We have analyzed proper motions of about 30000 K-M giants chosen from the astrometrie catalogue ACRS Part 1 (Corbin and Urban 1991). To avoid localized velocity fields, these K-M giants are chosen from the heliocentric distance interval 0.5 - 1.0 kpc. Starting from the initial trial of the luni-solar precessional correction Δρ ~ —0”.3/cy, we have found that the motion of stars are well expressed in terms of the Oort constants for the K-M giants. After confirming that the K-M giants are in a steady-state, we have applied the velocity-field model of the plane-parallel galactic rotation with non-zero Oort constants. Then, we have found a rational set of the corrections to the FK5 system: Δρ = -0”.27 ± 0”.03/cy and Δe + Δλ = —0”.12 ± 0”.03/cy, as is shown in Table 1 (Miyamoto and Sóma 1993). In consequence, the FK5 system is still rotating.

In 1991, IAU Resolution A4 introduced General Relativity as the theoretical background for defining celestial space-time reference sytems. It is now essential that units and constants used in dynamical astronomy be defined in the same framework, at least in a manner which is compatible with the minimum degree of approximation of the metrics given in Resolution A4.

This resolution states that astronomical constants and quantities should be expressed in SI units, but does not consider the use of astronomical units. We should first evaluate the usefulness of maintaining the system of astronomical units. If this system is kept, it must be defined in the spirit of Resolution A4. According to Huang T.-Y., Han C.-H., Yi Z.-H., Xu B.-X. (What is the astronomical unit of length?, to be published in Asttron. Astrophys.), the astronomical units for time and length are units for proper quantities and are therefore proper quantities. We fully concur with this point of view. Astronomical units are used to establish the system of graduation of coordinates which appear in ephemerides: the graduation units are not, properly speaking astronomical units. Astronomical constants, expressed in SI or astronomical units, are also proper quantities.

Starlink’s SLALIB library is a collection of algorithms used in astronomical position and time applications. After describing the library in the context of Starlink as a whole, we look at more general questions about the provision of such software.

In 1976, the IAU recommended for the value of the precession constant 50".290 966 per Julian year and, since 1984, most of the ephemerides have used the formulas of Lieske et al. (1977). In this paper, the motion of the ecliptic was based on Newcomb’s theory. The ecliptic was defined with an accuracy of 0".3 over 1000 years and of 6 mas over one century around J2000. For several years, new determinations of the precession constant have showed that this value is too high by about 3 mas per year. For instance, Williams et al. (1991) give 50".2882 per year. From this value and from the mean elements defining the ecliptic given by Simon et al (1994), we have built new expressions for precession formulae. The motion of the mean ecliptic is described through variables q and p: where t is the time reckoned in thousands Julian years from J2000. This solution has an accuracy of 1 mas over several thousands years and 0.1 mas over one century around J2000. The variations of the equator are obtained by integration of the differential equations of the precession in longitude and of the obliquity in Kinoshita (1977) and Kinoshita and Souchay (1990). The dynamical ellipticity is determined in order to obtain (dP/dt) = 50 288".2 at t = 0 as Hd = 0.003 273 7752. From this value for Hd, we can integrate the differential equations for P and ε:

In the future, the ephemerides produced at JPL will be based upon the reference frame of the radio source catalogues. Recent planetary observations have been made directly with respect to the radio frame, and these observations have shown a satisfying degree of absolute accuracy and internal consistency; they provide an automatic frame-tie.

