The Effect Of Zonal Tides On The DynamicalEllipticity Of The EarthAnd Its Influence On The Nutation

In this paper, the expressions of variations of the dynamical ellipticity and the principal moments of inertia due to the deformations produced by the zonal part of the tidal potential are obtained. Starting from these expressions, we have studied from equations related to Hamiltonian theory, their effects on the nutation and finally we have evaluated numerically such influences, with a level of truncation at 0.1 μas. Thus we have shown that some coefficients are quite large with respect to the usual accuracy of up-to-date observations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effects On the Nutation of the Non-Zonal Harmonics of Third Degree

In this paper, we calculate the coefficients of the nutation for a rigid Earth model due to the C _3m and S _3m (m ≠ 0) harmonics of the geopotential, starting from the Hamiltonian theory as developped by Kinoshita (1977). We show that these coefficients are far from being negligible as given the level of truncation of 0.1 μas which is necessary in the reconstruction of the tables of nutation, and also that their value is very close to that given by Bretagnon et al. (1997). This revised version was published online in July 2006 with corrections to the Cover Date.     

Effects of the Triaxiality on the Rotation of Celestial Bodies: Application to the Earth,Mars and Eros

In this paper we discuss the influence of the triaxiality of a celestialbody on its free rotation, i.e. in absence of any external gravitationalperturbation. We compare the results obtained through two different analytical formalisms, one established from Andoyer variables by usingHamiltonian theory, the other one from Euler's variables by usingLagrangian equations. We also give a very accurate formulation of thepolar motion (polhody) in the case of a small amplitude of this motion.Then, we carry out a numerical integration of the problem, with aRunge–Kutta–Felberg algorithm, and for the two kinds of methods above, that we apply to three different celestial bodies considered as rigid : the Earth, Mars, and Eros. The reason of this choice is that each of this body corresponds to a more or less triaxial shape.In the case of the Earth and Mars we show the good agreement betweenanalytical and numerical determinations of the polar motion, and theamplitude of the effect related to the triaxial shape of the body, whichis far from being negligible, with some influence on the polhody of theorder of 10 cm for the Earth, and 1 m for Mars. In the case of Eros, weuse recent output data given by the NEAR probe, to determine in detailthe nature of its free rotational motion, characterized by the presence ofimportant oscillations for the Euler angles due to the particularly largetriaxial shape of the asteroid.     

Diurnal and subdiurnal luni-solar nutations: comparisons and effects

We present a comparison of the diurnal and subdiurnal terms of the three last theories of rigid Earth's rotation: SMART97, RDAN97 and REN 2000. For a better interpretation of the observations, we characterize their contribution to the polar motion and we estimate the non-rigid effects, which are at the level of a few microarcseconds.     

Effects on the nutation of C4,m and S4,m Harmonics

In this paper, we make a study about the influence of the coefficients of the geopotential C_4,m and S_4,m, (m=1,2,3,4) on the nutation, starting from the Hamiltonian theory as developed by Kinoshita (1977).We obtain ten coefficients larger than 0.05 μ as for the nutation in longitude and six for the nutation in obliquity. The present results are included in the reconstruction of the theory of nutation (REN‐2000) at the level of truncation of 0.1 μ as (Souchay et al., 1997). This revised version was published online in July 2006 with corrections to the Cover Date.