Celestial Mechanics and Dynamical Astronomy

, Volume 103, Issue 2, pp 179–190 | Cite as

On the IAU 2000/2006 precession–nutation and comparison with other models and VLBI observations

  • N. CapitaineEmail author
  • P. M. Mathews
  • V. Dehant
  • P. T. Wallace
  • S. B. Lambert
Original Article


In this paper, we discuss the fundamental aspects of the semi-analytical precession–nutation models that were adopted by IAU Resolutions in 2000 and 2006. We show that no significant discrepancies appear between those models (Mathews et al., J Geophys Res 107:B4, ETG 3-1–3-26, 2002, Capitaine et al., Astron Astrophys 412:567– 586, 2003) and other semi-analytical solutions or the INPOP06 numerical integration (Fienga et al., Astron Astrophys 477:315–327, 2008), especially for the quadratic terms. We also report on the most recent comparisons of the models with VLBI observations. We have employed different empirical models to fit the residuals, in attempting to characterize the nature of the observed curvature. The efficiencies of those empirical models are compared and their interpretations in terms of physical mechanisms are discussed. We show that a combination of linear and 18.6-year corrections is the most credible model for explaining the currently observed residuals, but that a longer span of observations is required before the true character of the effect can be determined. We note that the predictions from the ERA-2005 theory (Krasinsky, Celest Mech Dyn Astron 96:169–217, 2006) have diverged from recent VLBI results and suggest that the empirical nature of the ERA model is responsible.