The location-independent part of TCB-TCG, the difference between the two new time scales adopted by the IAU (1992), was integrated numerically for three JPL planetary/lunar ephemerides; DE102, DE200, and DE245. The differences among these three integrations were mostly explained by the difference in the adopted constants of the ephemerides. It was shown that the post-Newtonian correction and the perturbation by asteroids are negligible except for the mean rate, LC. The comparison of these numerical integrations with the analytical formulas of Hirayama et al. (1987) and Fairhead and Bretagnon (1990) as well as their extended versions lead to the best estimate of LC as

Combining this with the recent value of the geoid potential in Bursa et al. (1992), we estimated the value of LB, the scale difference between TCB and TT, as

Table I summarizes these conclusions. These estimates of LC and LB are more reliable than the former values we gave (Fukushima et al. 1986). The new estimate of LB will be useful in converting the numerical values of some precisely determined astronomical constants such as AU measured in meter from those in TDB to those in TCB. Also the numerically integrated TCB-TCG, which are to be called Time Ephemeris, will be useful when converting between TCB and TDB, i.e. the time scales themselves. The full paper will be appeared in A & A with the title of Time Ephemeris.

Due to both precise time measurements and precise geodetic positioning methods (like Very Long Baseline Interferometry (VLBI), Lunar Laser Ranging (LLR), Satellite Laser Ranging (SLR) and Global Positioning System (GPS)), the position of the instantaneous axis of the Earth’s rotation in space is measured with a precision better than a tenth of milliarcsecond. Simultaneously the amplitudes of the nutations of the Celestial Ephemeris Pole (CEP) deduced from the observations, i.e. the periodic motions in space of the CEP due to the luni-solar attraction or to other planetary attractions, have also been improved. However, these observed nutation amplitudes differ with respect to the computated ones based on an elliptical, uniformly rotating and deformable Earth responding to the lunar and solar attractions, as adopted by the IAU in 1980. The first session on “Observations and data reduction” dealt with Earth’s orientation observations and data analysis for deriving precession and nutations, as well as the associated residuals with respect to the adopted precession constant and nutation series. Comparisons between the different results have been presented including in-phase and out-of-phase components of the prograde and retrograde nutations or of nutations in longitude and in obliquity (see Session 1 of our JD: Newhall et al., McCarthy and Luzum, Herring, and Session 2: Gross). These differences “observed - adopted” nutations achieve several milliarcseconds and exhibit periodic as well as secular characteristics.

From the analysis of 24 yr of lunar laser ranges, the correction to the IAU luni-solar precession constant is found to be −3.2 ± 0.3 mas/yr for a total value of 50.3846˝/yr at J2000. The size of the 18.6 yr nutation of the pole needs to be increased by about 2 mas over the 1980 IAU theory.

The previous analysis of McCarthy and Luzum (1991b) is repeated using an additional three years of VLBI observations. A new set of empirical corrections to the 1980 IAU Nutation Theory is determined and compared to current geophysical models.

We discuss the formulation of a new nutation series to be used in the reduction of modern space geodetic data. The motivation for developing such a series is to develop a nutation series that has smaller short period errors than the IAU 1980 nutation series and to provide a series that can be used with techniques such as the Global Positioning System (GPS) that have sensitivity to nutations but can directly separate the effects of nutations from errors in the dynamical force models that effect the satellite orbits. A modern nutation series should allow the errors in the force models for GPS to be better understood. The series is constructed by convolving the Kinoshita and Souchay rigid Earth nutation series with an Earth response function whose parameters are partly based on geophysical models of the Earth and partly estimated from a long series (1979-1993) of very long baseline interferometry (VLBI) estimates of nutation angles. Secular rates of change of the nutation angles to represent corrections to the precession constant and a secular change of the obliquity of the ecliptic are included in the theory. Time dependent amplitudes of the Free Core Nutation (FCN) that is most likely excited by variations in atmospheric pressure are included when the geophysical parameters are estimated. The complex components of the prograde annual nutation are estimated simultaneously with the geophysical parameters because of the large contribution to the nutation from the S1 atmospheric tide. The weighted root mean square (WRMS) scatter of the nutation angle estimates about this new model are 0.32 mas and the largest correction to the series when the amplitudes of the ten largest nutations are estimated is 0.17 ± 0.03 mas for the in phase component of the prograde 18.6 year nutation.

