Comparison between high precision precession models for the ecliptic and the equator

International audienceThree independent high precision solutions for precession were published in 2003 that provide expressions consistent with the IAU 2000A precession-nutation model (Mathews et al. \cite{Mat02}) and offer a possible replacement for the precession component of IAU 2000A, with improved dynamical consistency and a better basis for future improvement. Each is based upon an improved model for the precession of the ecliptic and, with respect to the IAU 1976 precession, they all provide higher-degree terms in the polynomials for the precession angles of the equator. This paper compares the expressions for the basic parameters of the above solutions for precession both of the ecliptic and the equator and investigates the possible physical and computational reasons for their differences. This leads to a realistic evaluation of the accuracy of the solutions and provides estimated deficiencies in them. These studies have identified expressions for the ecliptic precession quantities that are accurate to about 0.05 mas/cy over a two-millennium interval centered on J2000 instead of the few mas/cy accuracy of the current IAU model. They have also provided the theoretical and experimental basis for future improvements in the precession of the equator