Deformations of the viscoelastic layer of the Earth under the influence of the gravitational forces of the moon and sun


Аuthors

Myo Z. A.

e-mail: myozawaung53@gmail.com

Abstract

The presented article is studying the problem of the viscoelastic layer of the Earth deformations under the action of the forces of attraction of the Moon and the Sun through the modal approach. A viscoelastic solid consisting of an axisymmetric solid core and a viscoelastic axisymmetric (in anin-deformed state) shell subject to deformation according to the Kelvin–Voigt model was considered as the Earth model. There are no displacements on the inner boundary of the shell, and the outer boundary is free. The process of the Earth deformation is assumed to be considered as quasi-stationary.

Based on the deformation equations derived from the Dalembert-Lagrange variation principle, approximate expressions for the frequencies of solid-state tides are obtained in the work. A modal approach is used for this purpose. The author demonstrates that oscillations will occur only on the forms with 0, 1 and 2 indices. The frequencies of the forced tidal oscillations of the Earth mantle deformable layer are approximately determined for these forms The resulting set of harmonics includes not only the basic tidal harmonics, but the minor small-scale components with combinational frequencies as well. The results of the observation variations approximation in gravity acceleration in the city of Membach on a superconducting SG-gravimeter, built using the developed tidal model are presented as an example.

The models of tidal deformations of the viscoelastic Earth are employed in the problems that require a highly accurate description of the gravitational field, such as, in the problems of the spacecraft orbital motion. Thus, the lunar-solar tides in the of satellites motion lead to quite noticeable disturbing accelerations. For example, for high-orbit satellites with an orbit altitude of about 20,000 km (GLONASS, GPS), the disturbing acceleration is of the order of 2*10-9m/s2, and for low-orbit satellites with an orbit altitude of about 350-400 km (ISS), the acceleration value is already much greater, namely of the order of 1.5*10-7m/s2. For example, neglecting the perturbing acceleration of the order of 2*10-9m/s2for GLONASS leads to a daily orbital drift of about 2-3 meters.

However, the issues related to the description of tides turn out to be important not only in the tasks of clarifying coordinate-time and navigation support, but in the tasks of the tidal evolution of the planets motion and their satellites in celestial mechanics and astrodynamics.

Keywords:

deformations, viscoelastic Earth, tides, gravitational perturbation

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