Celestial Mechanics and Dynamical Astronomy

, Volume 116, Issue 2, pp 195–212 | Cite as

Asymmetric effects on Earth’s polar motion

  • Christian BizouardEmail author
  • Leonid Zotov
Original Article


Differential equations ruling the Earth’s polar motion are slightly asymmetric with respect to the pole coordinates. This is not only associated with the lack of axial symmetry around the Earth figure axis (triaxiality) but also with the longitude dependency of the pole tide (the main contribution). We propose a consistent handling of both asymmetric contributions, formulating a unique equation in the complex equatorial plane, of which we derive a general solution. Difference with respect to the usual symmetric solution is discussed and found significant in light of the present accuracy of the observed pole coordinates. For the same geophysical excitation, the prograde Chandler wobble is accompanied by a retrograde component up to 2 milliarcseconds (mas), transforming it in a slight elliptic motion. The asymmetric contribution is relatively larger in the geodetic excitation function, for Chandler wobble excitation mixes prograde and retrograde components of comparable level (1 mas).


Liouville equation Earth rotation Polar motion  Triaxiality Ocean  Pole tide Asymmetry Chandler wobble 



The second author is supported by Chinese Academy of Sciences Fellowship for Young International Scientists and RFBR Grant 12-02-31184. We greatly thank the reviewers for their remarks and corrections. One of them, by doing a very careful review, and making us aware of the work of Okamoto and Sasao (1977), permitted us to refine this study.


