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.