The report of the Sub-Group on Time (SGT) of the IAU Working Group on Reference Systems (WGRS) is divided as follows.

Sections 2 to 4 recall the scope of the work of the SGT and briefly describe its activity.

Section 5 summarizes the discussions on several topics which form the background of the draft recommendations and notes of Section 6.

The membership of the subgroup on coordinate frames and origins included the following: V.K. Abalakin, S. Aoki, F. Arias, С Boucher, N. Capitaine, K. Johnston, J. Kovalevsky (chairman), C. Ma, I.I. Mueller, C.A. Murray, H. Schwan, C.A. Smith, C. de Vegt and R. Wielen.

In addition, the following colleagues have contributed to the work: V.A. Brumberg, T. Damour, J. Dickey, M. Feissel, T. Fukushima, B. Guinot, T. Huang, M. Standish, J.G. Williams and B.X. Xu.

The IAU Working Group on Reference Systems (WGRS) Sub-Group on Astronomical Constants (SGAC) was established in June, 1989, as a consequence of resolutions adopted by Commissions 4, 7, 8 and 24 at the IAU General Assembly at Baltimore in 1988. The given missions of this sub-group were stated clearly by J. Hughes, the chairman of the WGRS, as:

This is a report of the activity of the SGAC prior to IAU Colloquium No.127. Section 2 summarizes the questionnaire prepared in trie course of discussion. In Section 3, the discussions on major issues are introduced. The drafts of Recommendations from the SGAC prepared before the Colloquium are shown in Section 4. Note that these drafts were very different from the final form as indicated in this Proceeding. Sections 5 and 6 deal with the current status of astronomical constants used widely now and the best estimates of some major constants which are available now, respectively. I believe these will serve as a guideline for current astronomical constants.

Relativistic hierarchy of reference systems (RS) developed in recent years by different authors is examined in detail. Metric expressions and transformation relations for solar system barycentric RS (BRS), heliocentric RS (HRS), Earth-Moon local RS (LRS), geocentric RS (GRS), topocentric RS (TRS)and Earth satellite RS (SRS) may be obtained explicitly in harmonic coordinates of GRT. The time coordinate of any RS involves the corresponding time scale. Particular attention is given to the closed form representation of GRS avoiding expansions in powers of the geocentric coordinates. GRS has been constructed in both versions of dynamically non-rotating GRS (DGRS) or kinematically non-rotating GRS (KGRS). DGRS and KGRS differ in their space axes orientation by the amount of the geodesic precession. Similarly, taking into account the motion of the Sun around the center of the Galaxy one should distinguish between dynamically non-rotating BRS (DBRS) and kinematically non-rotating BRS (KBRS) differing in their space axes orientation by the amount of the galactic precession. Reduction to the galactic time and the galactic space axes may be needed in the nearest future.

A new formalism for treating the relativistic celestial mechanics of systems of N, arbitrarily composed and shaped, weakly self-gravitating, rotating, deformabile bodies is presented. This formalism is aimed at yielding a complete description, at the first post-Newtonian approximation level, of (i) the global dynamics of such N-body systems (“external problem”), (ii) the local gravitational structure of each body (“internal problem”), and, (iii) the way the external and the internal problems fit together (“theory of reference systems”).

This paper reviews the links currently envisaged for a mission of duration 3½ years, with estimates of the precision of each link.

The Fine Guidance Sensors (FGSs) are the instrument of choice for most astrometric measurements with the Hubble Space Telescope (HST). The observed amount of spherical aberration in the Ritchey Chretien optical system does not affect positional measurements with perfectly aligned FGSs because they are interferometers. The FGSs combine wavefronts from points in the exit pupil with other points which are at the same radial distance from the optical axis. Asymmetric aberrations such as coma and astigmatism do affect the measured positions. The current knowledge of the HST wavefront error, the FGS operation and the implications for milliarcsecond relative astrometry are discussed. It is still planned to use the HST to tie the HIPPARCOS and VLBI Reference Frames together at the few milliarcsecond level.

This paper investigates the practical use of the nonrotating origin (NRO) (Guinot 1979) for estimating the Earth Rotation Parameters from VLBI data, which is based on the rotational transformation between the geocentric celestial and terrestrial frames as previously derived by Capitaine (1990). Numerical checks of consistency show that the transformation referred to the NRO is equivalent to the classical one referred to the equinox and considering the complete “equation of the equinoxes” (Aoki & Kinoshita 1983). The paper contains the expressions for the partial derivatives of the VLBI geometric delay to be used for the adjustment of the pole coordinates, UT1 and deficiencies in the two celestial coordinates of the Celestial Ephemeris Pole (CEP) in the multiparameters fits to VLBI data. The use of the NRO is shown to simplify the estimates of these parameters and to free the estimated UT1 parameter from the model for precession and nutation.

