Consistency Problems in the Improvement of the IAU Precession-Nutation Theories: Effects of the Dynamical Ellipticity Differences

The complexity of the modeling of the rotational motion of the Earth in space has produced that no single theory has been adopted to describe it in full. Hence, it is customary using at least a theory for precession and another one for nutation. The classic approach proceeds by deriving some of the fundamental parameters from the precession theory, like, e.g., the dynamical ellipticity , and then using those values in the nutation theory. The former IAU 1976 precession and IAU 1980 nutation theories followed that scheme. Along with the improvement of the accuracy of the determination of Earth orientation parameters, IAU 1980 was superseded by IAU2000, based on the application of the MHB2000 transfer function to the previous rigid Earth analytical theory REN2000. The latter was derived while the precession model IAU 1976 was still in force, therefore it used the corresponding values for some of the fundamental parameters, as the precession rate, associated to the dynamical ellipticity. The new precession model P03 was adopted as IAU 2006. That change introduced some inconsistency since P03 used different values for some of the fundamental parameters that MHB2000 inherited from REN2000. Besides, the derivation of the basic Earth parameters of MHB2000 itself comprised a fitted variation of the dynamical ellipticity adopted in the background rigid theory. Due to the strict requirements of accuracy of the present and coming times, the magnitude of the inconsistencies originated by this twofold approach is no longer negligible as earlier, hence the need of discussing the effects of considering slightly different values for in precession and nutation theories.