# Numerical theory of rotation of the deformable Earth with the two-layer fluid core. Part 1: Mathematical model

Ontology type: schema:ScholarlyArticle

### Article Info

DATE

2006-11-15

AUTHORS ABSTRACT

Improved differential equations of the rotation of the deformable Earth with the two-layer fluid core are developed. The equations describe both the precession-nutational motion and the axial rotation (i.e. variations of the Universal Time UT). Poincaré’s method of modeling the dynamical effects of the fluid core, and Sasao’s approach for calculating the tidal interaction between the core and mantle in terms of the dynamical Love number are generalized for the case of the two-layer fluid core. Some important perturbations ignored in the currently adopted theory of the Earth’s rotation are considered. In particular, these are the perturbing torques induced by redistribution of the density within the Earth due to the tidal deformations of the Earth and its core (including the effects of the dissipative cross interaction of the lunar tides with the Sun and the solar tides with the Moon). Perturbations of this kind could not be accounted for in the adopted Nutation IAU 2000, in which the tidal variations of the moments of inertia of the mantle and core are the only body tide effects taken into consideration. The equations explicitly depend on the three tidal phase lags δ, δc, δi responsible for dissipation of energy in the Earth as a whole, and in its external and inner cores, respectively. Apart from the tidal effects, the differential equations account for the non-tidal interaction between the mantle and external core near their boundary. The equations are presented in a simple close form suitable for numerical integration. Such integration has been carried out with subsequent fitting the constructed numerical theory to the VLBI-based Celestial Pole positions and variations of UT for the time span 1984–2005. Details of the fitting are given in the second part of this work presented as a separate paper (Krasinsky and Vasilyev 2006) hereafter referred to as Paper 2. The resulting Weighted Root Mean Square (WRMS) errors of the residuals dθ, sin θd \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi$$\end{document} for the angles of nutation θ and precession \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi$$\end{document} are 0.136 mas and 0.129 mas, respectively. They are significantly less than the corresponding values 0.172 and 0.165 mas for IAU 2000 theory. The WRMS error of the UT residuals is 18 ms. More... »

PAGES

169-217

### References to SciGraph publications

• 1999-09. Tidal effects in the earth–moon system and the earth's rotation in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
• 1991-03. A Hamiltonian theory for an elastic earth: Elastic energy of deformation in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
• 1991-03. A Hamiltonian theory for an elastic earth: First order analytical integration in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
• 2006-11-15. Numerical theory of rotation of the deformable Earth with the two-layer fluid core. Part 2: Fitting to VLBI data in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
• 1990-09. The theory of the nutation for the rigid earth model at the second order in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
• 2002-09. Dynamical History of the Earth–Moon System in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
• 1998-04. RDAN97: An Analytical Development of Rigid Earth Nutation Series Using the Torque Approach in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
• 1980. A Simple Theory on the Dynamical Effects of a Stratified Fluid Core upon Nutational Motion of the Earth in NUTATION AND THE EARTH’S ROTATION

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URI

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DOI

http://dx.doi.org/10.1007/s10569-006-9038-5

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