Due to the adoption of the new International Celestial Reference Frame (ICRF), the Earth’s Ori-entation Parameters (EOP) will be revised and their definitions will need to be re-examined and clarified. This implies that precession/nutation formulation will be also revised in the future.

The precession/nutation theories for a non-rigid Earth suffer from a lack of dissipation in the core and from a mismodeling of the ocean and of the atmospheric effects. The scientific community is examining these questions. The IAU community is consequently not yet ready to adopt a new precession/nutation geophysical model but the users may use the International Earth Rotation Service (IERS) empirical series.

In order to review those questions and prepare the future research, the Scientific Organizing Committee (SOC: P. Bretagnon, V.A. Brumberg, N. Capitaine, V. Dehant (Chair), T. Fukushima, E. Groten, H. Kinoshitä, B. Kolaczek, D.D. McCarthy, P.K. Seidelmann and P.T. Wallace) has proposed invited talks on the current situation concerning:

1. (1) the formulation of precession/nutation (N. Capitaine, see paper 1),

2. (2) the planetary theories and their relation to precession/nutation (P. Bretagnon, see paper 2),

3. (3) the precession/nutation for a rigid Earth (J. Souchay and H. Kinoshita, see paper 3),

4. (4) the DExxx JPL ephemerides precision and accuracy (E.M. Standish, see paper 4),

5. (5) the observations of the Celestial Ephemeris Pole (CEP) and in particular the pole offset from which precession/nutation corrections can be derived (M. Feissel and A.M. Gontier, see paper 5),

This paper describes the conventional models for precession and nutation, the current procedure for taking them into account in the reduction of highly accurate observations, the recent IAU recommendations on this topic, as well as the current situation for theory and observations. This emphasizes the imperfections in the conventional models and in the current procedure which are not in consistency either with the adoption of the new International Conventional Celestial Reference System (ICRS) or with the high accuracy and resolution of the current observations of Earth rotation. This addresses the question of the adoption of a new formulation and of an improved model combining precession and nutation of the equator with respect to the ICRS as well as the adoption of a revised definition of the Celestial Ephemeris Pole.

In this paper, I give the present state of the analytical planetary theories by describing the general theories and the secular variation theories, the variations of the ecliptic with respect to the ecliptic J2000, the utilization of the analytical planetary theories in the calculation of the precession-nutation of the equator and in the calculation of the expressions of transformation between the barycentric and geocentric reference systems. At last, I describe the construction of new planetary theories undertaken at the Bureau des longitudes.

The analytical planetary theories arise in two forms: the general theories give, with a low accuracy, the variations of the elements of the planets over several million years; the secular variation theories reach a high accuracy over time spans of a few thousands of years.

In all these solutions, the motion of the planets is represented with 6 elements: a, the semi major axis, λ, the mean longitude and the variables k = e cos ϖ, h = e sin ϖ, q = sin ½ cos Ω, p = sin ½ sin Ω where e represents the eccentricity of the orbit, w the longitude of the perihelion, i the inclination of the orbit about the ecliptic J2000 and Ω the longitude of the node.

Whereas no particular attention was paid to the theory of the nutation for a rigid Earth model, for more than a decade after the adoption by the International Astronomical Union (IAU) of coefficients as calculated and listed by Kinoshita (1977), an increasing number of studies have been done in the recent years aiming to improve this theory. The improvement became necessary mainly because of the big parallel improvement of the VLBI observations itself, which leads to present determinations of some coefficients of nutation at the level of a few 10μas. Therefore the amelioration of the theory of the nutation for a rigid Earth model can be divided in two aspects: one is to consider a smaller level of truncation of the coefficients of nutation; the other is to evaluate in the best way the coefficients already taken into account, particularly the leading coefficients which are typically those subject to the largest absolute differences.

The latest JPL planetary and lunar ephemerides, DE405, are now referenced to the ICRF with an accuracy of about 1 mas. This has been accomplished mainly by fitting the ephemerides to 18 VLBI observations of the Magellan Spacecraft in orbit around Venus, 1990-1994, and to 2 VLBI observations of the Phobos Spacecraft in its approach to Mars, 1989. The orientation of DE405 is discussed in more detail elsewhere in this volume (Standish, 1997). Since all of the parameters of the inner solar system are now determined to 1 mas or better, one should be able to extract numerically the fundamental arguments of the nutation theories to the level of 1 mas.

