4 Position angles of the inertial mean ecliptic J2000.0

We recall here the definition of the position angles of the inertial mean ecliptic J2000.0 with respect to various "equatorial'' reference systems (R). R stands either for ICRS (International Celestial Reference System), MCEP (Reference linked to the Mean Celestial Ephemeris Pole of J2000.0) or JPL (Reference system defined by a JPL numerical integration such as DE200, DE403 or DE405). We set:
- $\gamma_{2000}^{I}(R)$: ascending node of the inertial mean ecliptic J2000.0 on the equator of R;
- $\epsilon (R)$: Inclination of the inertial mean ecliptic on the equator of R;
- o(R): Origin of right ascensions in the equator of R;
- $\phi (R)$: Arc $o(R) \gamma_{2000}^{I}(R)$;
- $\psi (R)$: Arc $\gamma_{2000}^{I}({\rm ICRS})\gamma_{2000}^{I}(R)$.
Two solutions are investigated. They are denoted Sol. 1 (MCEP) and Sol. 2 (ICRS), corresponding to the reference systems MCEP or ICRS. In the reduction of LLR observations one has to transform the terrestrial coordinates of the station to celestial ones. Such a transformation depends of the daily values of the polar motion $x_{{\rm p}}, y_{{\rm p}}$, the difference UT1-UTC and a precession nutation matrix $P\times N$ which rotates the celestial instantaneous axes to a J2000.0 fixed celestial "equatorial'' system of axes.

In Sol. 1 (MCEP), the matrix $P\times N$ is provided by analytical solutions: polynomial expressions for the orientation of the Earth's equator (Williams 1994) and IERS 1996 theory of nutation (McCarthy 1996). The reference plane is the mean equator of the CEP for J2000.0. The corresponding system of axes is that of the MCEP.

In Sol. 2 (ICRS), $P\times N$ is computed via a system of corrections to a conventional set of values for the nutations in longitude and obliquity, i.e. $\delta\psi$ and $\delta\epsilon$ which are daily values provided by IERS (series C04). The corresponding system is the ICRS.

In both solutions, corrections to the precession constant and to the obliquity are fit. Sol. 1 (MCEP) involves the theoretical value of the obliquity rate due to (Williams 1994), -46.8340''/cy. Corrections to the principal terms of the nutations in longitude and obliquity are also fit in Sol. 1 (MCEP) (see Sect. 10).