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

Abstract

The luni-solar precession, derived by theoretical considerations from the precessi0n-o~ 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.

Cyclostratigraphy and its revolutionizing applications in the earth and planetary sciences

“…Thomson's (1990) ΔH estimate of ~1% for climate friction from Pleistocene ice loading should have been suffi cient for this resonance to have occurred. If evidence for resonance cannot be found, which appears to be the case so far, this may signify that presently assumed Earth models are not adequate, and that a fully dynamical H with mantle viscosity, core-mantle interface processes, and an active core needs to be considered (Dehant and Capitaine, 1997).…”

Expressions for IAU 2000 precession quantities

“…(14) of L77) expressing the motion of the mean pole of date about the ecliptic pole, once given the values at the reference epoch for the mean obliquity of the ecliptic, 0 , for the speed of precession, and for the geodesic precession (de Sitter & Brouwer 1938). The expression for general precession (denoted p A in L77) combines the precession in longitude of the equator and the precession of the ecliptic, the former being a function of the Earth's dynamical flattening and other constants related to orbital motion of the Moon and the Earth (see for example Kinoshita 1977;Dehant & Capitaine 1997). The geodesic precession is a general relativistic effect related to the rotation of the geocentric reference system with respect to the solar-system barycentric reference system (see for example Brumberg 1991).…”

Forced nutations of a two-layer Earth model

“…The numerical values of these coefficients cannot be computed from any well‐established geophysical theory with accuracy enough to provide accurate values for the nutation. Think for instance of the large error in the computation of the dynamical ellipticity H D following preliminary earth model (PREM) (Dziewonski & Anderson 1981) and 1066A (Gilbert & Dziewonski 1975) models, pointed out by Dehant & Capitaine (1997). The values of the parameters are thus obtained by means of a generalized least‐squares adjustment (Getino, Martín & Farto 1999) taking the IERS 96 series as a basic reference, so that we could afford the computational overhead more easily, as opposed to using a large set of observational data.…”