On the precession constant: Values and constraints on the dynamical ellipticity; link with Oppolzer terms and tilt-over-mode

The luni-solar precession, derived by theoretical considerations from the precession of the equator, is one of the most important parameters for computing not only precession but also nutations, due to its relation to the dynamical flattening. In this paper, we review the numerical values of this parameter, from the geodynamical point of view as well as the astronomical point of view, from the observational point of view as well as from the theoretical point of view. In particular, we point out a difference of about 1 percent between the global Earth dynamical flattening derived from the astronomical observations and the values derived from the different geophysical computations. The nutation amplitudes depend on the Earth dynamical flattening and this dependence is amplified by a resonance at an important normal mode, the Tilt-Over-Mode (TOM). Since the astronomical point of view as well as the geophysical one are confronted, we also take the opportunity to make the link between the TOM and the expressions of the nutations of the different axes which, in turn, are related with one another by the Oppolzer terms. Both, the Oppolzer terms and the TOM originate from a reference frame tilt effect. In writing the link between the nutational motions of the different axes, and so, in writing the Oppolzer terms, we also make the link with the precessional motion.