  1. Bizouard, C.: Interprétation géophysique du mouvement du pôle de l’heure au siècle. Mémoire d’Habilitation à diriger des recherches., Observatoire de Paris (2012) (in press)
  2. Bizouard, C., Seoane, L.: The atmospheric and oceanic excitation of the rapid polar motion. J. Geod. 84, 19–30 (2010)ADSCrossRefGoogle Scholar
  3. Brzeziński, A., Capitaine, N.: The use of the precise observations of the celestial ephemeris pole in the analysis of geophysical excitation of earth rotation. J. Geophys. Res 98B4, 6667–6675 (1993)CrossRefGoogle Scholar
  4. Breziński, A., Mathews, P.M.: Recent advances in modelling the lunisolar perturbation in polar motion corresponding to high frequency nutation. Journées Systèmes de Référence spatio-temporels 2002, Proceeding, N. Capitaine (eds) (2002)Google Scholar
  5. Chandler, S.C.: On the variation of latitude I. Astron. J. 11(248), 59–61 (1891)ADSCrossRefGoogle Scholar
  6. Chen, W., Shen, W.: New estimates of the inertia tensor and rotation of the triaxial nonrigid earth. J. Geophys. Res. 115, B12419 (2010). doi: 10.1029/2009JB007094 ADSCrossRefGoogle Scholar
  7. Desai, S.D.: Observing the pole tide with satellite altimetry. J. Geophys. Res. (Oceans) 107(C11), 1–7 (2002). doi: 10.1029/2001JC001224 CrossRefGoogle Scholar
  8. Escapa, A., Getino, J., Ferrándiz, J.M.: Indirect effect of the triaxiality in the Hamiltonian theory for the rigid Earth nutations. Astron. Astrophys. 389, 1047–1054 (2002)ADSCrossRefGoogle Scholar
  9. Eubanks, T.M.: Variations in the orientation of the Earth. In: Smith, D.E., Turcott, D.L. (eds.) Contributions of Space Geodesy to Geodynamics: Earth Dynamics, pp. 1–54. AGU, Washington (1993)CrossRefGoogle Scholar
  10. Euler, L.: Du mouvement de rotation des corps solides autour d’un axe variable, Mém. Acad. Sci. Belles Lettres Berlin 14: 154–193 (1758), 154–193 (1765); reprinted in his Opera omniu. Ser. Secunda, Vol. 8, Orell Fussli Turici, Lausanne, 1965: 200–235 (1758/1765)Google Scholar
  11. Euler, L.: Theoria motus corporum solidorum seu rigidorum: Ex primis nostrae cognitionis principiis stabilita et ad omnes motus, qui in huiusmodi corpora cadere possunt, accommodata, Rostochii et Gryphiswaldiae Ed (1765)Google Scholar
  12. Folgueira, M., Souchay, J.: Free polar motion of a triaxial and elastic body in Hamiltonian formalism: Application to the Earth and Mars. Astron. Astrophys. 432, 1101–1113 (2005)ADSCrossRefGoogle Scholar
  13. Gross, R.S.: The excitation of the Chandler wobble. Geophys. Res. Lett. 27(15), 2332–2392 (2000)ADSCrossRefGoogle Scholar
  14. Gross, R.S.: Earth rotation variations long period. In: Herring, T.A. (ed.) Physical Geodesy Treatise on Geophysics, vol. 3. Elsevier, Oxford (2007)Google Scholar
  15. IERS C04, Earth Rotation Parameters reference series downloaded from (2012)
  16. IERS Conventions (IERS Technical Note 36). Gérard Petit and Brian Luzum (eds.). (2010)
  17. IERS Global Geophysical Fluid Center. (2012)
  18. Jeffreys, H.: Causes contributory to the annual variation of latitude. Mon. Notices R. Astron. Soc. 76(6), 499–525 (1916)ADSGoogle Scholar
  19. Lambeck, K.: The Earth’s Variable rotation: Geophysical Causes and Consequences. Cambridge University Press, Cambridge (1980)CrossRefGoogle Scholar
  20. Liouville, J.: Développements sur un chapitre de la Mécanique de Poisson. J. de Math. Pures et Appl. Deuxième série, Tome 3, 1–25 (1858)Google Scholar
  21. Markowitz, W.: Latitude and longitude and the secular motion of the pole. In: Runcorn, S.K. (ed.) Methods and Techniques in Geophysics 1, pp. 325–361. Interscience, New York (1960)Google Scholar
  22. Mathews, P., Bretagnon, P.: Polar motions equivalent to high frequency nutations for a non rigid Earth with anelastic mantle. Astron. Astrophys. 400, 1113–1128 (2003)ADSCrossRefGoogle Scholar
  23. Mathews, P., Herring, T., Buffett, B.: Modeling of nutation and precession: New nutation series from non rigid Earth and insights into the Earth interior. J. Geophys. Res. 107, B4 (2002)CrossRefGoogle Scholar
  24. Munk, W.H., MacDonald, G.: The rotation of the Earth. Cambridge University Press, Cambridge (1960)Google Scholar
  25. Newcomb, S.: On the dynamics of the Earth’s rotation with respect to the periodic variations of latitude. Mon. Notices R. Astron. Soc. 248, 336–341 (1892)ADSGoogle Scholar
  26. Okamoto, I., Sasao, T.: On the ellipticity of the Chandler wobble. Publ. Astron. Soc. Jpn. 29, 107–127 (1977)ADSGoogle Scholar
  27. Seoane, L., Nastula, J., Bizouard, C., Gambis, D.: The use of gravimetric data from GRACE mission in the understanding of polar motion variations. J. Geophys. Int. 178, 614–622 (2009)ADSCrossRefGoogle Scholar
  28. Wilson, C.: Discrete polar motion equation. Geophys. J. R. Astron. Soc. 80(2), 551–554 (1985)CrossRefGoogle Scholar
  29. Zhu, Y., Gao, B.: Dissipation and ellipticity of the Chandler wobble. Polar Motion Hist. Sci. Prob. 208, 473–479 (2000)Google Scholar
  30. Zotov, L., Bizouard, C.: On modulations of the Chandler wobble excitation. J. Geodyn. (2012). doi: 10.1016/j.jog.2012.03.010

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Observatoire de Paris—SYRTE UMR 8630ParisFrance
  2. 2.Sternberg Astronomical Institute of Moscow State UniversityMoscowRussia

Personalised recommendations