## 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

Celestial Mechanics and Dynamical Astronomy, 101(4), 325-336 (2008)

**Keywords**:
Earth rotation, Tides, Love numbers, VLBI observations, Earth’s precession–nutation

### Abstract

The long-term systematic errors of the analytical theories IAU 2000 and IAU 2006 of the Earth’s precession–nutational motion are studied making use of the VLBI data of 1984–2007. Several independent methods give indubitable evidence of the significant quadratic error dϕ=(23±3)mas/cy2 in the IAU 2000 residuals of the precessional angle ϕ while the adopted value of the secular decrease e˙=−7.9×10−9 /cy of the Earth’s ellipticity e (derived from Satellite Laser Ranging data) should manifest itself in the residuals of ϕ as the negative quadratic trend dϕe˙≈−8mas/cy2. The problem with the precession of the IAU 2006 theory adopted as a new international standard and based on the precession model P03 (Capitaine et al., Astron Astrophys 432:355–367, 2005) appears to be even more serious because the above mentioned quadratic term dϕe˙dϕe˙ has already been incorporated into the P03 precession. Our analysis of the VLBI data demonstrates that the quadratic trend of the IAU 2006 residuals dϕ does amount to the expected value (30.0 ± 3) mas/cy2. It means, first, that the theoretical precession rate of IAU 2006 should be augmented by the large secular correction dps=2dϕ≈(60.0±6)mas/cy2dps=2 and, second, that the available VLBI data have potentiality of estimating the rate e˙e˙ . And indeed, processing these data by the numerical theory ERA of the Earth’s rotation (Krasinsky, Celest Mech Dyn Astron 96:169–217, 2006, Krasinsky and Vasilyev, Celest Mech Dyn Astron 96:219–237, 2006) yields the estimate e˙=−(14±4)×10−9 statistically in accordance with the satellite-based e˙. On the other hand, applying IAU 2000/2006 models, the positive value e˙=(27±4)×10−9 is found which is incompatible with the SLR estimate and, evidently, has no physical meaning. The large and steadily increasing error of the precession motion of the IAU 2006 theory makes the task of replacing IAU 2006 by a more accurate model be most pressing.