The IAU framework for relativistic reference systems is based upon the work by Brumberg and Kopeikin and by Damour, Soffel and Xu (DSX). We begin with a brief introduction into the DSX-formalism. After that the various IAU Resolutions concerning relativistic astronomical reference systems are discussed. Finally, it is indicated how the expansion of the universe can be considered in the BCRS.

We discuss three conceivable scenarios of extension and/or modification of the IAU relativistic resolutions on time scales and spatial coordinates beyond the Standard IAU Framework. These scenarios include: (1) the formalism of the monopole and dipole moment transformations of the metric tensor replacing the scale transformations of time and space coordinates; (2) implementing the parameterized post-Newtonian formalism with two PPN parameters – β and γ; (3) embedding the post-Newtonian barycentric reference system to the Friedman-Robertson-Walker cosmological model.

In the last years, a fully general relativistic definition of reference systems and of their application to astronomy and geodesy has been passed into Resolutions of the scientific unions, following work of several working groups and of the community at large. In this community, the role of the International Earth Rotation and Reference systems Service (IERS) is to generate the terrestrial and celestial reference systems and the transformation between them, and the IERS Conventions provide the set of models and procedures used in the generation of IERS products. It is therefore essential that the IAU framework for relativity is introduced in the IERS Conventions, and that this is done consistently and completely throughout the document. The paper reviews relativistic aspects in the IERS Conventions and presents recent and on-going work aiming at providing a complete and consistent presentation for a new reference edition of the IERS Conventions, expected to appear in the next year.

Relativistic effects play an important role in the performance of the Global Positioning System (GPS) and in world-wide time comparisons. The GPS has provided a model for algorithms that take relativistic effects into account. In the future exploration of space, analogous considerations will be necessary for the dissemination of time and for navigation. We discuss relativistic effects that are important for a navigation system such as at Mars. We describe relativistic principles and effects that are essential for navigation systems, and apply them to navigation satellites carrying atomic clocks in orbit about Mars, and time transfer between Mars and Earth. It is shown that, as in the GPS, relativistic effects are not negligible.

The similarities between linearized gravity and electromagnetism are known since the early days of General Relativity. Using an exact approach based on tidal tensors, we show that such analogy holds only on very special conditions and depends crucially on the reference frame. This places restrictions on the validity of the “gravito-electromagnetic” equations commonly found in literature.

We construct a set of reference frames for description of the orbital and rotational motion of the Moon. We use a scalar-tensor theory of gravity depending on two parameters of the parametrized post-Newtonian (PPN) formalism and utilize the concepts of the relativistic resolutions on reference frames adopted by the International Astronomical Union in 2000. We assume that the solar system is isolated and space-time is asymptotically flat. The primary reference frame has the origin at the solar-system barycenter (SSB) and spatial axes are going to infinity. The SSB frame is not rotating with respect to distant quasars. The secondary reference frame has the origin at the Earth-Moon barycenter (EMB). The EMB frame is local with its spatial axes spreading out to the orbits of Venus and Mars and not rotating dynamically in the sense that both the Coriolis and centripetal forces acting on a free-falling test particle, moving with respect to the EMB frame, are excluded. Two other local frames, the geocentric (GRF) and the selenocentric (SRF) frames, have the origin at the center of mass of the Earth and Moon respectively. They are both introduced in order to connect the coordinate description of the lunar motion, observer on the Earth, and a retro-reflector on the Moon to the observable quantities which are the proper time and the laser-ranging distance. We solve the gravity field equations and find the metric tensor and the scalar field in all frames. We also derive the post-Newtonian coordinate transformations between the frames and analyze the residual gauge freedom of the solutions of the field equations. We discuss the gravitomagnetic effects in the barycentric equations of the motion of the Moon and argue that they are beyond the current accuracy of lunar laser ranging (LLR) observations.

Many astronomical systems require for their description in the frame of Einstein's theory of gravity not just one but several reference systems. In the first post-Newtonian approximation the Damour-Soffel-Xu (DSX) formalism presents a new and improved treatment of celestial mechanics and astronomical reference systems for the gravitational N-body problem. In the DSX-formalism the astronomical bodies are characterized by their Blanchet-Damour (BD) mass- and spin-multipole moments. However, the time dependence of these moments requires additional dynamical equations, usually local flow equations describing the internal motions inside the bodies or additional assumptions about them. In this article the internal motion of astronomical bodies will be adressed within the 1st post-Newtonian approximation to Einstein's theory of gravity. A concept of quasi-rigid bodies will be introduced; after that, astronomical fluid and elastic bodies will be discussed.