The reference frames are of fundamental importance in all kinds of the precession and nutation studies involving the theory, the coordinate transformation and the observations. The aim of this paper is to review all the frames used in such studies and to lead to a better consistency between them in order that theory and reductions of observations be referred, as close as possible, to the frames to which observables are actually sensitive.

The equations of Earth rotation can be expressed either as Euler equations in the Terrestrial Reference System (TRS), or as perturbation theory in the Celestial Reference System (CRS) (Kinoshita 1977). Euler equations are transformed to the CRS in the astronomical approach (Woolard 1953) and solved by the method of variation of the parameters, whereas, in the geophysical approach (Melchior 1971), the solutions, first obtained in the TRS, are transformed to the CRS and then solved by an integration with respect to time.

Space-geodetic measurement systems are capable of determining: (1) a terrestrial, body-fixed reference frame defined in practice by the stated positions and secular motions of a set of observing stations, (2) a celestial, space-fixed reference frame defined in practice by the stated locations of celestial objects, and (3) the rotation parameters linking these two frames together. Five parameters are conventionally used to specify the orientation of the terrestrial frame with respect to the celestial frame: two nutation parameters, two polar motion parameters, and one spin parameter. The celestial ephemeris pole (CEP) is defined as the north pole of that axis about which the spin parameter (UT1) is measured. The two nutation parameters locate the CEP in the celestial frame, and the two polar motion parameters locate the CEP in the terrestrial frame. By examining the frame transformation matrices, an expression relating the location of the rotation pole to that of the CEP can be derived. In order to compare theoretical predictions with observations, results of models for the effect on the nutations of geophysical excitation processes such as diurnal oceanic current and sea level height variations should not only be given in terms of the location of the CEP (rather than of the rotation pole), but must also account for the resonance effects of the free core nutation.

Although the main questions remaining in the frame of the study of the nutation-precession phenomena concern principally the effects due to physical interactions, recent works have shown that even in the simplified case of a rigid Earth model of nutation, important changes have to be taken into account. Here we present the various steps having led to a more complete and more accurate rigid Earth nutation theory, since the pionnier work of Woolard (1953), insisting on the most recent improvements.

Geophysical modeling of nutations involves (a) the formulation of a general theory of the forced nutations of an idealized Earth (spheroidal, oceanless, elastic), supplemented by separate theoretical treatments of the effects of the oceans, anelasticity, and other deviations from the ideal, and (b) fitting of the theoretical expressions to VLBI-estimated amplitudes of the various spectral components of the nutations. The aim is to obtain best-fit estimates of Earth parameters which influence the nutations; and the degree of success of the modeling is judged by the precision of the estimates obtained, as well as the quality of the fit as measured by χ2red, the chisquared per degree of freedom.

We present here our findings from two types of fits using, for the observational input, the nutation amplitude estimates for seven important pairs (retrograde and prograde) of circular nutations, together with their standard errors and mutual correlations, which were kindly furnished by T.A. Herring (private communication, 1993). The theoretical framework employed was that of Mathews et al. (1991), hereinafter referred to as MBHS, together with the Zhu and Groten (1989) rigid Earth nutation series modified to take account of the recently-estimated correction of −0.3 mas/cy to the precession constant. Estimates of ocean tide effects, and of anelasticity effects based on Wahr and Bergen’s (1986) results for model QMU with α = 0.15 (hereafter abbreviated to WB), were taken from Herring et al. (1991). Alternative estimates of anelasticity effects (DZ, due to Dehant (1990) based on the Zschau model), were also considered.

The IAU General Assembly has adopted in 1980 a nutation series, on the one hand, based on rigid Earth’s contributions theorically computed from celestial mechanics, and on the other hand, based on non-rigid Earth’s contributions theoretically computed from Earth deformation equations using geophysical parameters.

