Due to the accuracy now reached by space geodetic techniques, and also considering some modelisations, the temporal variations of some Earth Gravity Field coefficients can be determined. They are due to Earth oceanic and solid tides, as well as geophysical reservoirs masses displacements. They can be related to the variations in the Earth's orientation parameters (through the inertia tensor). Then, we can try to improve our knowledge of the Earth Rotation with those space measurements of the Gravity variations. We have undertaken such a study, using data obtained with the combination of space geodetic techniques. In particular, we use CHAMP data that are more sensitive to such variations and that complete the ones already accumulated (for example with Starlette and LAGEOS I). In this first approach, we focus on the Earth precession nutation, trying to refine it by taking into account the temporal variations of the Earth dynamical flattening. The goal is mainly to understand how Geodesy can influence this field of science. Like this, we will be able to compare our computation with up to date determinations of precession nutation.
Due to the accuracy now reached by space geodetic techniques, the temporal variations of a few Earth gravity field coefficients can be determined. Such variations result from Earth oceanic and solid tides, as well as from geophysical reservoirs masses displacements and postglacial rebound. They are related to variations in the Earth's orientation parameters through their effect in the inertia tensor. We use (i) time series of the spherical harmonic coefficients C 20 (C 20 = -J 2 ) of the geopotential and also (ii) ∆C 20 models for removing a part of the geophysical effects. The series were obtained by the GRGS (Groupe de recherche en Géodésie Spatiale, Toulouse) from the orbitography of several satellites (e.g. LAGEOS, Starlette, CHAMP) from 1985 to 2002 (Biancale et al., 2000). In this preliminary approach, we investigate how these geodesic data can influence precession-nutation results.
From the C 20 variation series, we can derive the corresponding variations of the dynamical flattening H, according to : ∆H
C , where M is the mass of the Earth, R e its mean equatorial radius and C its principal moment of inertia. The ∆H series obtained in this way are mostly composed of an annual, semi-annual and 18.6-year terms. In order to investigate the influence of the variations in dynamical flattening on the precession-nutation, we integrate the following precession equations (Williams 1994, Capitaine et al. 2003 = P03) based on the observed ∆H series :
where r ψ and r ǫ are the total contributions to the precession rate, respectively in longitude and obliquity, depending on the factor H.
We use the precession equations (1) and the software GREGOIRE (Chapront, 2003), together with the ∆C 20 data, to compute the effects in precession nutation. We find differences in the coefficients of the polynomial development of the precession angle ψ A , depending on the ∆C 20 contribution and the J 2 rate implemented (J 2 rate = J2 ). The results are composed of a polynomial part and a periodic part (i.e. Fourier and Poisson terms) discussed in the next paragraph. The effect due to the J 2 rate (i.e. effect on the t 2 term of ψ A ) can be taken into account using a series from 1985 to 1998 (Bourda and Capitaine, 2004). In Table 1, our results rely on ∆C 20 data from 1985 to 2002 and then do not take into account this effect.
The precession rate (i.e. term in t in the ψ A development) derived from the C 20 obtained by space geodetic techniques is smaller than the one obtained by VLBI (see Table 1). The difference is about 400 mas/c, i.e. ≃ 10 -4 × the precession rate value (this corresponds to a constant part of -2.6835 10 -7 in the H value). Dehant and Capitaine (1997) already mentioned such a discrepancy relative to the IAU 1976 precession. Considering an error of about 10 -10 in the ∆C 20 data, we deduce an error of about 0.5 mas/c in the precession constant, which means that the difference obtained above is significant. In the future, several causes for this discrepancy will be investigated, such as the effect of the violation of hydrostatic equilibrium.
Then, the H variations coming from the residuals (i.e. ∆C 20 data without atmospheric, oceanic tides or solid Earth tides ∆C 20 models) observed by space geodetic techniques involved effects on the precession angle of about 1 µas or less (see Table 2). We also observed that the oceanic and atmospheric contributions were negligible. The principal periodic change, is due to the ∆C 20 solid Earth Tides 18.6-yr variation, and is about 120 µas (in sine).
For further studies, the Earth model has to be improved by considering (i) a refine Earth model, with core-mantle couplings and (ii) a reliable J 2 rate value.
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