Celestial Mechanics and Dynamical Astronomy

, Volume 57, Issue 1–2, pp 279–292 | Cite as

On the tidal variation of the geopotential

  • José M. Ferrándiz
  • Juan Getino
Geodynamics

Abstract

In this paper analytical expressions are derived for the temporal variations ofJ2 andJ22 due to the tides of the solid Earth, taking into account only the deformation of the mantle, and employing a procedure already used by the authors in their Hamiltonian theory of the Earth's rotation, which obtain the necessary parameters in a direct way by integration of those provided by a selected model of Earth interior.

Numerical tables giving the periodic variation of coefficients are given, as well as a new prediction for ΔUT1. For δJ2 and δJ22 the amplitudes reach such a magnitude that both two variations should not be ignored in studies involving the analysis of highly precise satellite tracking data. Moreover, the possibility of improving our knowledge of the value of those harmonic coefficients in only a more exact digit appears as to be strongly dependent on the limitations in the theoretical modeling of the variations of the inertia tensor due to solid tides.

Key words

Solid tides Earth potential artificial satellites 

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References

  1. Bursa, M.: 1987,Secular deceleration of the Moon and of the Earth's rotation and variation in the zonal geopotential harmonic, Bull. Astron. Inst. Czechosl.38, 309–313.Google Scholar
  2. Carpino, M. et al.: 1986,Sensitivity of LAGEOS to changes in Earth's gravity coefficients, Celes. Mech.39, 1–13.Google Scholar
  3. Farrell, W.E.: 1972,Deformation of the Earth by surface loads. Rev. Geophys. Space Phys.,10, 761–797.Google Scholar
  4. Getino, J. and Ferràndiz, J.M.: 1990,A Hamiltonian theory for an elastic Earth: canonical variables and kinetic energy, Celes. Mech.49, 303–326.Google Scholar
  5. Getino, J. and Ferràndiz, J.M.: 1991a,A Hamiltonian theory for an elastic Earth: Elastic energy of deformation, Celes. Mech.51, 17–34.Google Scholar
  6. Getino, J. and Ferràndiz, J.M.: 1991b,A Hamiltonian theory for an elastic Earth: First Order Analytical Integration, Celes. Mech.51, 35–65.Google Scholar
  7. Getino, J. and Ferràndiz, J.M.: 1991c,A Hamiltonian theory for an elastic Earth: secular rotational acceleration, Celes. Mech.52, 381–396.Google Scholar
  8. Kinoshita, H.: 1977,Theory of the rotation of the rigid Earth, Celes. Mech.15, 277–326.Google Scholar
  9. Kubo, Y.: 1991,Solution to the rotation of the elastic Earth by method of rigid dynamics, Celes. Mech.50, 165–187.Google Scholar
  10. Lerch et al.: 1979,Gravity model improvement using GEOS 3 (GEM 9 and 10), J. Geophys. Res.84, 3897–3916.Google Scholar
  11. Lerch et al.: 1983,A refined gravity model from LAGEOS (GEM–L2), NASA, Technical Memorandum 84986.Google Scholar
  12. Milani et al.: 1987,Non-gravitational perturbations and satellite geodesy, ed. Adam Hilger.Google Scholar
  13. Moritz, H. and Mueller, I.: 1987,Earth rotation, ed. Ungar, New York.Google Scholar
  14. Takeuchi, H.: 1950,On the Earth tide of the compressible Earth of variable density and elasticity, Trans. Am. Geophys. Union,31 (5), 651–689.Google Scholar
  15. Yoder, C.F. et al.: 1981,Tidal variations of Earth rotation, J. Geophys. Res.,86 (B2), 881–891.Google Scholar
  16. Yoder, C.F. et al.: 1983,Secular variation of Earth's gravitational harmonic J 2 coefficient from LAGEOS and nontidal acceleration of Earth rotation, Nature303, 757–762.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • José M. Ferrándiz
    • 1
  • Juan Getino
    • 2
  1. 1.Departamento de Matematica Aplicada a la IngenieríaE.T.S. de Ingenieros IndustrialesValladolidSpain
  2. 2.Departamento de Matemática Aplicada FundamentalFacultad de CienciasValladolidSpain

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