Contributions of the Elasticity to the Precession of a Two-Layer Earth Model

Abstract

We focus on the updating of a specific contribution to the precession of the equator in longitude, usually named as "second order." It stems from the crossing of certain terms of the lunisolar gravitational potential. The IAU2006 precession theory assigns it the value of −46.8 mas/cy that was derived for a rigid Earth model. Instead of that model, we consider a two-layer Earth composed of an elastic mantle and a liquid core, working out the problem within the Hamiltonian framework developed by Getino and Ferrándiz. The targeted effect is obtained without further simplifying assumptions through Hori's canonical perturbation method applied up to the second order of perturbation. On account of using a more realistic Earth model, the revised value of the second-order contribution is significantly changed and reaches −55.29 mas/cy. That variation of the second-order contribution is larger than other contributions included in IAU2006. It must be compensated with an increase of −8.51 mas/cy in the value of the lunisolar first-order component ¢ p A of the precession of the equator rate, which is derived from the total rate by subtracting the remaining contributions accounted for in IAU2006 precession. The updating of the second-order contribution implies that the ¢ p A parameter has to be changed, from 5040684.593 to 5040693.104 mas/cy in absence of potential revisions of other contributions. It entails a proportional variation of Earth's dynamical ellipticity H d , for which the estimation associated with IAU2006, 0.00327379448, should be updated to 0.00327380001, about 1.7 ppm larger.

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

“…We show that the changes of the precession rates are not negligible when realistic hypotheses about the Earth's rheology and dynamics are assumed. The resulting contributions are numerically comparable to some of the components of the current precession theory, displayed, for example, in Table 2 of Baenas et al (2017).…”

“…The mechanisms entering into this process are complex and lead to a resonance expansion of the Love number k 2 , as it is explained in the comprehensive work by Mathews et al (1995). Recently, this problem has been revisited within the Hamiltonian formalism by Baenas et al (2017), achieving closed-analytical formulae compatible with the previous works. That expansion can be written in the general form (e.g., Mathews et al 1995) in the frequency domain as…”

“…(31)), it is necessary to quantify its contribution to the Earth precession rates in longitude and obliquity. Although other approaches are possible, the formulation of this problem in the Hamiltonian formalism of the rotation of the non-rigid Earth (e.g., Getino & Ferrándiz 1995Escapa et al 2001, or Escapa 2011 presents some advantages (e.g., Baenas et al 2017).…”

“…Next, the main elements necessary for this construction will be sketched. Further details can be found in two recent works by the authors, Baenas et al (2017) and Escapa et al (2017), and references therein.…”

“…In a previous study by the authors (Baenas et al 2017), the revision of such components of the secular motion of the equator was initiated, and it was shown that the second-order lunisolar contribution changes significantly when the assumed rigid Earth model is replaced by a two-layer one that incorporates some of the effects of the deformation one (achieving a difference of −8.51 mas cy −1 in the precession in longitude with respect to the IAU2006 reference value).…”