Earth rotation Precession-nutation VLBI observations Reference systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bourda G., Capitaine N.: Precession, nutation, and space geodetic determination of the Earth’s variable gravity field. Astron. Astrophys. 428, 691–702 (2004)zbMATHCrossRefADSGoogle Scholar
  2. Bretagnon P., Fienga A., Simon J.-L.: Expressions for precession consistent with the IAU 2000A model. Considerations about the ecliptic and the Earth Orientation Parameters. Astron. Astrophys. 400, 785–790 (2003)CrossRefADSGoogle Scholar
  3. Brumberg, V.: Essential Relativistic Celestial Mechanics. Adam Hilger, Bristol (1991)Google Scholar
  4. Buffett, B.A., Mathews, P.M., Herring, T.A.: Modeling of nutation and precession: effects of electromagnetic coupling. J. Geophys. Res. 107, B4, ETG 5-1–5-14 (2002). doi: 10.1029/2000JB000056
  5. Capitaine N., Wallace P.T., Chapront J.: Expressions for IAU 2000 precession quantities. Astron. Astrophys. 412, 567–586 (2003)CrossRefADSGoogle Scholar
  6. Capitaine, N., Mathews, P.M., Dehant, V., Wallace, P.T., Lambert, S.: Comparisons of precession-nutation models. In: Finkelstein, A., Behrend, D. (eds.) Proceedings of the fifth IVS General Meeting, Russian Science Series pp. 211–220 (2008)Google Scholar
  7. Chapront J., Chapront-Touzé M., Francou G.: A new determination of lunar orbital parameters, precession constant and tidal acceleration from LLR measurements. Astron. Astrophys. 387, 700–709 (2002)CrossRefADSGoogle Scholar
  8. Cheng M., Tapley B.D.: Variations in the Earth’s oblateness during the past 28 years. J. Geophys. Res. 109(B9), B09402 (2004). doi: 10.1029/2004JB003028 CrossRefGoogle Scholar
  9. Fienga A., Manche H., Laskar J., Gastineau M.: INPOP06: a new numerical planetary ephemeris. Astron. Astrophys. 477, 315–327 (2008)CrossRefADSGoogle Scholar
  10. Fukushima T.: New precession formulas. Astron. J. 126(1), 494–534 (2003)CrossRefADSGoogle Scholar
  11. Hilton J.L., Capitaine N., Chapront J. et al.: Report of the International Astronomical Union Division I working group on precession and the ecliptic. Celest. Mech. Dyn. Astron. 94, 351–367 (2006)CrossRefADSGoogle Scholar
  12. IERS Conventions 2003, IERS Technical Note 32. McCarthy, D.D., Petit, G. (eds.) Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main (2004)Google Scholar
  13. Koot L., Rivoldini A., de Viron O., Dehant V.: Estimation of Earth interior parameters from a Bayesian inversion of very long baseline interferometry nutation time series. J. Geophys. Res. 113(B8), B08414 (2008)CrossRefGoogle Scholar
  14. Krasinsky G.: Numerical theory of rotation of the deformable Earth with the two-layer fluid core. Part 1: Mathematical model. Celest. Mech. Dyn. Astron. 96, 169–217 (2006)zbMATHCrossRefADSMathSciNetGoogle Scholar
  15. Krasinsky, G.: Secular decrease of the Earth’s ellipticity from the analysis of VLBI data of 1984–2006, and the long-term systematic errors of the precession-nutation models IAU 2000 and IAU 2006. In: Finkelstein, A., Behrend, D. (eds.) Proceedings of the fifth IVS General Meeting, Russian Science Series, pp. 211–220 (2008a)Google Scholar
  16. Krasinsky G.: Earth’s precession-nutation motion: the error analysis of the theories IAU 2000 and IAU 2006 applying the VLBI data of the years 1984–2006. Celes. Mech. Dyn. Astron. 101, 325–336 (2008b)CrossRefADSGoogle Scholar
  17. Krasinsky G., Vasilyev M.V.: Numerical theory of rotation of the deformable Earth with the two-layer fluid core. Part 2: fitting to VLBI data. Celest. Mech. Dyn. Astron. 96, 219–237 (2006)zbMATHCrossRefADSMathSciNetGoogle Scholar
  18. Lambert, S.B., Mathews, P.M.: Second-order torque on the tidal redistribution and the Earth’s rotation. Astron. Astrophys. 453, 363–369 (2006), and Erratum, Astron. Astrophys. 481(3), 883–884 (2008)Google Scholar
  19. Mathews, P. M., Lambert, S.B.: Effect of mantle and ocean tides on the Earth’s rotation rate. Astron. Astrophys. Accepted (2008). doi: 10.1051/0004-6361:200810343
  20. Mathews, P.M., Herring, T.A., Buffett B.A.: Modeling of nutation and precession: New nutation series for nonrigid Earth and insights into the Earth’s interior. J. Geophys. Res. 107, B4, ETG 3-1–3-26 (2002). doi: 10.1029/2001JB000390
  21. Mathews, P.M., Capitaine, N., Dehant, V.: Comments on the ERA-2005 numerical theory of Earth rotation, arXiv:0710.0166 (2007)Google Scholar
  22. Sasao T., Okubo S., Saito M.: A simple theory on dynamical effects of stratified fluid core upon nutational motion of the earth. In: Federov, E.P., Smith, M.L., Bender, P.L. (eds) Proceedings of the IAU Symposium 78, pp. 165–183. D. Reidel Publishing Co., Dordrecht (1980)Google Scholar
  23. Souchay J., Loysel B., Kinoshita H., Folgueira M.: Corrections and new developments in rigid Earth nutation theory. III. Final tables “REN-2000" including crossed-nutation and spin-orbit coupling effects. Astron. Astrophys. 135, 111–131 (1999)Google Scholar
  24. Wahr J., Bergen Z.: The effect of mantle anelasticity on nutations, Earth tides, and tidal variations in the rotation rate. Geophys. J. Astron. Soc. 87, 633–668 (1986)ADSGoogle Scholar
  25. Williams J.G.: Contributions to the Earth’s obliquity rate, precession and nutation. Astron. J. 108(2), 711–724 (1994)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • N. Capitaine
    • 1
    Email author
  • P. M. Mathews
    • 2
  • V. Dehant
    • 3
  • P. T. Wallace
    • 4
  • S. B. Lambert
    • 1
  1. 1.SYRTE, Observatoire de ParisCNRS, UPMCParisFrance
  2. 2.Department of Theoretical PhysicsUniversity of MadrasChennaiIndia
  3. 3.Royal Observatory of BelgiumBrusselsBelgium
  4. 4.Space Science & Technology DepartmentSTFC/RALDidcot, OxonUK

Personalised recommendations