There are two ways of extracting the ecliptic, for example, from a numerical ephemeris: 1) one computes the node and obliquity of the instantaneous ecliptic at multiple points in time and then fits these with analytic functions, or 2) one fits an analytical planetary theory to the ephemerides and then computes the node and obliquity from the theory’s parameters. This paper relates a short example using method #1 and concludes that method #2 is probably more preferable.

The accurate observation of the celestial motion of the Earth’s pole requires careful connection of the VLBI observables with quantities and reference frames related to the theoretical description of precession-nutation models. The analysis of the derived celestial pole offsets beyond the semi-empirical IERS(1996) precession-nutation model shows variability of some components, such as the seasonal term and a ~ 430 day term.

The whole scope of problems related with the rotational motion of celestial bodies is briefly discussed. Relativistic modeling of the Earth rotation is considered from a conceptual point of view. Relativistic effects in rotational equations of motion of an extended body in general relativity are discussed. Numerical values of the effects are given.

The IERS nutation series was developed as a nutation series which would match observations and could be used with geodetic systems which have sensitivity to nutations but are not able to determine accurately corrections to the IAU-1980 nutation series. After experimentation with different methods for parameterizing the nutation estimation problem, the best fit to the VLBI observed nutation angle data was found by estimating selected coefficients in the Mathews et al. (1991a) nutation response function (see equation (1) below), along with other parameters to be discussed below. The estimation of the response function coefficients was also found to account for mantle anelasticity and the loading part of the ocean tide correction and therefore no corrections were applied for these effects. Their contributions should be absorbed into the estimated response coefficients. These initial analyses also showed: setting the inner-core response to zero yielded better fits to the nutation angle data than the Mathews et al. (1991b) theoretical response and resonance frequency; the amplitude of the RFCN free mode appeared to be time dependent; and the prograde annual nutation was significantly affected by the SI thermal tide which is not proportional to the S1 gravitational potential.

The data set used to estimate the IERS conventions series was the GSFC nutation angle data set with 2040 pairs of adjustments to the IAU 1980 nutations in obliquity and longitude spanning the interval between 1979 and 1995. Here we also compare the IERS conventions series with a US Naval Observatory analysis of VLBI data between 1979 and August 1997. This data set consists of 2152 pairs of nutation angle estimates and extends by 1.8 years the interval covered by the GSFC data set. It also contains less pre-1984 data than the GSFC data set which accounts for the smaller increase in total number of observations than would be expected for the additional time interval covered.

We present a first description of the changes in the current procedures that will have to be performed in order to take into account the adoption of the ICRS as the new reference system and new nutation-precession series. A number of choices will have to be made: they are presented in this paper.

Systematic errors caused by the use of inconsistent models and constants currently limit the accuracy of the most precise astro-geodetic observations. It is important, therefore, to provide conventional estimates of astronomical constants for general use in astronomy and geodesy. Establishment of such a set raises issues involving the accuracy of the constants, their internal consistency, and the reference system in which they are expressed. Future sets of constants will be updated at regular intervals to provide the most accurate values at that instant. Careful consideration must be given to their internal consistency. It is likely that they will be provided only in electronic format with references to their determination and to procedures for their use.

At its 1994 General Assembly, the International Astronomical Union resolved to introduce new arrangements to establish and maintain an accessible and authoritative set of constants, algorithms and procedures that implement standard models used in fundamental astronomy. The initiative was the responsibility of the Working Group on Astronomical Standards (WGAS), part of Division 1 of the IAU, and the set of procedures and constants was named SOFA, for “Standards Of Fundamental Astronomy”. The background to the IAU Resolution is given by Fukushima (1995) and Wallace (1996).

RCMA SWG was appointed by the IAU WGAS (Working Group on Astronomical Standards) in accordance with IAU Resolution C6 (1994) with the aim ‘to provide definitions of the astronomical units, of the quantities linking these astronomical units to the units of the International System (SI), and of other astronomical quantities, compatible with the theory of General Relativity’. It is evident that the relativistic aspects of units of measurement cannot be isolated from the more general problem of astronomical constants and fundamental astronomy concepts in the relativistic framework. Therefore, along with the problem of units the main topics of discussion of RCMA SWG concerned also the IAU (1991) Resolutions on References Systems (RSs) and Time Scales (TSs) and their interpretation in IERS Standards (1992) and IERS Conventions (1996). In what follows we tried to summarize the results of these discussions.