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

¹ Dept. of Sciences and Informatics, University Centre of Defence at the Spanish Air Force Academy, 30720 Santiago de la Ribera, Spain
e-mail: tomas.baenas@cud.upct.es
² Dept. of Aerospace Engineering, University of León, 24071 León, Spain
³ Dept. of Applied Mathematics, University of Alicante, PO Box 99, 03080 Alicante, Spain

Received: 14 March 2019
Accepted: 25 April 2019

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.