The various relativistic effects occuring in VLBI measurements are discussed. A concrete example showing the influence of the gravitational delay due to the Sun upon the delay residuals from fit in a Mark III geodetic VLBI experiment is given. It is argued that regular geodetic VLBI observations might provide the best test of Einstein's theory of gravity on the post-Newtonian level in the near future.

This paper discussed the algorithm of the calculation of relativistic effects in numerical prediction of the artificial satellites motion. An attempt to estimate the values of relativistic effects in the motion of two artificial satellites Navstar and Lageos is made. These values are compared with the quantities of other weak perturbations and the errors of the calculated position of the satellite due to the inaccurate approximation of perturbations.

On the basis of observational data on atmospheric pressure (1963–1967), the variation of the moment of inertia, and, with certain restrictions, the changes in the angular velocity of the Earth are obtained. The numerical results derived are compared to the relativity effects in Earth rotation. The comparison shows that both effects are equal in periods and very close in amplitudes.

The motion of a geosynchronous satellite has been studied under the combined gravitational effects of the oblate Earth (including its equatorial ellipticity), the Sun, the Moon and the solar-radiation pressure. It is observed that the orbital plane rotates with an angular velocity the maximum value of which is 0.058°/yr. and regresses with a period which increases both as the orbital inclination and the altitude increase. The effect of earth's equatorial ellipticity on the regression period is oscillatory whereas that of Solar-radiation pressure is to decrease it.

The synchronism is achieved when the angular velocity of the satellite is equal to the difference between the spin-rate of the Earth and the regression rate of the orbital plane. With this angular velocity of the satellite, the ground trace is in the shape of figure eight, though its size and position relative to the Earth change as the time elapses. The major effect of earth's equatorial ellipticity is to produce a change in the relative angular position of the satellite as seen from the Earth. If the satellite is allowed to execute large angle oscillations the mid-point of oscillation would be at the position of the minor axis of the earth's equatorial section. The oscillatory period T has been determined in terms of the amplitude Γ and the tesseral harmonic J2(2). From this result we can determine the value of J2(2) as T and Γ can be observed accurately.

The International Atomic Time TAI is a realized time scale which is ultimately used for comparisons between the observations and dynamical theories. Its definition should tell us unambiguously what an ideal TAI should be. It is also important know the uncertainties of the implementation of this definition.

Concerning the definition, there is an apparent divergence between the physicists for whom TAI is a coordinate-time and the astronomers who often consider it as a proper time. This matter should be clarified and it might be advisable that IAU adopts a recommendation on this topic, based on the already existing CCDS and CCIR definitions, but completed for the specific uses in astronomy. The present TAI definition refers to the geoid. Some years will elapse before the tidal effects be observable. Nevertheless, it is desirable to have some exchanges of views on an improved definition.

The accuracy (conformity with the definition), stability and precision of reading of TAI are progressively improving. Present and past properties will be briefly reported.

Atomic clock accuracies continue to improve rapidly, requiring the inclusion of general relativity for unambiguous time and frequency clock comparisons. Atomic clocks are now placed on space vehicles and there are many new applications of time and frequency metrology. This paper addresses theoretical and practical limitations in the accuracy of atomic clock comparisons arising from relativity, and demonstrates that accuracies of time and frequency comparison can approach a few picoseconds and a few parts in 1016, respectively.

Lunar and planetary observations of different types are discussed for the time span 1717–1982. The modern ranging observations and the historical ones (mainly transits of Mercury and Venus, solar eclipses and occultations of the inner planets by the Moon) are treated separately and some attempts to detect relativistic effects are carried out. From time delay observations linear combination ν = (2 + 2 γ-β) /3 of the parameters of the PPN formalism is evaluated: ν =0.997±0.003. Statistically significant estimate for the rate Ġ of changing of the gravitational constant G is found: Ġ/G=(4±0.8) · 10−11 /yr. (An alternative interpretation of this result due to Canuto et al. (1979) gives negative sign for Ġ). From transits of Mercury and Venus corrections to the adopted system of differences between the ephemeris (dynamic) and the atomic time scales and a correction to the Mercury's perihelion advance are deduced. With new ephemeris time scale it became possible to determine unambigiously lunar tidal deceleration ṅM making use of the historical lunar observations. The derived value ṅM = (−22.2 ± 0.8)′′/cy2 is in good agreement with reported lunar laser results. By comparing the estimates ṅM obtained by the two methods the rate Ġ has also been evaluated: Ġ/G=(0.5+0.5)·10−11/yr. The origin of the disagreement with the radar based result for Ġ is not yet clear. All the conclusions were checked by making use of different planetary and lunar theories and appear to be practically theory-independent.

Over the past two decades, radar and radio observations of planets and spacecraft have been made by stations of the Deep Space Network (DSN), which by the unprecedented nature of their accuracy have produced the most accurate tests of general relativity available. We review the history of the instrumentation and data analysis of the first spacecraft test, the three percent determination of the effect of solar gravity on radio signals between DSN stations and the two spacecraft, Mariner 6 and Mariner 7 (Anderson et al., 1975), as well as later more accurate tests using the Mariner 9 spacecraft anchored to Mars (Reasenberg and Shapiro, 1977; Anderson et al., 1978) and the Viking orbiters and landers (Shapiro et al., 1977; Hellings, 1985). We also review tests of the metric nature of gravity using radar, optical observations, and radio astrometry of the planets (Anderson et al., 1978; Reasenberg, 1985; Hellings, 1985) and the limits placed on the variability of the gravitational constant G (Hellings et al., 1983). Finally, we discuss the prospects for improved accuracy through ongoing upgrades of DSN instrumentation and show the results of covariance analyses for a possible future NASA mission to the Sun (Solar Probe) in the mid 1990's (Mease et al., 1984) and the next NASA mission to Mars, the Mars Observer mission planned for launch in late 1990.

