New precession formulae by T. Fukushima (National Astronomical Observatory of Japan)
We modified Williams' formulation (Williams 1994) of the 3-1-3-1 rotation matrix to express the precession and the precession-nutation matrices with respect to the ICRF in a robust form. By using the latest determination of the planetary precession of DE405 in the inertial sense (Harada and Fukushima 2003) and one of the recent nutation theories (Shirai and Fukushima 2001), we determined the luni-solar precession from the VLBI observation of celestial pole offsets during 1979 to 2000. We also determined the best estimate of the geodesic precession and nutation. As by-products, we obtained the new determinations of (1) the mean equatorial pole offset at J2000.0, (2) the speed of general precession in longitude at J2000.0, (3) the mean obliquity of ecliptic at J2000.0, and (4) the dynamical flattening of the Earth.
Expressions for IAU 2000 precession quantities by N. Capitaine(1), P.T. Wallace(2) and J. Chapront(1) ((1) Syrte, Observatoire de Paris, France, (2) H.M. Nautical Almanac Office, RAL, United Kingdom)
We discuss precession models consistent with the IAU 2000 precession-nutation and a range of products that implement them. We first present the expressions for the currently used precession quantities, in agreement with the MHB corrections to the precession rates, that appear in the IERS Conventions 2000. We then discuss a more sophisticated method that we used to develop P03 precession expressions that are dynamically consistent. We obtained expressions for the precession of the ecliptic based on most recent theories for the Earth and the Moon and the most precise numerical ephemerides. We then used these new expressions for the ecliptic together with the MHB corrections to precession rates to solve the precession equations for providing a 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. We also 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.
Precession expressions consistent with the IAU 2000A model. Consideration about the EOP and a conventional ecliptic by W. Thuillot, P. Bretagnon1, A. Fienga and J.L. Simon (IMCCE, Observatoire de Paris, France)
Since the adoption of an accurate nutation model, the IAU encourages the development of new expressions for precession consistent with the new model. We present here the new precession quantities given in Bretagnon et al. (2003). These expressions are issued from the analytical solution of the rotation of the rigid Earth SMART97 (Bretagnon et al. 1998) which provides together precession and nutation. These expressions include the new value of the precession rate of the equator in longitude. As the SMART97 series are close to the Souchay et al. (1999) series used to build the new model, they are consistent with the IAU 2000 Precession-Nutation Model. We give the differences between our expressions and the Lieske et al. ones (1977) improved in the IERS Conventions 2000 and show that those differences are superior to the precision of the low-precision model IAU 2000B. We also give the derivatives of our expressions with respect to the precession constant and to the obliquity in order to compute the corrections of the precession quantities given by future improvements of these constants. Following Bretagnon et al.'s model for Earth rotation (1998, 2003), we show that the celestial pole offsets as well as polar motion can be included with precession and nutation in a global modeling of the Earth rotation, thanks to the Euler angles and we discuss the use of such angles in IERS publications. In the end, we propose the definition of a conventional ecliptic plane close to the mean ecliptic J2000 and with a non-rotating origin.
Future directions in precession and nutation by J. Hilton (U.S. Naval Observatory)
The IAU 2000A precession-nutation theory is computationally expensive, requiring over one thousand evaluations of sine and cosine functions required to evaluate IAU 2000A just once. In response to this another precession-nutation theory, IAU 2000B, was adopted at the same time. However, IAU 2000B has a reduced precision and was designed to cover only a limited time span around the epoch J2000.0. At the same time, applications such as the Multiyear Interactive Computer Almanac (MICA), are being developed that require long coverage periods and the ability to reach the accuracy of modern day observations. To address this deficiency future precession and nutation theories will need to do one or more of the following: (a) make a serious effort to optimize the code; (b) reduce its precision to match the accuracy with which the Earth orientation can accurately be determined; (c) no longer separate terms that are so close together in frequency space that their individual contributions cannot be determined at the level of accuracy of the observations; (d) move from representation as an analytic theory to a numerically integrated representation.
