Dynamical adjustments in IAU 2000A nutation series arising from IAU 2006 precession

Abstract

The adoption of International Astronomical Union (IAU) 2006 precession model, IAU 2006 precession, requires IAU 2000A nutation to be adjusted to ensure compatibility between both theories. This consists of adding small terms to some nutation amplitudes relevant at the microarcsecond level. Those contributions were derived in previously published articles and are incorporated into current astronomical standards. They are due to the estimation process of nutation amplitudes by Very Long Baseline Interferometry (VLBI) and to the changes induced by the J 2 rate present in the precession theory. We focus on the second kind of those adjustments, and develop a simple model of the Earth nutation capable of determining all the changes arising in the theoretical construction of the nutation series in a dynamical consistent way. This entails the consideration of three main classes of effects: the J 2 rate, the orbital coefficients rate, and the variations induced by the update of some IAU 2006 precession quantities. With this aim, we construct a first order model for the nutations of the angular momentum axis of the non-rigid Earth. Our treatment is based on a Hamiltonian formalism and leads to analytical formulae for the nutation amplitudes in the form of in-phase, out-of-phase, and mixed secular terms. They allow numerical evaluation of the contributions of the former effects. We conclude that the accepted corrections associated with the J 2 rate must be supplemented with new, hitherto unconsidered terms of the same order of magnitude, and that these should be incorporated into present standards.

Consistency Problems in the Improvement of the IAU Precession–Nutation Theories: Effects of the Dynamical Ellipticity Differences

“…The computation of this effect (Escapa et al 2014(Escapa et al , 2015, following the perturbation equations, leads to the appearance of mixed secular terms (proportional to t, previously reported in Capitaine et al 2005), and to in-and out-of-phase nutations. Namely, the following expressions to be summed to equations (3) are 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 obtained…”

“…To be consistent in the development of the theory, the inclusion of the J 2 time rate forces the consideration of the time rate of the orbital coefficients A (0,1,2) i (Kinoshita 1977), due to the secular variation of Sun eccentricity (Escapa et al 2014(Escapa et al , 2015. Analytically its treatment is similar to that of J 2 rate, providing also out-of-phase nutations and mixed secular terms with formulas similar to equations (10).…”

“…out of the scope of this paper, which focuses on effects associated to the variations of the dynamical ellipticity. However, for the sake of completeness, let us say that the former corrections were completed by Escapa et al (2014,2015), the total 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 …”

A First Assessment of the Corrections for the Consistency of the IAU2000 and IAU2006 Precession-Nutation Models

“…However, the WG in charge considered that nutations were out of the scope of its task, and the fact was not mentioned in the IAU resolution. Later, Escapa et al (2014Escapa et al ( , 2016Escapa et al ( , 2017 showed that a few additional terms of the same order of magnitude have to be added to the 2005 expressions to get complete dynamical consistency between the official precession and nutation models. The issue was discussed in several occasions, particularly inside the IAU/ International Association of Geodesy (IAG) Joint Working Group on Theory of Earth rotation and validation (JWG TERV), and the main authors were invited to propose actions.…”

“…The latter amplitudes are implicitly factorized by J 2 through H d or the K S;M Kinoshita's constants (Kinoshita and Souchay 1990), and besides they depend on several circular functions of the 0 obliquity. Therefore, the total induced variations of the non-rigid Earth amplitudes cannot be got by simply making a rescaling associated only to J 2 (Escapa et al 2014(Escapa et al , 2016(Escapa et al , 2017Escapa and Capitaine 2018a,b).…”