New precession expressions, valid for long time intervals^⋆

¹ Astronomical Institute, Acad. Sci. Czech Rep., Boční II, 141 31 Prague 4, Czech Republic
e-mail: vondrak@ig.cas.cz
² SYRTE, Observatoire de Paris, CNRS, UPMC, 61 avenue de l’Observatoire, 75014 Paris, France
e-mail: n.capitaine@obspm.fr
³ STFC/Rutherford Appleton Laboratory, Harwell Oxford, Oxon OX11 0QX, UK
e-mail: patrick.wallace@stfc.ac.uk

Received: 17 May 2011
Accepted: 28 July 2011

Abstract

Context. The present IAU model of precession, like its predecessors, is given as a set of polynomial approximations of various precession parameters intended for high-accuracy applications over a limited time span. Earlier comparisons with numerical integrations have shown that this model is valid only for a few centuries around the basic epoch, J2000.0, while for more distant epochs it rapidly diverges from the numerical solution. In our preceding studies we also obtained preliminary developments for the precessional contribution to the motion of the equator: coordinates X,Y of the precessing pole and precession parameters ψ_A,ω_A, suitable for use over long time intervals.

Aims. The goal of the present paper is to obtain upgraded developments for various sets of precession angles that would fit modern observations near J2000.0 and at the same time fit numerical integration of the motions of solar system bodies on scales of several thousand centuries.

Methods. We used the IAU 2006 solutions to represent the precession of the ecliptic and of the equator close to J2000.0 and, for more distant epochs, a numerical integration using the Mercury 6 package and solutions by Laskar et al. (1993, A&A, 270, 522) with upgraded initial conditions and constants to represent the ecliptic, and general precession and obliquity, respectively. From them, different precession parameters were calculated in the interval  ± 200 millennia from J2000.0, and analytical expressions are found that provide a good fit for the whole interval.

Results. Series for the various precessional parameters, comprising a cubic polynomial plus from 8 to 14 periodic terms, are derived that allow precession to be computed with an accuracy comparable to IAU 2006 around the central epoch J2000.0, a few arcseconds throughout the historical period, and a few tenths of a degree at the ends of the  ± 200 millennia time span. Computer algorithms are provided that compute the ecliptic and mean equator poles and the precession matrix.