The regular photographic observations of Galilean satellites has been made with 26″ refractor at Pulkovo since 1975. The relative positions of satellites are obtained by means of “scaletrail” technique. During 1975–1979 over 600 observations of Galilean satellites were carried out. The observed positions were compared with the ephemeris based on Sampson's and Lieske's E-1 theories, the corresponding computations being made at the Institute for Theoretical Astronomy. The standard deviations of one observed relative position “Satellite minus Jupiter” don't exceed ±0″.10. The comparison of Sampson's theory with observations showed some systematic error which can be considered as an error in longitude of about 1 min. Lieske's theory E-1 showed a better agreement with the observations, the absolute deviations not exceeding 0″.3.

A construction of highly precision theories of motion of planet's satellites and of Galilean satellites, in particular, demands appropriately accurate observations (the error not exceeding 0″.10). At present such observations of satellites can be obtained with the help of long-foci telescopes (focal length of about 10 m), using rigorous technique of astrometric reduction.

The effect of different perturbing factors on the rectangular coordinates of outer satellites of Jupiter (VI-XII) and Saturn (VI-IX) is investigated by the numerical integration of the equations of motion. The effect of relativistic terms in the equations of motion is considered among other perturbations. The effect of weak perturbations is compared with the accuracy of modern observations of satellites.

Very accurate theories of the libration of the Moon have been recently built by Migus (1980), Eckhardt (1981, 1982) and Moons (1982, 1984). All of them take into account the perturbation due to the Earth and the Sun on the motion of a rigid Moon about its center of mass. Additional perturbations (influence of the planets, shape of the Earth, elasticity of the Moon, …) are also often included.

We present here the perturbations due to the shape of the Earth and the motion of the ecliptic plane on our theory which already contains planetary perturbations. This theory is completely analytical with respect to the harmonic coefficients of the lunar gravity field which is expanded in spherical harmonics up to the fourth order. The ELP 2000 solution (Chapront and Chapront-Touzé, 1983) supplies us with the motion of the center of mass of the Moon.

The treatment of the coordinate systems is briefly reviewed in the Newtonian mechanics, in the special theory of relativity, and in the general relativistic theory, respectively. Some reference frames and coordinate systems proposed within the general relativistic framework are introduced. With use of the ideas on which these coordinate systems are based, the proper reference frame comoving with a system of mass-points is defined as a general relativistic extension of the relative coordinate system in the Newtonian mechanics. The coordinate transformation connecting this and the background coordinate systems is presented explicitly in the post-Newtonian formalism. The conversion formulas of some physical quantities caused by this coordirate transformation are discussed. The concept of the rotating coordinate system is reexamined within the relativistic framework. A modification of the introduced proper reference frame is proposed as the basic coordinate system in the astrometry. The relation between the solar system barycentric coordinate system and the terrestrial coordinate system is given explicitly.

The coordinate dependence of the definition of light deflexion is discussed and the concepts of “natural” and “proper” reference frame are introduced in order to derive astrometric observables from coordinate quantities. Confusion in published formulations of VLBI data analysis is discussed in the context of the IAU definition of the coordinate time scale TDB. It is pointed out that with this definition, the unit of TDB differs from that of TDT and it is suggested that the speed of light in barycentric units be adopted as a defining constant in the system of astronomical constants.

In connection with the precision growth in modern astrometry, General Relativity (GR) has become a necessary basis of celestial mechanics and of computations of ephemerides of planets and other space objects, from the point of view of both the laws of motion and the expression of measurable (observable) quantities in terms of Reference Frames (RFs) notions. In this report we summarize the RF theory in GR (in the monad as well as in the tetrad representation) and give examples of specific gravitational effects. In any theory of RFs an important element consists on separation of the RF and system-of-coordinates (SC) notions, with a constructive description of projectors onto the physical temporal and spatial directions, of the observables as invariants (scalars) under SC transformations, as well as of the transformation laws of these observables under transitions between different RFs. For a more detailed though still incomplete synopsis of the monad and tetrad methods of RF representation in GR, see our preprint [1].

The relation between the units and the readings of time and space coordinates of the terrestrial and the barycentric frames is discussed from the viewpoint of general relativity. Attention is paid to the unit of space coordinates since the International Astronomical Union (IAU) regulates only the unit of time coordinate in the above two frames. Two definitions on unit of length are examined and their effects on the numerical expression of coordinate transformation, equations of planetary motions, and those for light propagation time are discussed. A clear conflict is found between the IAU(1976) recommendation on the definition of the time-scales in different frames and the statement that all constants in the IAU(1976) new system of astronomical constants are defined in terms of the international system of units (SI units). In order to dissolve this conflict, one of the two examined definitions on unit of length is proposed to be adopted, which requests the least alteration on the current procedures to analyze the astrometric observations such as radar/laser rangings, range and range-rate measurements, and very long baseline interferometric observations. An interpretation of numerical values in the IAU(1976) system of astronomical constants is also presented. It is stressed that the definition proposed in this paper requires that a slightly different formula from the current one be used in the numerical transformation of coordinates between the terrestrial and the barycentric frames.

The relations between the local measurements achieved in the solar system for testing the metric theories of gravity and the cosmological background are far from being clear. In most cases, some heuristic assumptions are made in order to take into account cosmological boundary conditions. In particular, the light rays from distant stars or extragalactic objects are often believed on the basis of the so-called Mach principle to determine “fixed” directions defining inertial frames. However, it has been already shown in theoretical cosmology that in any anisotropic, inhomogeneous cosmological model, the apparent directions of a distant object varies with respect to locally non rotating inertial frames. Restricting in the first step our attention to some exact anisotropic models obeying to the Einstein equations, we study the order of magnitude of this effect in the context of observational devices such as the HIPPARCOS satellite, the Space Telescope and the gyroscope experiment planned at the Stanford University. Then we try to interpret the effect and more generally the various influences of cosmological terms, within the framework of the parametrized post-newtonian formalism.

