The astonomical consequences of recently developed theoretical methods of relativistic astrometry are discussed. The set of practically important reference systems is described. These reference systems generalize the locally inertial frames of general relativistic test observer, the hierarchy of Jacoby coordinates for dynamical problems and the dynamically inertial reference systems of fundamental astrometry. In practical application of this formalism much attention is paid for relativistic transformation functions relating the ∗∗ecliptical coordinates corresponding to the baryecnters of the Solar system, the Earth-Moon subsystem and the Earth. Solutions to several kinds of relativistic precession are also presented.

In a considerable number of works on relativistic astrometry (see, e.g. Kovalevsky and Brumberg 1986) the reference frames (RFs) are introduced either by means of coordinate representation of a space-time metric, such as using harmonicity conditions (Brumberg and Kopejkin 1989), or on the basis of invariant constructions like Fermi coordinates (Synge 1960; Ashby and Bertotti 1986; Boucher 1986). Both approaches must, probably, be combined in applications. We consider the local observer RFs (LORFs) based on the Fermi coordinates and on the optical ones (Synge 1960), which are rigorously defined for a general metric and are directly related to observable quantities. In particular, the optical RF operates with the observed direction of the light source, whereas the Fermi RF seems to be a natural generalization of the classical Cartesian RF.

The optimum Conventional Terrestrial System (CTS) can be defined by accurate coordinates of some number of stations distributed homogeneously all over the world. There are scores of laser and VLBI stations whose coordinates are known with high accuracy of the order of 1-2 cm. There are many CTS defined by the sets of station coordinates determined in the process of determination of the Earth rotation paramaters and the Earth gravity field. Presently existing stations are not distributed homogeneously on the Earth. They are located mostly in Europe and in North America. In this situation, the errors of orientation of axes and origin positions are not equal. Some of them, based on a small number of not homogeneously distributed stations, are not well-defined (stable).

The celestial system of the International Earth Rotation Service (IERS) is materialized by the J2000.0 positions of more than 250 extragalactic compact radio sources observed by VLBI. The source coordinates are evaluated from the combination of individual celestial frames obtained by the Goddard Space Flight Center, the Jet Propulsion Laboratory and the U.S. National Geodetic Survey.

The combination model and the maintenance algorithm are described. To free the IERS celestial frame from inconsistencies due to the inaccuracy of the IAU conventional models for precession and nutation, it is implemented on individual frames which have been obtained in parallel to the adjustment of corrections to the direction of the celestial pole.

The IERS celestial reference frame is consistent with FK5 at a few milliarcsecond level. To be made denser and more accessible for astronomical uses, it will be related to the HIPPARCOS stellar frame.

Based on the expected precision and characteristics of the Low Latitude Meridian Circle (LLMC), and the development of CCD astrometry at Yunnan Observatory, an internally consistent and non-rotating optical celestial coordinate system can be set up through observations with the LLMC and CCDs. To obtain this goal, the main work we plan to do are (1) to establish a fundamental stellar reference system of several thousand stars based on the absolute obsrvations with the LLMC; (2) to provide the accurate zero-point corrections for the system from observations of minor planets with the LLMC and CCDs; (3) to determine the precessional rotation of the system with respect to an extragalactic reference system with the LLMC and CCDs, thus transforming the system into a quasi-inertial coordinate system; and (4) to obtain the atmospheric refraciton corrections from the observations with the LLMC.

Transformation procedures from the FK4 reference system of B1950.0 to the FK5 reference system of J2000.0 have been developed by Standish (1982) and by Aoki et al. (1983). We review here these procedures and discuss the differences between them. Especially we note that among researchers of this field a misunderstanding still exists in the problem at which stage the equinox correction should be applied. We show that the equinox correction should be applied in the precessing frame as Aoki et al. did. We also show that the epoch of the transfer from the FK4 to the FK5 in the transformation procedure is related to the systematic and individual corrections to the FK4.

This paper investigates the estimation of mean positions and proper motions given independent solar-system barycentric positions observed at different epochs, reduced to the same equator and equinox and freed of systematic errors. Past practices are reviewed and the relative quality of the data is studied to determine the appropriate form of the model.

The topic (Seidelmann, 1986) is one of the unresolved questions in the field of celestial mechanics because the definitions of an inertial system are all controversial (Mach, 1893; Eichhorn, 1984). Eichhorn's definition enlarges its connotation and is not acceptable either. Connotation of a concept is endowed through defining it. One of the reasons why the existing definitions of an inertial system are all controversial is that the connotations that are endowed by them are not unique, in other words, they do not draw up the same area of ideas. Taking the interplay of all of them for its connotation is an acceptable solution.

While HIPPARCOS is expected to measure positions and proper motions with more accuracy than those obtained by ground-based instruments, what can we do in the future for ground-based instruments? The observations with them still are important for establishing an inertial frame because of the long history of observations with them and improvements in the instruments. Moreover, it is necessary to have data of observations from them for research on problems related to the Earth. The horizontal meridian circle in China (DCMT) is expected to have advantage over the classical meridian circles. The DCMT will be assembled and tested this year. It should work in the following fields: (1) observing radio stars, (2) observation of minor planets, (3) absolute determinations of IRS.