Time series of the coordinates of the ICRF radio sources were analyzed. It was shown that part of radio sources, including even the so-called “defining” sources, show a the significant apparent motion. Corrections for their a priori coordinates are time functions. The celestial reference frame stability is provided by the no-net-rotation condition applied to the selected subset of sources, which leads in our case to a rotation of the frame axes with time. Parameters of this rotation were calculated for different subsets of sources.

To improve stability of the celestial reference frame new methods of selection of the extragalactic radio sources were suggested. The first one was called “cosmological” and the second one “kinematical”. It was shown that a selected subset of the ICRF sources, according to cosmological criteria, determines the most stable coordinate system during next decade.

By the early 1970s, the improved accuracy of astrometric and time measurements enabled researchers not only to experimentally compare relativistic gravity with the Newtonian predictions, but also to compare different relativistic gravitational theories (e.g., the Brans-Dicke Scalar-Tensor Theory of Gravitation). For this comparison, Kip Thorne and others developed the Parameterized Post-Newtonian Formalism (PPN), and derived the dependence of different astronomically observable effects on the values of the corresponding parameters.

Since then, all the observations have confirmed General Relativity. In other words, the question of which relativistic gravitation theory is in the best accordance with the experiments has been largely settled. This does not mean that General Relativity is the final theory of gravitation: it needs to be reconciled with quantum physics (into quantum gravity), it may also need to be reconciled with numerous surprising cosmological observations, etc. It is, therefore, reasonable to prepare an extended version of the PPN formalism, that will enable us to test possible quantum-related modifications of General Relativity.

In particular, we need to include the possibility of violating fundamental principles that underlie the PPN formalism but that may be violated in quantum physics, such as scale-invariance, T-invariance, P-invariance, energy conservation, spatial isotropy violations, etc. In this paper, we present the first attempt to design the corresponding extended PPN formalism, with the (partial) analysis of the relation between the corresponding fundamental physical principles.

In the Newtonian approximation of General Relativity, employed for the dynamical modelling in the solar system, the coordinates have the dimension of time and length. As these coordinates are close to their Newtonian counterpart, the adherence to the rules of the Quantity Calculus does not raise practical difficulties: the second and the metre should be used as their units, in an abstract conception of these units. However, the scaling of coordinate times, applied for practical reasons, generates controversies, because there is a lack of information about the metrics to which they pertain. Nevertheless, it is not satisfactory to introduce specific units for these scaled coordinate times.

The celestial Earth's orientation is required for many applications in fundamental astronomy and geodesy; it is currently determined with sub-milliarcsecond accuracy by astro-geodetic observations. Models for that orientation rely on solutions for the rotation of a rigid Earth model and on the geophysical representation of non-rigid Earth effects. Important IAU 2000/2006 resolutions on reference systems have been passed (and endorsed by the IUGG) that recommend a new paradigm and high accuracy models to be used in the transformation from terrestrial to celestial systems. This paper reviews the consequences of these resolutions on the adopted Earth orientation parameters, IAU precession-nutation models and associated nomenclature. It summarizes the fundamental aspects of the current IAU precession-nutation models and reports on the consideration of General Relativity (GR) in the solutions. This shows that the current definitions and nomenclature for Earth's rotation are compliant with GR and that the IAU precession-nutation is compliant with the IAU 2000 definition of the geocentric celestial reference system in the GR framework; however, the underlying Earth's rotation models basically are Newtonian.

This note suggests nomenclature for dealing with the units of various astronomical quantities that are used with the relativistic time scales TT, TDB, TCB and TCG. It is suggested to avoid wordings like “TDB units” and “TT units” and avoid contrasting them to “SI units”. The quantities intended for use with TCG, TCB, TT or TDB should be called “TCG-compatible”, “TCB-compatible”, “TT-compatible” or “TDB-compatible”, respectively. The names of the units second and meter for numerical values of all these quantities should be used without any adjectives. This suggestion comes from a special discussion forum created within IAU Commission 52 “Relativity in Fundamental Astronomy”.

Today's time and frequency standards range from the most sophisticated reference standards to the smallest oscillator for handheld radios. The technical requirements and technologies needed are different for the various applications but they derive from similar physical concepts. These different technologies can be categorized into four major areas, reference standards, mobile systems, man-portable (handheld) and space systems. These areas are the core areas of time and frequency standard applications and different areas of technology are needed to address them. This presentation discusses the time and frequency standards used or available for these areas.

