Effects of zonal deformations and the Earth's rotation rate variations on precession-nutation

International audienceBecause of their importance in the accurate modeling of the Earth's orientation in space, some non-negligible predictable effects on precession-nutation are investigated. This paper considers the coupling effects between the axial and the equatorial components of the Earth's rotation vector in the dynamical equations, and the effects of the second order lunisolar torque due to the Earth's zonal deformations. Firstly, the coupling effects are shown to contribute for less than 0.1 muas and are therefore negligible. Secondly, we demonstrate that the 0.7 mas contribution of the rotation rate variations due to zonal tides to the nutation in obliquity deduced by Bretagnon et al. (\cite{Bretagnon00}, Proc. IAU Coll., 180, 230; \cite{Bretagnon01}, Celest. Mech. Dyn. Astr., 80, 177) is an artefact which comes from an incomplete way of taking into account the effect of the rotation rate variations. The net contribution is shown to be negligibly small. Thirdly, for an Earth model with an elastic mantle and decoupled liquid core, the contribution of the second-order lunisolar torque due to the Earth's zonal deformations is shown to be 207.9 muas and -9.7 muas on the 18.6-year nutation respectively in longitude and in obliquity, and a correction of -4925.9 muas/century on the precession in longitude