The fine structure of the acoustic and gravity mode multiplets of the Sun have been analyzed to infer the internal rotation of the Sun and upper limits of the internal magnetic field. Observed fine structure for 137 multiplets has been obtained (Hill 1984b, 1985a, 1985b) and the fine structure has been examined for dependence on the angular order, m, of the modes. The inferred angular velocity distribution, together with the estimated upper limits on the internal magnetic fields, yields a gravitational quadrupole moment, J2, of ≈7.7 × 10−6. This result is consistent with the result obtained by Hill, Bos and Goode (1982) and has important implications for planetary tests of theories of gravitation.

We review the status of experimental tests of general relativity. These include tests of the Einstein Equivalence Principle, which requires that gravitation be described by a curved-spacetime, “metric” theory of gravity. General relativity is consistent with all tests to date, including the “classical tests”: light deflection using radio interferometers, radar time delay using Viking Mars landers, and the perihelion shift of Mercury; and tests of the strong equivalence principle, such as lunar laser ranging tests of the “Nordtvedt effect”, and tests for variations in G. We also review ten years of observations of the Binary Pulsar, in which the first evidence for gravitational radiation has been found.

Among the few parameters that describe the generalized space time metrics, astrometric techniques are essentially sensitive to the displacement of the apparent positions of celestial bodies. This includes the relativistic light deflection and aberration. The possibilities of small field and wide field astrometry in measuring these effects are described. The case of the second order aberration terms is considered with some detail from the theoretical point of view, both for stellar and planetary aberration. New results are presented in the latter case.

A section is devoted to a description of the existing space astrometry projects among which Space Telescope and HIPPARCOS are approved but will not contribute significantly to relativistic studies. Several “second generation” projects exist that aim at 2 or 3 orders of magnitude improvement in precision. They would yield results on second order relativistic effects and may be used to determine masses of some single stars. However, the present state of engineering of space astrometric missions has permitted to identify several limitations of the present and future missions. They will not all be readily suppressed and one should be very careful in assessing now their potentialities. It seems however that interferometric techniques have more chance to reach the 10−4 and 10−5 arc second precision than the imaging methods.

The solar system is the traditional laboratory for testing theories of gravitation. The results of all tests are consistent with the predictions of general relativity. The differences between these predictions and those of Newton's theory of gravitation have been confirmed with uncertainties as small as one part in a thousand. To enhance significantly the accuracy of such tests, one must investigate novel techniques. In this paper we concentrate on an experiment that promises a dramatic improvement in a classical test of general relativity – the deflection of light by solar gravity. The goal is to measure the post-post-Newtonian contribution of nearly 11 microarcseconds to this deflection. The technique we propose is based on use of an astrometric optical interferometer, POINTS, which could be operated from the bay of the Space Shuttle, mounted on the proposed Space Station, or supported by an independent spacecraft. POINTS should be able to measure the separation of stars about 90° apart with an uncertainty of only a few microarcseconds.

Parallel to the determination of astrometric parameters for some 100,000 stars, the HIPPARCOS data may also be used to study the light deflection produced by the sun. Cowling (1983 thesis) has calculated the light deflection observable by HIPPARCOS for a general space-time metric, and we have included his list of fifteen metric coefficients as “global” parameters in simulated HIPPARCOS reductions. The estimated covariance matrices show that only 7–9 linear combinations of the Cowling parameters may be determined with some accuracy (~10−10). The value for the standard GR light deflection may be determined if the thermal effects on the satellite are small, but not to better than about 0.5%.

Some experiments are discussed for measuring the earth's gravitomagnetic field, using a pendulum or an oscillator rather than a gyroscope.

A summary of the main relativistic effects in the motion of the Moon is presented. The results are based on the application of a novel approach to the restricted three-body problem in general relativity to the lunar motion. It is shown that the rotation of the Sun causes a secular acceleration in the relative Earth-Moon motion. This might appear to be due to a temporal “variation” of the gravitational constant.

The gravitational time delay of signals in a gravitational field of a rotating massive body is considered both in a weak field approximation and in a strong field caused by a rotating black hole. The expressions describing the time of propagation of signals are obtained by integrating the light geodesics of the Kerr metric in a frame reference of a distant observer using the Boyer-Lindquist coordinates and assuming that the wave length of radiation is much less than the characteristic scale of the field. The existence of the asymmetry in the time delay is shown depending on the mutual orientation of a photon propagation direction and of the rotation axis. As a result of this asymmetry, the effects of relative time delay are predicted and calculated for the signals focused by a rotating gravitational lens.

New cosmological and quantum mechanical evidence for the existence of an ether has made it appropriate to investigate again the effect of such a medium upon the motions of planets and satellites within the solar system. The properties of a medium of this kind are as yet unknown except that it may be the ultimate origin of inertia and therefore that it may have a fundamental link to the gravitational force.