Dynamic analysis of the perturbed motion of the Earth’s pole

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Abstract

Within the framework of the spatial variant of the “deformable Earth–Moon” problem in the solar gravitational field for the viscoelastic Earth model, tidal deformations caused by long-period lunar disturbances are determined. The dynamics of the Earth’s pole motion with Chandler and annual frequencies is analyzed taking into account the obtained expressions for the centrifugal moments of inertia of the Earth. Using numerical integration of the equations of pole motion, it is shown that the found structure of variations in the centrifugal moments of inertia leads to oscillations in the amplitudes of the Chandler and annual harmonics with an 18-year period of precession of the Moon’s orbit.

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About the authors

V. V. Perepelkin

Moscow Aviation Institute (National Research University)

Author for correspondence.
Email: vadimkin1@yandex.ru
Russian Federation, Moscow

References

  1. International Earth Rotation and Reference Systems Service – IERS Annual Reports (http://www.iers.org).
  2. Munk W.H., MacDonald G.J.F. The Rotation of the Earth. Cambridge: Cambridge Univ. Press, 1960; M.: Mir, 1964.
  3. Markov Yu.G., Mikhailov M.V., Perepelkin V.V. et al. Analysis of the effect of various disturbing factors on high-precision forecasts of spacecraft orbits // Cosmic. Res. 2016. V. 54. № 2. P. 155–163 https://doi.org/10.1134/S0010952515060015
  4. Akulenko L.D., Klimov D.M., Kumakshev S.A. The main properties and peculiarities of the Earth’s motion relative to the center of mass // Dokl. Phys. 2014. V. 59. № 10. P. 472–475. https://doi.org/10.1134/S1028335814100073
  5. Kumakshev S.A. Gravitational-tidal model of oscillations of Earth’s poles // Mech. Solids. 2018. V. 53. P. 159–163. https://doi.org/10.3103/S0025654418020061
  6. Akulenko L.D., Klimov D.M., Markov Yu.G., Perepelkin V.V. Oscillatory-rotational processes in the Earth motion about the center of mass: interpolation and forecast // Mech. Solids. V. 47. № 6. P. 601–621. https://doi.org/10.3103/S0025654412060015
  7. Filippova A.S. Dynamic analysis of the earth pole oscillation process // Mech. Solids. 2015. V. 50. P. 622–632. https://doi.org/10.3103/S0025654415060035
  8. Markov Yu.G., Perepelkin V.V., Krylov S.S. Terrestrial pole oscillations with allowance for fluctuation dissipation perturbations // Dokl. Phys. 2016. V. 61. P. 630–635. https://doi.org/10.1134/S1028335816120132
  9. Sidorenkov N.S. Priroda amplitudnoy modulyacii chandlerovskogo dvigeniya poljusa // Izvestiya GAO RAN. 2013. V. 220. P. 143–148 (In Russian).
  10. Zharov V.E. Spherical Astronomy. Fryazino, 2006 (in Russian).
  11. Sidorenkov N.S. Soizmerimosti mejdu chastotami zemnyh processov I chastotami sistemy Zemlya-Luna-Solnce // Processy v geosredah. 2015. V. 3. № 3. P. 88–99 (In Russian).
  12. Sidorenkov N.S. Geodinamicheskie prichiny dekadnyh izmenenij klimata // Zemlya I Vselennaya. 2016. № 3. P. 25–36 (In Russian).
  13. Akulenko L.D., Perepelkin A.A. Earth pole motion due to nonstacionary perturbations // Mech. Solids. 2019. V. 54. P. 1108–1114. https://doi.org/10.3103/S0025654419070112
  14. Perepelkin V.V., Rykhlova L.V., Filippova A.S. Long-period variations in oscillations of the Earth’s Pole due to Lunar perturbations // Astron. Rep. 2019. V. 63. P. 238–247. https://doi.org/10.1134/S1063772919020070
  15. Perepelkin V.V., Rykhlova L.V., Wai Yan Soe. In-phase variations in the parameters of the Earth’s Pole motion and the Lunar orbit precession // Astron. Rep. 2022. V. 66. P. 80–91. https://doi.org/10.1134/S1063772922020081
  16. Krylov S.S., Perepelkin V.V. Short-term forecast of the Earth’s Pole motion, taking into account Lunar disturbances // Mech. Solids. 2020. V. 55. P. 892–897. https://doi.org/10.3103/S002565442006014X
  17. Vilke V.G. Analytical and qualitative methods in the mechanics of systems with an infinite number of degrees of freedom. M.: Mosk. Gos. Univ., 1986 (in Russian).
  18. Smart W.M. Celestial mechanics. Longmans Green, 1961.
  19. Markov Yu.G., Minyaev I.S. Prostranstvennyj variant zadachi “deformiruemaya planeta-sputnik” v pole prityagivayuschego centra // Cosmic. Res. 1994. V. 32. № 6. P. 89–98 (In Rissian).
  20. Perepelkin V.V., Skorobogatykh I.V., Myo Zaw Aung. Dynamic analysis of the steady state oscillations of the Earth’s Pole // Mech. Solids. 2021. V. 56. P. 727–736. https://doi.org/10.3103/S0025654421050162

Supplementary files

Supplementary Files
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2. Fig. 1. Variations of the amplitudes of the Chandler and annual components, respectively, measured in milliarcseconds. The abscissa axis shows years.

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3. Fig. 2. Amplitude spectrum of coordinates , pole, measured in angular milliseconds (dashed line for x, solid line for y), where the vertical dotted lines indicate the fundamental harmonics. The abscissa axis shows time, measured in cycles per year.

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4. Fig. 3. Relative orientation of the terrestrial coordinate system and the Koenig coordinate system and Andoyer variables.

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5. Fig. 4. The amplitude spectrum of the coordinate observations (first graph) in comparison with the amplitude spectra of the coordinate of the solution of equations (4.4) (on the second and third graphs in logarithmic and linear scales, respectively).

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