We describe a long-term program designed to obtain and interpret high-precision radar range measurements of a number of near-Earth objects (NEOs) that have trajectories reaching deep inside the gravitational well of the Sun. Objects in our sample have perihelion shift rates 1.5 to 2.5 times that of (1566) Icarus (10″/cy) and span a wide range of inclinations and semi-major axes, allowing for an unambiguous separation of general relativistic and solar oblateness effects. Four objects have been observed at Arecibo on at least two apparitions since 2000, with typical uncertainties of a few hundred meters. Within the next three years, we anticipate securing a total of 15 observations of 5 different NEOs. This program is expected to provide a purely dynamical measurement of the oblateness of the Sun (J2 at the 10−8 level) and to constrain the Eddington parameter β at the 10−4 level. Although our objects are selected to minimize Yarkovsky orbital drift, we also anticipate measuring Yarkovsky drift rates, which are orthogonal to the GR and J2 signatures.

Supermassive black holes are common in centers of galaxies. Among the active galaxies, quasars are the most extreme, and their black hole masses range as high as to 6⋅1010M⊙. Binary black holes are of special interest but so far OJ287 is the only confirmed case with known orbital elements. In OJ287, the binary nature is confirmed by periodic radiation pulses. The period is twelve years with two pulses per period. The last four pulses have been correctly predicted with the accuracy of few weeks, the latest in 2007 with the accuracy of one day. This accuracy is high enough that one may test the higher order terms in the Post Newtonian approximation to General Relativity. The precession rate per period is 39°.1 ± 0°.1, by far the largest rate in any known binary, and the (1.83 ± 0.01)⋅1010M⊙ primary is among the dozen biggest black holes known. We will discuss the various Post Newtonian terms and their effect on the orbit solution. The over 100 year data base of optical variations in OJ287 puts limits on these terms and thus tests the ability of Einstein's General Relativity to describe, for the first time, dynamic binary black hole spacetime in the strong field regime. The quadrupole-moment contributions to the equations of motion allows us to constrain the ‘no-hair’ parameter to be 1.0 ± 0.3 which supports the black hole no-hair theorem within the achievable precision.

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.

Recent experiments have successfully tested Einstein's general theory of relativity to remarkable precision. We discuss recent progress in the tests of relativistic gravity in the solar system and present motivations for the new generation of high-accuracy gravitational experiments. We especially focus on the concepts aiming to probe parameterized-post-Newtonian parameter γ and evaluate the discovery potential of the recently proposed experiments.

The orbits of the planets as represented by the JPL planetary ephemerides are now primarily determined by radio tracking of spacecraft. Analysis of the data and propagation of the orbits relies on an internally consistent set of equations of motion and propagation of radio signals including relativistic effects at the centimeter level. The planetary ephemeris data set can be used to test some aspects of the underlying theory such as estimates of PPN parameters γ and β, time variation in the gravitational constant G, rotation of the solar system relative to distant objects (Mach's principle), and place stringent limits on the possible violation of the inverse-square law.

We present here several gravity tests made with the latest INPOP08 planetary ephemerides. We first propose two methods to estimate the PPN parameter β and its correlated value, the Sun J2, and we discuss the correlation between the Sun J2 and the mass of the asteroid ring. We estimate a possible advance in the planet perihelia. We also show that no constant acceleration larger than 1/4 of the Pioneer anomaly is compatible with the observed motion of the planets in our Solar System.

The Joint Milliarcsecond Astrometry Pathfinder Survey (JMAPS) is a small, space-based, all sky, visible wavelength, astrometric and photometric survey mission for 0th through 14th I-band magnitude stars with a planned 2013 launch. The primary objective of the JMAPS mission is the generation of an astrometric star catalog with 1 milliarcsecond (mas) positional accuracy or better and photometry to the 1% accuracy level or better at 1st to 12th mag. A 1-mas all–sky survey will have a significant impact on our current understanding of galactic and stellar astrophysics. JMAPS will improve our understanding of the origins of nearby young stars, provide insight into the dynamics of star formation regions and associations, investigate the dynamics and membership of nearby open clusters.

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.

Lunar laser ranging (LLR) has long provided many of our best measurements on the fundamental nature of gravity, including the strong equivalence principle, time -rate-of-change of the gravitational constant, the inverse square law, geodetic precession, and gravitomagnetism. This paper serves as a brief overview of APOLLO: a recently operational LLR experiment capable of millimeter-level range precision.

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].

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.

Future high-accuracy space astrometry missions, such as Gaia and SIM, will need a time-tagging of observations consistent with General Relativity nowadays used as standard background for global data processing scheme. In this work, we are focusing on the realization of the onboard time scale. The onboard clock, being not ideal and consequently tainted with systematic biases, has to be carefully calibrated to the ideal relativistic proper time of the satellite. We present here a modeling of this essential step to provide a reliable relation between the onboard time and TCB, a time scale suitable for global data processing.

Einstein-Aether gravity theory has been proven successful in passing experiments of different scales. Especially its Eddington parameters β and γ have the same numerical values as those in general relativity. Recently Xie and Huang (2008) have advanced this theory to a second post-Newtonian approximation for an N-body model and obtained an explicit metric when the bodies are point-like masses. This research considers light propagation in the above gravitational field, and explores the light deflection, time delay, frequency shift etc. The results will provide for future experiments in testing gravity theories.

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.

Two pairs of solid test-masses have been considered to perform in space the test of the universality of free fall with an accuracy of at least 10−15. These cylindrical masses are precisely at the heart of the MICROSCOPE mission instrument comprising two differential electrostatic accelerometers. These masses shall exhibit material quality, shapes, positions and alignments in regard to stringent experimental requirements. Indeed the space experiment is based on the control of the two masses submitted to the same gravity acceleration along the same orbit at 810 km altitude with an accuracy of 10−11 m. Thus effects of Earth and satellite gravity gradients shall be contained as well as any other disturbances of the mass motions induced by their magnetic susceptibility or electrical dissymmetries, by outgassing of the materials or radiation emissivity. Furthermore, the electrostatic levitation of the two masses depends dramatically on the mass shapes and electrical properties in particular for the definition of the sensitive axes orientation. All these aspects will be presented from the mass characteristics to the space MICROSCOPE experiment performance.

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 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 present a review on relativistic effects and best estimates of the relativistic PPN parameter γ obtained by analysis of data from the International VLBI Service for Geodesy and Astrometry (IVS). Relativistic implications are also considered in view of the upcoming new generation VLBI System: VLBI2010.

Within the framework of linearized Einstein field equations we compute the gravitomagnetic effects on a test particle orbiting a slowly rotating, spherical body with a rotating matter ring fixed to the equatorial plane. Our results show that the effect on the precession of particle orbits is increased by the presence of the ring.

Pulsars are amongst the most stable rotators known in the Universe. Over many years some millisecond pulsars rival the stability of atomic clocks. Comparing observations of many such stable pulsars may allow the first direct detection of gravitational waves, improve the Solar System planetary ephemeris and provide a means to study irregularities in terrestrial time scales. Here we review the goals and status of current and future pulsar timing array projects.