6 Arguments and constant terms used in REN-2000 series

It seems useful to gather in Table 8 the values of all the constant terms and parameters which have been used for the construction of the series REN-2000 through the present study and the two other ones (Souchay & Kinoshita 1996, 1997). In fact all those which are related to the lunar potential are taken from the theory ELP-2000 (Chapront-Touzé & Chapront 1988), as the polynomial expressions of the Delaunay's arguments which have to be used when calculating the nutation for a given date. All those which are related to the Sun and to the planets are taken from the theory VSOP82 (Bretagnon 1982), as the mean longitudes of the planets, but it must be noticed that the mean longitude of the Sun $L_{\rm S}$ is replaced in some cases by the expression in function of the Delaunay's variables, that is to say: $L_{\rm S} = F - D + \Omega$ as it is was already mentioned in the paragraph above related to the effects of the Sun. This substitution was already adopted in the rigid Earth nutation tables for the IAU conventional nutation theory (Seidelmann 1982).

The corrections which are about to occur concerning the expressions of the arguments and of the values constant terms in the recent past (Simon et al. 1994) or in the future seem to be too small to affect in a significant manner the value of the global nutation. The general precession in longitude constitutes the only exception to this assertion, for it has been shown by Souchay & Kinoshita (1996) that the correction of -0.3266''/cy. with respect to the conventional IAU value (Lieske et al. 1977) lead to individual corrections of the coefficients of nutation proportional to their amplitude, reaching 1 mas for the leading term of 18.6 y nutation in longitude. Notice that our value for the general precession in longitude $p_{\rm A}$ at J2000.0 is then $5028\hbox{$.\!\!^{\prime\prime}$}7700$/cy instead of $5029\hbox{$.\!\!^{\prime\prime}$}0966/$cy (Lieske et al. 1977).

In our tables REN-2000, the coefficients having the same argument but with different kinds of contributions are not mixed together. They are kept separately in order to have a clear insight of the weigh of each contribution. The general presentation is quite similar to the presentation of the tables established from precedent rigid Earth nutation theories (Kinoshita 1977; Kinoshita & Souchay 1990) and of the present conventional tables of the IAU1980 nutation theory. Only the argument $\Phi$ has been added, in order to include the quasi-diurnal and sub-diurnal nutations.

  

Figure 3: Variables used to characterize the diurnal and sub-diurnal nutations

The definition of the angle $\Phi$ is a little subtle, so that we can refer to the Fig. 3 in order to understand it: $\Phi$ corresponds to the angle $(l+g+\Delta \Phi_{0})$ where (Kinoshita 1977): g is the angle between the equinox of date and the node N between the equator of figure ($E_{\rm q}$) and the plane ($\Sigma_{\rm am}$) perpendicular to the angular momentum vector. l is the angle between N and A where A is along the principal axis of the Earth corresponding to the minimum moment of inertia. Note that the the angle J between ($E_{\rm q}$) and ($\Sigma_{\rm am}$) is very small (of the order of 10^-6 rd) so that (l+g) can be considered along ($E_{\rm q}$). The phase shift $\Delta \Phi_{0}$ correponds to the angle between the Greenwich prime meridian and A, along the equator of figure ($E_{\rm q}$). This phase shift explains the presence of out-of-phase components both in longitude and in obliquity. Then we can remark that $\Phi$ is the angle of sidereal rotation of the Earth.

Then $\Phi$ can be noted as follows, with the same kind of calculations as Bretagnon et al. (1997): $\Phi = 4.89496121282 + 2301216.7526278 t$, where t is expressed in rd/1000 y.

Notice that $\Phi$ is reckoned from the moving equinox of the date instead of the fixed one so that the secular component is a little different as for these last authors (the difference correponds in fact to the planetary precession $\chi$).

As for the value for the phase $\Delta \Phi_{0}$, it can be taken from the components C_2,2 and S_2,2 of the geopotential: $\Delta \Phi_{0} = {1 \over 2}$arctan $\left( {S_{2,2} \over C_{2,2}} \right)$. By taking the values of C_2,2 and S_2,2 from the the IERS standards (Mc. Carthy 1992), we thus find: $\Delta \Phi_{0} = -14\hbox{$.\!\!^\circ$}928537 = -0.2605521$ rd.