Skip to main content

In-phase Variations in the Parameters of the Earth’s Pole Motion and the Lunar Orbit Precession


We found an oscillatory process of the Earth’s pole associated with the precession motion of the Moon’s orbit using numerical processing a series C01 of observational data and measurements of the Earth’s pole motion over a long time interval starting from 1900. Several methods have been proposed for converting the coordinates of the Earth’s pole to a system in which its motion occurs in phase with a change in the orientation of the plane of the lunar orbit in relation to the Earth’s equator. The performed transformation depends only on the average parameters of the Earth’s pole motion and does not explicitly depend on time. In this system, we showed that the polar radius oscillates in phase with oscillations of the inclination angle of the lunar orbit plane to the Earth’s equator, and the polar angle oscillations occur in phase with the deviation along the equator of the intersection point of the lunar orbit with the equator.

This is a preview of subscription content, access via your institution.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.


  1. International Earth Rotation and Reference Systems Service. IERS Annual Reports,;;

  2. H. Moritz and I. Mueller, Earth Rotation: Theory and Observation (Ungar, New York, 1987).

    Google Scholar 

  3. W. Munk and G. MacDonald, The Rotation of the Earth: A Geophysical Discussion, Cambridge Monographs on Mechanics (Cambridge Univ. Press, Cambridge, 1975).

    MATH  Google Scholar 

  4. Yu. G. Markov, L. V. Rykhlova, and I. N. Sinitsyn, Astron. Rep. 54, 861 (2010).

    ADS  Article  Google Scholar 

  5. D. M. Klimov, L. D. Akulenko, and S. A. Kumakshev, Dokl. Phys. 59, 472 (2014).

    ADS  Article  Google Scholar 

  6. V. E. Zharov, Spherical Astronomy (Fryazino, 2006) [in Russian].

    Google Scholar 

  7. N. S. Sidorenkov, Physics of Instabilities of the Earth’s Rotation (Nauka, Moscow, 2002) [in Russian].

    Google Scholar 

  8. C. Bizouard, L. Zotov, and N. Sidorenkov, J. Geophys. Res. Atmos. 119, 21 (2014).

    Article  Google Scholar 

  9. G. S. Kurbasova and L. V. Rykhlova, Astron. Rep. 39, 845 (1995).

    ADS  Google Scholar 

  10. G. S. Kurbasova, L. V. Rykhlova, and G. N. Shlikar’, Astron. Rep. 47, 525 (2003).

    ADS  Article  Google Scholar 

  11. C. Bizouard, F. Remus, S. Lambert, L. Seoane, and D. Gambis, Astron. Astrophys. 526, A106 (2011).

    ADS  Article  Google Scholar 

  12. L. Zotov, C. Bizouard, and C. K. Shum, Geodesy Geodyn. 7, 216 (2016).

    Article  Google Scholar 

  13. L. V. Zotov and C. Bizouard, J. Geodyn. 62, 30 (2012).

    Article  Google Scholar 

  14. G. S. Kurbasova, L. V. Rykhlova, and M. N. Rybalova, Astron. Rep. 46, 515 (2002).

    ADS  Article  Google Scholar 

  15. V. V. Perepelkin, L. V. Rykhlova, and A. S. Filippova, Astron. Rep. 63, 238 (2019).

    ADS  Article  Google Scholar 

  16. H. Schuh, S. Nagel, and T. Seitz, J. Geodesy 74, 701 (2001).

    ADS  Article  Google Scholar 

  17. D. D. McCarthy and B. J. Luzum, Geophys. J. Int. 125, 623 (1996).

    ADS  Article  Google Scholar 

  18. D. Rumyantsev and V. Perepelkin, in Proceedings of the 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy’s Conference) STAB-2020 (IEEE, Moscow, 2020).

    Google Scholar 

  19. Z. Malkin and N. Miller, Earth, Planets Space 62, 943 (2010).

    ADS  Article  Google Scholar 

  20. W. M. Smart, Celestial Mechanics (Literary Licensing, 2013).

  21. The JPL Horizons,

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to V. V. Perepelkin.

Additional information

Translated by E. Seifina

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Perepelkin, V.V., Rykhlova, L.V. & Soe, W.Y. In-phase Variations in the Parameters of the Earth’s Pole Motion and the Lunar Orbit Precession. Astron. Rep. 66, 80–91 (2022).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Earth’s pole motion
  • Chandler oscillation
  • annual oscillation
  • Earth’s rotation
  • gravitational perturbation
  • lunar orbit precession