A dynamic model of Earth's polar motion accounting for lunar orbital precession

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Abstract

This study addresses the challenge of enhancing the accuracy of Earth's polar motion modeling. Observational data indicate that variations in the parameters of the principal oscillatory modes (Chandler and annual wobbles) exhibit a component synchronous with the precession of the lunar orbit ($\sim 18.61$ years), which remains unaccounted for in standard models incorporating geophysical excitations. To incorporate this effect, a refined dynamic model is proposed and formulated as a system of differential equations with periodic coefficients dependent on the longitude of the Moon's ascending node.
Through numerical simulations based on International Earth Rotation and Reference Systems Service (IERS) data for the period 1976--2025, the optimal parameters of the model are determined: the lunar node coupling coefficient $\chi = 0.07$ and the quality factor $Q = 63$. The inclusion of the long-period lunar forcing is shown to reduce the standard deviation of the model from the observations. In test simulations, the accuracy in determining the pole position improves by an amount corresponding to 3.7 cm on the Earth's surface, with a maximum achievable improvement of up to 5 cm.
These results substantiate the necessity of explicitly incorporating long-period variations linked to the lunar orbit into high-precision models of polar motion.

About the authors

Vadim V. Perepelkin

Moscow Aviation Institute (National Research University)

Author for correspondence.
Email: vadim802@gmail.com
ORCID iD: 0000-0002-9061-4991
Scopus Author ID: 8263058800
ResearcherId: S-6900-2019
https://www.mathnet.ru/rus/person68736

Dr. Phys. & Math. Sci.; Professor; Dept. of Mechatronics and Theoretical Mechanics

Russian Federation, 125993, Moscow, Volokolamskoe Shosse, 4

Dmitry S. Rumyantsev

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

Email: n3030@mail.ru
ORCID iD: 0009-0003-1363-474X
SPIN-code: 5424-9860
Scopus Author ID: 14833232600
https://www.mathnet.ru/eng/person70195

Cand. Phys. & Math. Sci.; Senior Researcher; Lab. of Optimal Control Systems named after V. F. Krotov

Russian Federation, 117997, Moscow, Profsoyuznaya st., 65

Alexandra S. Filippova

Moscow Aviation Institute (National Research University)

Email: filippovaas@mai.ru
ORCID iD: 0000-0002-8596-3556
SPIN-code: 9265-7597
Scopus Author ID: 55747497100
ResearcherId: K-9211-2014
https://www.mathnet.ru/rus/person236720

Cand. Phys. & Math. Sci.; Associate Professor; Dept. of Mechatronics and Theoretical Mechanics

