ROTATION OF THE RIGID EARTH

Bretagnon P.

Bureau des longitudes, avenue Denfert-Rochereau, 75014 PARIS, FRANCE

We present the computation of the precession and nutation expressions built with the analytical theories of the motion of the Moon, the Sun and the planets of the Bureau des longitudes. We take into account the influence of the Moon, the Sun and all the planets on the potential of the Earth limited to

We determine the 3 Euler angles calculating the components of the torque of the external forces with respect to the geocenter in the case of the rigid Earth. The equations are solved by iterations and so are taken into account the nutations-on-the-nutations effects. We have determined the analytical variations of the angles \psi and \omega fixing the equator with respect to the ecliptic J2000. We find, in \omega, a secular term of -26.5026 mas per century. We have used the VSOP87A solution for the Sun and the planets and the ELP82 solution for the Moon. For the latter, we have now retained only the terms greater than 0''.001. The analytical solution of the precession-nutation has been compared to a numerical integration over the time span 1900--2050. The differences do not exceed 16 for \psi and 12 for \omega.