All Tables

Table 1: Comparison between constants used for different determinations of the dynamical flattening (H): (1) the precession rate in longitude ( $\psi _1$ ); (2) the speed of the general precession in longitude (p₁); (3) the geodesic precession (p_g); and (4) the obliquity of the ecliptic at J2000.0 ( $\epsilon _0$ ). The observational value actually used for each study is written in bold.
Table 2: Numerical values used in this study. H, $\psi _1$ and $\omega _1$ are integration constants.
Table 3: Comparison between different values of the coefficient $C/\left (M {R_{\rm e}}^2\right )$ and of the constant part for H: (1) IAG values (Groten 1999) - (2) MHB values (Mathews et al. 2002) - (3) Constant part H^** obtained from Eq. (8) using the M, $R_{\rm e}$ and C IAG values - (4) Method of "Clairaut'' (Sect. 3.2), assuming hydrostatic equilibrium. The third and fourth methods use a constant part for $\bar{C}_{20}$ of $-4.841695 \times 10^{-4}$ in Eq. (8) (i.e. $J_2=1.0826358 \times 10^{-3}$ ). The sense of the computation is indicated by the arrows.
Table 4: Summary of the constant parts for H and C₂₀ (Constant part + Permanent tide) used in this study.
Table 5: Adjustment of periodic terms in the $\Delta H$ contributions, for the data span 1985-2002 for various $\Delta H$ geophysical sources (atmospheric $\Delta H_{\mbox{\scriptsize ~atm.}}$ , oceanic tides $\Delta H_{\mbox{\scriptsize ~oc.}}$ and solid earth tides $\Delta H_{\mbox{\scriptsize ~soltid.}}$ , as well as the residuals $\Delta H_{\mbox{\scriptsize ~res.}})$ - Units are in 10^-10 rad.
Table 6: Specific adjustment of the $\Delta H$ residual series ( $\Delta H_{\mbox{\scriptsize ~res.}}$ ), from 1985 to 1998. The secular trend is considered as in Eq. (30) - Units are in 10^-10 rad.
Table 7: Adjustment of the total series of $\Delta H$ ( $\Delta H_{\mbox{\scriptsize ~tot.}}$ ), from 1985 to 2002 - Units are in 10^-10 rad.
Table 8: Influence of $\dot{J}_2$ on the polynomial development of $\psi _A$ (more particularly on the t² and t³ terms): (1) IAU2000 (Mathews et al. 2002); (2) P03 (Capitaine et al. 2003); and (3) Same computation as in P03 but with other $\dot{J}_2$ values. The J₂ secular trend estimation based on our C₂₀ residuals series is: $\dot{J}_2 = -2.5 \times 10^{-9}$ /cy.
Table 9: Polynomial part of the $\psi _A$ and $\omega _A$ developments (units in arcseconds): comparison of (1) IAU2000 (Mathews et al. 2002) - (2) P03 (Capitaine et al. 2003) - (3) Differences of Geod04 (this study) with respect to P03, considering all the contributions for $\Delta H$ (Table 7, $\Delta H_{\rm tot}$ ) - (4) Differences of Geod04 with respect to P03, obtained with a H constant part different from $H_{\rm MHB}$ , but not used in the following (see Table 3 for the H^* and H^** constant values).
Table 10: Polynomial part of the $\psi _A$ development (units in arcseconds) for various $\Delta H$ sources used in our study, with respect to P03: comparison of (1) P03 (Capitaine et al. 2003) - (2) Difference between P03 and Geod04 (i.e. the effect of the total $\Delta H$ ) - (3) Difference between P03 and the effect of the $\Delta H$ residuals.
Table 11: Fourier part of the $\psi _A$ development, depending on the contribution considered for the $\Delta H$ periodic effect (units in $\mu$ as).