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

José M Ferrándiz,M C Martínez-Belda,Juan F Navarro,Juan Getino,Alberto Escapa

doi:10.1051/0004-6361/201730840

José M Ferrándiz, M C Martínez-Belda + Show 3 more

Open Access

https://doi.org/10.1051/0004-6361/201730840

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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.

Highlights

Resolution B1.6 of the twenty fourth General Assembly of the International Astronomical Union (IAU) endorsed the nonrigid-Earth solution MHB2000 (Mathews et al 2002) as the IAU2000A nutation model, which is concisely described in paragraph [8] of Herring et al (2002) as “generated by the convolution of the transfer function from Mathews et al (2002) with the rigid-Earth nutation series REN2000” (Souchay et al 1999)
The second block is formed by 687 terms corresponding to the direct and indirect planetary perturbations, which are directly taken from the underlying rigid theory, and have amplitudes smaller than 0.5 mas (Herring et al 2002); the planetary nutations are expressed in a different set of arguments, namely the eight mean longitudes of the planets and the precession parameter pA
As shown in the previous section, the rigorous computation of the Oppolzer terms for the non-rigid-Earth model reveals that their amplitudes are not negligible at all

Summary

Introduction

Resolution B1.6 of the twenty fourth General Assembly of the International Astronomical Union (IAU) endorsed the nonrigid-Earth solution MHB2000 (Mathews et al 2002) as the IAU2000A nutation model, which is concisely described in paragraph [8] of Herring et al (2002) as “generated by the convolution of the transfer function from Mathews et al (2002) with the rigid-Earth nutation series REN2000” (Souchay et al 1999). The differences in the nutations of the figure axis and angular momentum axis (Oppolzer terms) with planetary origin were never determined in Kinoshita & Souchay (1990), Souchay & Kinoshita (1997), or REN2000 We consider it proper to recall briefly the terminology and concepts relative to the Poisson and Oppolzer terms, as they are not visible when a solution for a non-rigid-Earth model is computed through a transfer function method. Let us notice that the missing convolution could have been done without any problem, since for example, another contemporary solution, SF2000 (Shirai & Fukushima 2001), applied a simpler transfer function based on Sasao et al (1980) to the rigid-Earth solution RDAN97 (Roosbeek & Dehant 1998a), and provided 32 planetary terms for a (non-rigid) two-layer Earth model It may not be out of place to recall that the rigid-Earth RDAN97 theory does not give separately the (direct) lunisolar and the indirect and direct planetary nutations, nor does it indicate the body that originates each term. The careful estimation of the associated deficiencies, which are the origin of deviations or systematic errors in the model, is presented

Computation of Oppolzer terms in the planetary nutations

Kp sin I

Discussion and conclusions