The work on construction and operation of automated systems for collection and processing astrometric and meteorological information and also of automated television systems with remote control have placed before us a number of fundamental difficulties in that hundreds of correct solutions to these problems require a systematic approach.

The most suitable cybernetics-mathematical composite for solving the problems of astronomical refraction may become the so-called hybrid-expert systems — a union of traditional expert systems with calculation-logical ones. In these systems logical-linguistic models are used together with mathematical ones.

The basic problem of ARA-C consists in obtaining a model of the environment in which light propagates and also to give a notion of interaction between electrons (environment) and photons (light).

It is proposed to use in this system a model of light interaction with environment built up on special formalisms of artificial intellect (logical-linguistic model). The basic principal in hybrid-expert system ARA-C operation must be mathematical modelling and calculation experimentation. In the proposed hybrid-expert system knowledge is presented on three levels—object, mathematical and programmed. Functioning of the lower levels of ARA-C is connected with formulation of the calculation problems. A calculation problem presented to a technical model determines a partial order on a twopart column of mathematical correlations.

Recent progress of precision in astrometric studies is summarized and the weights of systematic errors in astrometric observation are analysed.

The 1980 IAU nutation series includes effects of the Earth's non-rigidity. Certain simplifying assumptions were made in the model, including that the Earth is elastic and hydrostatically pre-stressed. The rationale was that geophysicists didn't understand the Earth well enough to justify a relaxation of those assumptions, and that the nutation observations were not accurate enough to detect the difference, anyway. Geophysicists are still not able to construct a more accurate model that is independent of the nutation observations, themselves. But, the observations have improved enormously. Recent results obtained from VLBI data show discrepancies with the IAU model of close to 2 milliseconds of arc: many times the observational uncertainty. Thus, the nutation observations are beginning to tell us things about the Earth that cannot presently be inferred as accurately from other techniques. I will discuss some of these possible geophysical applications. Among them are the shape and internal structure of the core, and the Earth's anelasticity.

There are a variety of reasons why in geodesy an improved formula for nutation is needed; related topics of interest are the determination of time-dependences in low degree zonals of the earth gravity field, ocean tide modeling, determination of odd harmonics of gravity field etc. in satellite geodesy. A combined model of deterministic and stochastic components is used in order to evaluate two new nutation series where, in an adjustment, mainly VLBI data (IRIS, GSFC, IERS) have been applied. Contrary to earlier revisions of the present nutation formula, not only the five significantly affected waves (annual, semi-annual, FCN etc.) are corrected but rather all constituents are revised in such a way that white noise residuals result from the adjusted observations, based on the new formula. Still remaining problems (such as the separation of long-period terms from precession etc.) are outlined.

In view of the present accuracy of the astrometric observations and of the development of the theory of the nutation, it became necessary to make a complete revision of this theory for a rigid Earth model. We present the results of our recent one (Kinoshita and Souchay, 1989), which includes planetary effects and second order effects no considered in the previous tables (Kinoshita, 1977). We analyze the difference between these tables and the new ones providing from the revision above and the comparison between the theory and numerical integrations recently performed (Kubo and Fukushima, 1987; Shastok et al., 1987; Shastok et al., 1989). The results of this comparison are much better after revision than before.

A re-reduction of observations made with ZTF-135 in Pulkovo during 1948.7-1989.0 (all together about 87 000 observations) has been carried out with the aim of determing the amplitude of the principal terms of nutation in longitude and obliquity. The derived coefficients of nutation M=6.“8445±″0033 and N=9.”2028±0.″0025 are in good agreement with similar astrometric determinations.

The attempt was made to determine the corrections to the coefficients of the IAU 1980 nutation series together with other geodesical and geodynamical parameters by the use of the Kiev-Geodynamics-3 program complex for LAGEOS laser data analysis. This complex is based on the MERIT standards and on numerical integration techniques for satellite orbit computation. An integration is carried out in cartesian coordinates by the Adams method of variable step and order.

Hydrodynamical computations of the major partial tides in the oceans have been evaluated for the changes both in moment of inertia and relative angular momentum due to ocean currents. If the system solid Earth plus oceans is seen as an isolated system for these time scales, the oceanic variations lead to mirror-like changes in the rotation of the solid Earth. Amplitudes are of the order of 0.1 ms in Universal time. In contrast to the effects of solid Earth tide, phases are away from equilibrium phases.

The software for the reduction of the VLBI observations of the Main Astronomical Observatory of the Ukrainian Academy of Science is described.

Our program complex has three parts:

1) calculation of geometrical delay τ,

2) calculation of required corrections to values of τ,

3) data analysis procedures.

This software has been tested using the NGS VLBI data for the obtaining of corrections to the ERP. The parameters of the clock were derived. Our results were compared with similar results, which were published by Shanghai observatory (China) and IRIS bulletin.

The differences between our results and the data given in the IRIS bulletin are within 5 mas, and for UT are within 0.1 ms.