Precession of the non-rigid Earth: Effect of the mass redistribution

Abstract

This research is focused on determining the contribution to the precession of the Earth’s equator due to the mass redistribution stemming from the gravitational action of the Moon and the Sun on a rotating solid Earth. In the IAU2006 precession theory, this effect is taken into account through a contribution of −0.960 mas cy−1 for the precession in longitude (with the unspecific name of non-linear effect). In this work, the revised value of that second-order contribution reaches −37.847 mas cy−1 when using the Love numbers values given in IERS Conventions, and −43.945 mas cy−1 if those values are supplemented with the contributions of the oceanic tides. Such variations impose a change of the first-order precession value that induces relative changes of the Earth’s dynamical ellipticity of about 7.3 and 8.5 ppm, respectively. The corresponding values for the obliquity rate are 0.0751 and 0.9341 mas cy−1, respectively, in contrast to 0.340 mas cy−1 considered in IAU2006. The fundamentals of the modeling have been revisited by giving a clear construction of the redistribution potential of the Earth through the corresponding changes in the Earth tensor of inertia. The dynamical problem is tackled within the Hamiltonian framework of a two-layer Earth model, introduced and developed by Getino and Ferrándiz. This approach allows for the achievement of closed-analytical formulae for the precession in longitude and obliquity. It makes it possible to obtain numerical values for different Earth models once a set of associated Love numbers is selected. The research is completed with a discussion on the permanent tide and the related estimation of the variation of the second degree zonal Stokes parameter, J2, and also the indirect effects on nutations arising from the relative change of the Earth’s dynamical ellipticity.

Nutation of the non-rigid Earth: Effect of the mass redistribution

“…In this research, the contributions to the nutations of the figure axis arising from the tidal redistribution potential were derived and computed. This paper thus completes the study of the redistribution effects on the precession and nutation initiated by the authors in Baenas et al (2019).…”

“…The effects of the mass redistribution of the Earth on the precession of the equator were studied in two research works by Baenas et al (2017aBaenas et al ( , 2019, who derived updated values of the precession rates in longitude and obliquity. Those values are a correction of the current ones adopted by the IAU2006 precession theory (Capitaine et al 2003(Capitaine et al , 2005, which is included in that formulation among the second order components of the precession rates that were taken from previous results of several authors.…”

“…Namely, they stemmed from extending that solution up to the second order in the sense of mathematical perturbation methods. In contrast, Baenas et al (2019) -hereinafter referred to as Paper I -worked out the effects raised by the redistribution tidal potential, that is, the additional potential due to the Earth's anelastic yielding resulting from the lunisolar attraction. Here, the same approach is extended in order to derive the nutations of the Earth's figure axis.…”

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

“…Besides, those findings imply that the value of the Earth's dynamical ellipticity, H d , must be adjusted since the observed precession rate is of course unchanged. The H d variation is of some ppm and the resulting corrections to nutations, or indirect effects, are non-negligible since they approach near 100 as for certain terms (Baenas et al 2019). 6.…”

Secular changes in length of day: Effect of the mass redistribution

“…It arises from the tidal deformation exerted on the Earth by the perturbing bodies (Munk & MacDonald 1960;Peale 1973). The main features of this potential energy were recently revisited by Baenas et al (2019Baenas et al ( , 2020a who studied the effect of mass redistribution with a tidal origin on the precessional and nutational motions of the Earth's figure axis. These latter authors apply the Hamiltonian formalism to a deformable two-layer Earth model (Getino & Ferrándiz 2001) with an anelastic mantle and fluid core, and derive analytical closed-form formulae describing those motions.…”