In papers (Pavlov, 1984 a,b and 1985), a complete and self consistent procedure of relativistic reduction for fundamental and radio-interferometric observations of distant sources has been developed. Relativistic formulae of apparent star positions, time delay and fringe frequency were derived. These formulae include all relativistic corrections due to the gravitational field of the Sun and the observer's motion. In the case of ground observations relativistic corrections are calculated to a relative accuracy of 5.10−9 or 0.001 arcsec.

The heliocentric motion of stars is investigated by taking into account all effects due to the geometry and due to the finite speed of light. It is shown that the proper motions as given in star catalogues contain the main light retardation term; an additional term of this type modifies Schlesinger's (1917) term but is less significant than a 3rd order perspective term neglected in conventional astrometry. Kapteyn's star serves as a numerical example. The ambiguous relativistic relation between Doppler shifts and radial velocities is discussed and demonstrated in a diagram. The ambiguity is solved with rigorous equations which allow to compute the inertial motion of a star from its proper motion, classical radial velocity, and distance. -

In the geometrical optics approximation a uniform approach to the description of the influence of strong Schwarzschild field on astronomical observations is given.

Observations of the sun and major and minor planets made by transit circle telescopes are used to determine positions of the equinox and the celestial equator and, by repeated observing programs, the motions of these fiducial references. Long series of such absolute observations, when combined into catalogs such as the FK5, yield a fundamental coordinate system which is an observational approximation to an ideal, dynamically defined coordinate system. In such a system the equinox, for example, is defined implicitly by the right ascensions (at mean epoch) and the proper motions of the stars included in the catalog system, together with the adopted constant of precession. It may be noted that independent, highly accurate determinations of the latter quantity thus help to improve the fundamental proper motion system.

In astrometry, construction of stellar catalogues favors solar barycentric coordinates. Classically, they are calculated by linearly removing stellar aberration and annual parallaxes from measured quantities yielded by Earth-bound instruments. A global approach is proposed to account for those two effects from a more general relativistic point of view. Implications for VLBI measurements and HIPPARCOS measurements of stellar positions are discussed.

The paper discusses influence of relativistic effects in gamma-burst propagation and the time sync. It is shown that the phenomenon of gamma-source aberration, while using the localization algorithm based on the estimates of gamma-burst arrival time instants should be regarded as relativistic effect. Criterions are derived which determine whether it is necessary to account for the relativistic effects, depending on the localization accuracy.

The relativistic effects included in the APFS from 1984 onwards are described. They are discussed in comparison with the accuracy available with modern techniques of observation.

To test any theory such as theories of motion–Newtonian or relativistic–of solar system objects, one must compare the predictions of theory with observation. But discordant observations habitually plague the reducer of astronomical data. To alleviate the baleful effects, particularly harmful when the observations are reduced by the method of least squares, of discordant data investigators almost invariably reject observations whose corresponding (0-C)'s or post-solution residuals exceed a cutoff. But techniques that are insensitive to the assumption that the observational errors are normally distributed, called robust estimation in the literature, have also been developed.

Following some work by N. Ashby and myself, it is shown how the Fermi construction of local inertial frames can be generalized, in the slow motion approximation, to the neighbourhood of the earth. This allows a clear and simple description of the relativistic effects for the motion of an earth satellite. A proposal by I. Ciufolini to measure the relativistic precession is reviewed.

Geodesy has now reached such an accuracy in both measuring and modelling that time variations of the size, shape and gravity field of the Earth must be basically considered under the name of Geodynamics. The objective is therefore the description of point positions and gravity field functions in a terrestrial reference frame, together with their time variations.

For this purpose, relativistic effects must be taken into account in models. Currently viable theories of gravitation such as Einstein's General Relativity can be expressed in the solar system into the parametrized post-newtonian (PPN) formalism. Basic problems such as the motion of a test particle give a satisfactory answer to the relativistic modelling in Geodynamics.

The relativistic effects occur in the definition of a terrestrial reference frame and gravity field. They also appear widely into terrestrial (gravimetry, inertial techniques) and space (satellite laser, Lunar laser, VLBI, satellite radioelectric tracking …) measurements.

With present day technology the technique which provides the greatest precision in astrometric and geodetic measurement is Very Long Baseline Interferometry (VLBI) (Robertson, 1975; Dravskykh, 1981; Gubanov, 1983). The precision of present day astrometrical measurements by VLBI exceeds those of the best modern optical observations by an order and a half of magnitude and is capable of further improvement by the future development of phase stable, wide band, global networks and by the future deployment of VLBI antennas in space. Such precision of observation places the technique of VLBI well within the regime of special and general relativity. The present paper presents an analysis of relativistic effects on VLBI measurements with an accuracy of 0.0001 arc seconds.

A geocentric relativistic reference frame is established which is close to the conventional non-relativistic equatorial frame of reference. Within post-Newtonian approximation the worldline of the geocentre is used to connect points by spacelike geodesics on the equal proper time hypersurface and to establish a properly chosen tetrad reference frame. Points on the earth surface and near the earth-space are coordinated making use of the Frobenius matrix of integrating factors which connects the geocentric orthonormal tetrad with the tangent spacetime of relativistic pseudo-Riemann geometry. The gravity field of the earth and its relative velocity with respect to the solar system barycentre cause coordinate effects of the order of 10 cm for topocentric point positioning.