Expressions for IAU 2000 precession quantities

Abstract

Abstract.A new precession-nutation model for the Celestial Intermediate Pole (CIP) was adopted by the IAU in 2000 (Resolution B1.6). The model, designated IAU 2000A, includes a nutation series for a non-rigid Earth and corrections for the precession rates in longitude and obliquity. The model also specifies numerical values for the pole offsets at J2000.0 between the mean equatorial frame and the Geocentric Celestial Reference System (GCRS). In this paper, we discuss precession models consistent with IAU 2000A precession-nutation (i.e. MHB 2000, provided by Mathews et al. 2002 and we provide a range of expressions that implement them. The final precession model, designated P03, is a possible replacement for the precession component of IAU 2000A, offering improved dynamical consistency and a better basis for future improvement. As a preliminary step, we present our expressions for the currently used precession quantities ζ A , θ A , z A , in agreement with the MHB corrections to the precession rates, that appear in the IERS Conventions 2000. We then discuss a more sophisticated method for improving the precession model of the equator in order that it be compliant with the IAU 2000A model. In contrast to the first method, which is based on corrections to the t terms of the developments for the precession quantities in longitude and obliquity, this method also uses corrections to their higher degree terms. It is essential that this be used in conjunction with an improved model for the ecliptic precession, which is expected, given the known discrepancies in the IAU 1976 expressions, to contribute in a significant way to these higher degree terms. With this aim in view, we have developed new expressions for the motion of the ecliptic with respect to the fixed ecliptic using the developments from Simon et al. (1994) and Williams (1994) and with improved constants fitted to the most recent numerical planetary ephemerides. We have then used these new expressions for the ecliptic together with the MHB corrections to precession rates to solve the precession equations for providing new solution for the precession of the equator that is dynamically consistent and compliant with IAU 2000. A number of perturbing effects have first been removed from the MHB estimates in order to get the physical quantities needed in the equations as integration constants. The equations have then been solved in a similar way to Lieske et al. (1977) and Williams (1994), based on similar theoretical expressions for the contributions to precession rates, revised by using MHB values. Once improved expressions have been obtained for the precession of the ecliptic and the equator, we discuss the most suitable precession quantities to be considered in order to be based on the minimum number of variables and to be the best adapted to the most recent models and observations. Finally we provide developments for these quantities, denoted the P03 solution, including a revised Sidereal Time expression.

The Green Bank North Celestial Cap Pulsar Survey. III. 45 New Pulsar Timing Solutions

“…Additional timing observations resulted in the measurement of the amplitude of the Einstein delay due to gravitational redshift and time dilation, γ = 0.0046(3) s. With Table 4 Coordinates and DMs of GBNCC Pulsars PSR Measured Derived Note. Ecliptic coordinates use the IERS2010 value of the obliquity of the ecliptic referenced to J2000 (Capitaine et al 2003). Values in parentheses are the 1σ uncertainty in the last digit as reported by TEMPO.…”

The IAU 2009 system of astronomical constants: the report of the IAU working group on numerical standards for Fundamental Astronomy

“…This value is taken from the P03 precession model of Capitaine et al (2003) and was adopted in IAU 2006 Resolution B1. The value was determined by Chapront et al (2002) using lunar laser ranging observations.…”

Celestial pole offsets from lunar laser ranging and comparison with VLBI

“…The reference to the GCRS was obtained through the link to the GCRS of the dynamical reference frame as determined in the first step. Mathews et al 2002;Capitaine et al 2003). For this analysis, the partial derivatives of the matrix transformation for the GCRS motion of the CIP are calculated (for more details see Gontier 1991, andIERS Conventions 2003).…”