Russian Federation, 125993, Moscow, Volokolamskoe Shosse, 4

References

  1. IERS Conventions, IERS Technical Note; no. 36, eds. G. Petit, B. Luzum. Frankfurt am Main, Verlag des Bundesamts für Kartographie und Geodäsie, 2010, 179 pp.
  2. Munk W. H., MacDonald G. J. F. The Rotation of the Earth. A Geophysical Discussion, Cambridge Monographs on Mechanics. Cambridge, Cambridge Univ., 2009, xix+323 pp.
  3. Perepelkin V. V., Soe W. Y., Rykhlova L. V. In-phase variations in the parameters of the Earth’s pole motion and the lunar orbit precession, Astron. Rep., 2022, vol. 66, no. 1, pp. 80–91. EDN: WADBCR. DOI: https://doi.org/10.1134/S1063772922020081.
  4. Krylov S. S., Perepelkin V. V., Filippova A. S. Estimation of the contribution of geophysical perturbations to the Earth pole oscillatory process at the precession frequency of the lunar orbit, IOP Conf. Ser.: Mater. Sci. Eng., 2020, vol. 927, 012036. EDN: KKRGYE. DOI: https://doi.org/10.1088/1757-899X/927/1/012036.
  5. Kurbasova G. S., Rykhlova L. V. Chandler wobble of the Earth’s pole in the Earth–Moon system, Astron. Rep., 1995, vol. 72, no. 6, pp. 845–850.
  6. Kurbasova G. S., Shlikar G. N., Rykhlova L. V. The empirical Melchior laws and parametric excitation of the Chandler wobble, Astron. Rep., 2003, vol. 47, no. 6, pp. 525–530. EDN: LHTSPT. DOI: https://doi.org/10.1134/1.1583780.
  7. Bizouard C., Remus F., Lambert S., et al. The Earth’s variable Chandler wobble, Astron. Astrophys., 2011, vol. 526, A106. DOI: https://doi.org/10.1051/0004-6361/201015894.
  8. Bizouard C., Zotov L., Sidorenkov N. Lunar influence on equatorial atmospheric angular momentum, J. Geophys. Res. Atmos., 2014, vol. 119, no. 21, pp. 11,920–11,931. EDN: TAATTQ. DOI: https://doi.org/10.1002/2014JD022240.
  9. Perepelkin V. V., Filippova A. S., Rykhlova L. V. Long-period variations in oscillations of the Earth’s pole due to Lunar perturbations, Astron. Rep., 2019, vol. 63, no. 3, pp. 238–247. EDN: SNXSWQ. DOI: https://doi.org/10.1134/S1063772919020070.
  10. Schuh H., Nagel S., Seitz T. Linear drift and periodic variations observed in long time series of polar motion, J. Geod., 2001, vol. 74, no. 10, pp. 701–710. EDN: ATABEP. DOI: https://doi.org/10.1007/s001900000133.
  11. McCarthy D. D., Luzum B. J. Path of the mean rotational pole from 1899 to 1994, Geophys. J. Int., 1996, vol. 125, no. 2, pp. 623–629. DOI: https://doi.org/10.1111/j.1365-246X.1996.tb00024.x.
  12. Sidorenkov N. S. The Interaction between Earth’s Rotation and Geophysical Processes. Weinheim, Wiley, 2009, xi+305 pp. DOI: https://doi.org/10.1002/9783527627721.
  13. Zharov V. E. Sfericheskaya astronomiya [Spherical Astronomy]. Fryazino, Vek-2, 2006, 480 pp. (In Russian)
  14. Smart W. M. Nebesnaya mekhanika [Celestial Mechanics]. Moscow, Mir, 1965, 504 pp. (In Russian)
  15. Moritz H., Müller I. I. Earth Rotation: Theory and Observation. New York, Ungar, 1987, xx+617 pp.
  16. Klimov D. M., Akulenko L. D., Kumakshev S. A. The main properties and peculiarities of the Earth’s motion relative to the center of mass, Dokl. Phys., 2014, vol. 59, no. 10, pp. 472–475. EDN: UCKIOF. DOI: https://doi.org/10.1134/S1028335814100073.
  17. Akulenko L. D., Klimov D. M., Markov Y. G., Perepelkin V. V. Oscillatory-rotational processes in the Earth motion about the center of mass: Interpolation and forecast, Mech. Solids, 2012, vol. 47, no. 6, pp. 601–621. EDN: RGHQPX. DOI: https://doi.org/10.3103/S0025654412060015.
  18. Perepelkin V. V., Skorobogatykh I. V., Myu Z. A. Dynamic analysis of the steady state oscillations of the Earth’s pole, Mech. Solids, 2021, vol. 56, no. 5, pp. 727–736. EDN: MUWZNU. DOI: https://doi.org/10.3103/S0025654421050162.

Supplementary files

Supplementary Files
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1. JATS XML
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2. Figure 1. The relative positions of the great circles of the lunar orbital plane, the equatorial plane, and the ecliptic plane on the celestial sphere

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3. Figure 2. Variations of the inclination angle $I$ of the lunar orbital plane relative to the Earth's equator

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4. Figure 3. Dependence of the standard deviation $\sigma _{xy}$ on the coefficient $\chi$

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5. Figure 4. Dependence of the standard deviations $\sigma_{x}$ (solid line) and $\sigma_{y}$ (dashed line) on the coefficient $\chi$

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6. Figure 5. Pole coordinate oscillations $x_{p}$, $y_{p}$. Dots represent thinned observational data from the IERS, the solid line represents the calculated model

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