1. 1. From the previous papers (see Session 1) of this Joint Discussion, we know that there are differences of this adopted theory with respect to the observations of precession and nutations. These differences can reach several mas, which is well above the present accuracy of the observations.

2. 2. From previous papers (see Session 2) and from the posters, we also know that there exist new rigid-Earth nutations (Kinoshita-Souchay, Roosbeek, Hartmann) of which the accuracy has increased by one order of magnitude.

3. 3. From Session 3 papers, we know that there are some additional geophysical effects that are not yet taken into account in Wahr’s nutation theory adopted in 1980 by the IAU which have a contribution at a level above the present precision of the observations. These additional geophysical aspects can be accounted for either from a semi-analytical theory (like Mathews, Herring, Shapiro and Buffett are doing), or from an integration of deformation equations through the whole Earth (Dehant, Wahr).

The establishment of the TAI is done in two steps: the construction of the EAT from clocks in laboratories, then its steering by primary frequency standards. Great progress in the precision and stability of EAL was made by the generalized use of GPS time transfer and by the introduction of hydrogen masers and new very performant clocks. Only two primary frequency standards are sufficiently accurate to steer the frequency of TAI, but new standards are now being assessed. The present stability of TAI is 5.10−15 and the accuracy 2.10−14. Improvements should occur in the years to come.

The establishment of the International Atomic Time (TAI) and the resulting Coordinated Universal Time (UTC) by the time section of BIPM is done in two steps (Guinot and Thomas, 1988). At first, a free atomic scale, EAL (Echelle atomique libre) is built in two month blocks combining data from about 200 atomic clocks kept by 60 laboratories and regularly reported to the BIPM by 45 centres which maintain a local coordinated universal time, UTC(k). Then, the duration of the scale interval of EAL is compared with data from primary caesium standards producing the SI second which, in turn, is converted on the rotating geoid as the unit scale of TAL A linear function of time with the necessary slope is added to EAL to ensure the accuracy of the TAI scale interval.

The new (1991) IAU recommendations on reference systems and time scales are based completely on general relativity. But the metric forms determining the corresponding reference systems are specified in these recommendations not sufficiently definitive to take into account non-geodesic accelerations in the motion of the geocentre or topocentre, to distinguish between relativistic dynamically or kinematically non-rotating systems and to exclude a possible ambiguity in the time scales due to the relativistic coordinate gauge. There is a hidden ambiguity in the relativistic definition of the geocentre due to the difference bewteen Newtonian-type and Blanchet-Damour multipole moments used, respectively, in Brumberg-Kopejkin (Brumberg and Kopejkin, 1989; Kopejkin, 1991a; Brumberg et al., 1993; Klioner, 1993; Klioner and Voinov, 1993) and Damour-Soffel-Xu (1991-1994) approach to construct relativistic hierarchy of reference systems. In using TAI as physical realization of TT one should specify the constant LG (Fukushima, 1994) once for ever not introducing the relativistic ill-defined notion of the geoid (Kopejkin, 1991b). It might be reasonable not to separate this constant at all (as having no sense for moving clocks on the surface of the Earth or in the circumterrestrial space) and to use TAIM as physical realization of TCG itself relating TCG directly with the observer’s proper time avoiding the intermediate scale TT (Brumberg, 1992).

The location-independent part of TCB–TCG, the difference between the two new time scales adopted by the IAU (1992), was integrated numerically for three JPL planetary/lunar ephemerides; DE102, DE200, and DE245. The differences among these three integrations were mostly explained by the difference in the adopted constants of the ephemerides. It was shown that the post-Newtonian correction and the perturbation by asteroids are negligible except for the mean rate, LC The comparison of these numerical integrations with the analytical formulas of Hirayama et al. (1987) and Fairhead and Bretagnon (1990) as well as their extended versions lead to the best estimate of LC as

Combining this with the recent value of the geoid potential in Bursa et al. (1992), we estimated the value of LB, the scale difference between TCB and TT, as