Time ephemeris is the location-independent part of the transformation formula relating two time coordinates such as TCB and TCG (Fukushima 1995). It is computed from the corresponding (space) ephemerides providing the relative motion of two spatial coordinate origins such as the motion of geocenter relative to the solar system barycenter. The time ephemerides are inevitably needed in conducting precise four dimensional coordinate transformations among various spacetime coordinate systems such as the GCRS and BCRS (Soffel et al. 2003). Also, by means of the time average operation, they are used in determining the information on scale conversion between the pair of coordinate systems, especially the difference of the general relativistic scale factor from unity such as LC. In 1995, we presented the first numerically-integrated time ephemeris, TE245, from JPL's planetary ephemeris DE245 (Fukushima 1995). It gave an estimate of LC as 1.4808268457(10) × 10−8, which was incorrect by around 2 × 10−16. This was caused by taking the wrong sign of the post-Newtonian contribution in the final summation. Four years later, we updated TE245 to TE405 associated with DE405 (Irwin and Fukushima 1999). This time the renewed vale of LC is 1.48082686741(200) × 10−8 Another four years later, by using a precise technique of time average, we improved the estimate of Newtonian part of LC for TE405 as 1.4808268559(6) × 10−8 (Harada and Fukushima 2003). This leads to the value of LC as LC = 1.48082686732(110) × 10−8. If we combine this with the constant defining the mean rate of TCG-TT, LG = 6.969290134 × 10−10 (IAU 2001), we estimate the numerical value of another general relativistic scale factor LB = 1.55051976763(110) × 10−8, which has the meaning of the mean rate of TCB-TT. The main reasons of the uncertainties are the truncation effect in time average and the uncertainty of asteroids' perturbation. The former is a natural limitation caused by the finite length of numerical planetary ephemerides and the latter is due to the uncertainty of masses of some heavy asteroids. As a compact realization of the time ephemeris, we prepared HF2002, a Fortran routine to compute approximate harmonic series of TE405 with the RMS error of 0.446 ns for the period 1600 to 2200 (Harada and Fukushima 2003). It is included in the IERS Convention 2003 (McCarthy and Petit 2003) and available from the IERS web site; http://tai.bipm.org/iers/conv2003/conv2003_c10.html.

Two atomic time scales maintained at the International Bureau of Weights and Measures (BIPM) are realizations of terrestrial time: International Atomic Time (TAI) and TT(BIPM). They are calculated from atomic clocks realizing proper time in national laboratories. The algorithm for the calculation of TAI has been designed to optimize the frequency stability and accuracy of the time scale. Plans for the future improvement of the reference time scales are presented.

Highly relativistic equations of motions will play a crucial role for the detection and analysis of gravitational waves emitted by inspiralling compact binaries in detectors LIGO/VIRGO on ground and LISA in space. Indeed these very relativistic systems (with orbital velocities of the order of half the speed of light in the last orbital rotations) require the application of a high-order post-Newtonian formalism in general relativity for accurate description of their motion and gravitational radiation [1]. In this contribution the current state of the art which has reached the third post-Newtonian approximation for the equations of motion [2–6] and gravitational waveform [7–9] has been described (see [10] for an exhaustive review). We have also emphasized the successful matching of the post-Newtonian templates to numerically generated predictions for the merger and ring-down in the case of black-hole binaries [11].

We present a review of the different methods currently developed to determine the deflection of light rays due to gravity. The aim of these methods is primarily to calculate the angular distances with an accuracy of the order of microarcsecond.

Relativistic modelling of rotational motion of extended bodies represents one of the most complicated problems of Applied Relativity. The relativistic reference systems of IAU (2000) give a suitable theoretical framework for such a modelling. Recent developments in the post-Newtonian theory of Earth rotation in the limit of rigidly rotating multipoles are reported below. All components of the theory are summarized and the results are demonstrated. The experience with the relativistic Earth rotation theory can be directly applied to model the rotational motion of other celestial bodies. The high-precision theories of rotation of the Moon, Mars and Mercury can be expected to be of interest in the near future.

The LISA mission is an interferometer, formed by three spacecraft, that aims at the detection of gravitational waves in the [10−4, 10−1] Hz frequency band. Present LISA TDI simulators, aimed at validating the novel Time Delay Interferometry method, use a classical Keplerian orbit model at first order in eccentricity in the gravitational field of a spherical non-rotating Sun, without planets. We propose to use the same model but described in the framework of relativistic gravity, and we focus here on quantifying the differences between classical and relativistic orbits for the LISA spacecraft, under the same assumptions.

The general relativistic definition of astrometric measurement needs an appropriate use of the concept of reference frame, which should then be linked to the conventions of the IAU Resolutions (Soffel et al., 2003), which fix the celestial coordinate system. A consistent definition of the astrometric observables in the context of General Relativity is also essential to find uniquely the stellar coordinates and proper motion, this being the main physical task of the inverse ray tracing problem. Aim of this work is to set the level of reciprocal consistency of two relativistic models, GREM and RAMOD (Gaia, ESA mission), in order to guarantee a physically correct definition of light direction to a star, an essential item for deducing the star coordinates and proper motion within the same level of measurement accuracy.