The procedures are summarized in order to obtain a reference system which is available at the present moment and in the near future for the astronomical purposes. The target of the present discussions is the IAU General Assembly to be held in the summer of year 1991, in order to find out an agreeable result there. Discussions beyond this are postponed to a further occasion.

The term “frame of reference” or “reference frame” has long been established in physics. The recent emergence of the use of this very term in astronomy to denote “a catalogue of the adopted coordinates of reference points that serves to define, or realize, a particular coordinate frame” is misleading because “a catalogue of adopted coordinates” must necessarily consists of estimates which cannot uniquely define a coordinate system.

The celestial reference system and the terrestial reference system of the International Earth Rotation Service (IERS) are realized on the basis of observation programs in Very Long Baseline radio Interferometry and laser ranging to the Moon and artificial satellites. The celestial frame is materialized by the equatorial coordinates of radio sources observed in VLBI; the terrestrial frame is materialized by the cartesian coordinates of the terrestrial sites monitored by the three techniques. Series of the Earth Orientation Parameters are derived from the same observations. These series provide a permanent link between the celestial system and the terrestrial system at the level of 0.001”.

The global adjustment in which the reference systems are defined and realized is described, and the metrological properties of the frames and of the derived EOP are evaluated.

The PTRF is based on 43 sites with 64 SSC collocation points with the optimum geographic distribution, which were selected from all stations of the ITRF89 according to the criterion of the minimum value of the errors of 7 parameters of transformation. The ITRF89 was computed by the IERS Terrestrial Frame Section in Institut Geographique National - IGN and contains 192 VLBI and SLR stations (points) with 119 collocation ones. The PTRF has been compared with the ITRF89. The errors of the 7 parameters of transformation between the PTRF and 18 individual SSC as well as the mean square errors of station coordinates are of the same order as those for the ITRF89. The transformation parameters between the ITRF89 and the PTRF are negligible and their errors are of the order of 3 mm.

The different procedures of the transforation from FK4 to FK5 are reviewed. With these procedures some numerical examples for selected FK4 stars are given. Basing on the original work of Fricke (1985), we prefer to select the procedure developed by Standisti (1982). One of the main reasons for the procedure of Aoki et al. (1983) is to consist with the new definition of UT. Since the corrections “FK5 - FK4” for many stars are significant, even if adopting this procedure, it is still impossible to avoid the effect of the right ascension discontinuities on UT.

The present status and prospects of program CONFOR-Connection of Frames in Optic and Radio, are described. It is supposed that positions of extragiactic objects and intermediate stars in 200 areas will be obtained in FK5 system.

The celestial positions of extragalactic radio sources may be determined to a precision of less than a milliarcsecond. Further, since these sources are believed to be at great distances from the galaxy, little or no proper motion is expected on scales of order a milliarcsecond. Therefore a reference frame based on the positions of carefully selected sources so that display compact radiation on scales less than a milliarcsecond will noticeably improve the precision of present celestial reference frames. If the radio objects making up the reference frame also emit radiation at optical wavelengths, and assuming the optical/radio radiation is coincident, the radio frame can update the optical frame to the accuracy of the individual optical positions.

Comparisons between sets of radio source coordinates determined from independent VLBI measurements show that rotational offsets can be as large as several milliarcseconds (mas), and are considerably larger than the positional uncertainties (≤1 mas). The 1 to 2 mas discrepancies remaining after removal of the rotational offsets indicate the present true level of accuracy. Analyses of DSN and CDP astrometric data are performed to explore the effects of alternative schemes of nutation modeling on such catalog comparisons. It is concluded that rotations between different source catalogs are minimized or eliminated if the nutation models employed are consistent. Intrinsic source coordinate discrepancies, however, remain at the 1 mas level.

The 318 compact extragalactic radio sources with positions derived from dual frequency Mark III VLBI data acquired by the geodetic and astrometric programs of NASA, NOAA, NRL and USNO form a celestial reference frame with stability in orientation and relative position at the 1 mas level. This paper examines the reference frame realized using 461,000 observations from 1021 observing sessions between 1979 August and 1990 August in the NASA Crustal Dynamics Project VLBI data base. Catalogs of positions estimated from subsets of data (annual, seasonal, network) show differences in orientation typically less than 1 mas provided precession and nutation are adjusted using a reference day. For 17 sources with >5 year time span and >200 one-day position estimates, the rates of change of right ascension and declination are generally less than 5 mas/century, giving upper limits on real motion.