Limitations of the IAU2000 nutation model accuracy due to the lack of Oppolzer terms of planetary origin

Abstract

Context. The current IAU2000 nutation model performed different approximations, one of them being that the Oppolzer terms associated to the planetary perturbations of the nutations were assumed to be smaller than 5 μas and thus were neglected. At present, the uncertainties of the amplitudes of individual components of the observed nutations are better, and the conventional nutation model does not fit the accuracy requirements pursued by the International Astronomical Union (IAU) and the International Association of Geodesy (IAG). Aims. The objective of this work is to estimate the magnitude of the lacking Oppolzer terms of the planetary nutations and find out whether they are still negligible or not. Methods. The Oppolzer terms resulting from the direct and indirect planetary perturbations of the Earth’s rotation have been computed for a two-layer Earth model following the Hamiltonian theory of the non-rigid-Earth. Results. The planetary Oppolzer terms for the non-rigid Earth are not really negligible as believed, and some of them have amplitudes larger than 10 μas, therefore significantly above the current level of uncertainty of individual harmonic constituents. Conclusions. In the short term, the IAU2000 nutation model must be supplemented with suitable corrections accounting for those missing components; its planetary component must be thoroughly revised in the medium term.

Report of the IAU/IAG Joint Working Group on Theory of Earth Rotation and Validation

“…The joint effect of the neglected terms can be above the GGOS threshold. Those facts are illustrated in Table 1 (an abridged version of Table 1 in Ferrándiz et al 2018) and Fig. 1.…”

“…2. Also for nutation theory, it has been found that the two independent blocks that compose the IAU2000 series, namely lunisolar and planetary, are inconsistent with each other (Ferrándiz et al 2018). In fact, the MHB2000 transfer function was not applied to the amplitudes of the 687 planetary terms, either direct or indirect; instead, those terms were taken without change from an early version of the rigid-Earth theory REN2000.…”

The Rotation of the Nonrigid Earth at the Second Order. II. The Poincaré Model: Nonsingular Complex Canonical Variables and Poisson Terms

“…However, Souchay et al (2007, Tables 2-5) pointed out the existence of some arguments present in MHB2000 and not in REN2000, and vice versa. Recently, Ferrándiz et al (2018) found that the transfer function was not applied to the planetary terms, limiting in this way the accuracy of IAU 2000A nutation. 6 From a numerical point of view, the friction-generated effects in the secondorder solution would be, in principle, negligible, considering the different magnitudes of first-order in-phase and out-of-phase amplitudes (IERS Conventions 2010).…”