonance. This is particularly true for the Oppolzer terms of the angular momentum axis.
The Earth model adopted is a little bit different in each case: for the Liouville system solution, we have limited the model
to a homogeneous elastic mantle and a homogeneous liquid core. Another source of some of the small differences in the results
is the presence of a solid inner core in Wahr's theory. We confirm through the analytical calculation the strong effect of
the core on the Oppolzer terms of the angular momentum axis for a non-rigid Earth at the precession frequency. Finally, an
application is given in the determination of the axes' position at J2000 for a non-rigid Earth.
Received: 23 February 1998 /Accepted: 18 November 1998 |
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Keywords: | , Non-rigid Earth,Nutations,Transfer function,Oppolzer terms |
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