High-precision radial-velocity techniques, which enabled the detection of extra-solar planets, are now sensitive to the lowest-order relativistic effects in the data of spectroscopic binary stars (SBs). We show how these effects can be used to derive the absolute masses of the components of eclipsing single-lined SBs and double-lined SBs from Doppler measurements alone. High-precision stellar spectroscopy can thus substantially increase the number of measured stellar masses, thereby improving the mass-radius and mass-luminosity calibrations.

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.

Today, the motion of spacecraft is still described by the classical Newtonian equations of motion plus some relativistic corrections. This approach might become cumbersome due to the increasing precision required. We use the Relativistic Motion Integrator (RMI) approach to numerically integrate the native relativistic equations of motion for a spacecraft. The principle of RMI is presented. We compare the results obtained with the RMI method with those from the usual Newton plus correction approach for the orbit of the BepiColombo (around Mercury) and Mars-NEXT (around Mars) orbiters. Finally, we present a numerical study of RMI and we show that the RMI approach is relevant to study the orbit of spacecraft.

In this communication, the effects of vibrations at high frequencies onto a freely falling two-body system in Schwarzschild spacetime are investigated. We present these effects for different kinds of reference motions, all of which are placed in regions of weak gravitation: circular orbits, radial free fall (with different initial velocities) and radial free fall with a small tangential velocity. The vibrations induce a change in the motion of the vibrating system, which is characterized by a radial deviation between the vibrating system and the reference motion of the non-vibrating system. For a circular orbit, we show that the maximal radial deviation increases linearly with the initial radius. For a radial free fall, the radial deviation after one oscillation decreases quadratically with respect to the initial radius.

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.

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.

In the seventies of the last century the EPM ephemerides (Ephemerides of Planets and the Moon) of IAA RAS originated and have been developed since that time. These ephemerides are based upon relativistic equations of motion of celestial bodies and light rays and upon relativistic time scales. The updated model of EPM2008 includes the new values of planet masses and other constants, the improved dynamical model with adding Trans–Neptunian Objects and the expanded database (1913–2008). More than 260 parameters have been determined while improving the planetary part of EPM2008 to 550000 observations. EPM2008 have been oriented to ICRF by including into the total solution the VLBI data of spacecraft near the planets. The real uncertainty of EPM ephemerides has been checked by comparison with the JPL's DE ephemerides. Some estimates of the post–model parameters have been obtained: |1−β| < 0.0002, |1−γ| < 0.0002, /G = (−5.9±4.4) ⋅ 10−14 per year, the statistic zero corrections to the planet perihelion advances.

The planetary ephemerides are used to examine different suggested forms of the gravitational equations of motion which could possibly cause the observed Pioneer Anomaly. It is shown that most of the forms would be unacceptable, including that generally assumed – a constant acceleration directed toward the Sun. The tests show that three other forms could not exist within 10 au's of the Sun. Only one suggested form would be compatible with the Pioneer Anomaly affecting Saturn or any other more inward planet. Additional planetary observations in the future may possibly eliminate this form also.

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.

There are at least four unexplained anomalies connected with astrometric data. Perhaps the most disturbing is the fact that when a spacecraft on a flyby trajectory approaches the Earth within 2000 km or less, it often experiences a change in total orbital energy per unit mass. Next, a secular change in the astronomical unit AU is definitely a concern. It is reportedly increasing by about 15 cm yr−1. The other two anomalies are perhaps less disturbing because of known sources of nongravitational acceleration. The first is an apparent slowing of the two Pioneer spacecraft as they exit the solar system in opposite directions. Some astronomers and physicists, including us, are convinced this effect is of concern, but many others are convinced it is produced by a nearly identical thermal emission from both spacecraft, in a direction away from the Sun, thereby producing acceleration toward the Sun. The fourth anomaly is a measured increase in the eccentricity of the Moon's orbit. Here again, an increase is expected from tidal friction in both the Earth and Moon. However, there is a reported unexplained increase that is significant at the three-sigma level. It is prudent to suspect that all four anomalies have mundane explanations, or that one or more anomalies are a result of systematic error. Yet they might eventually be explained by new physics. For example, a slightly modified theory of gravitation is not ruled out, perhaps analogous to Einstein's 1916 explanation for the excess precession of Mercury's perihelion.

We review the experimental evidence for Einstein's general relativity. A variety of high precision null experiments confirm the Einstein Equivalence Principle, which underlies the concept that gravitation is synonymous with spacetime geometry, and must be described by a metric theory. Solar system experiments that test the weak-field, post-Newtonian limit of metric theories strongly favor general relativity. Binary pulsars test gravitational-wave damping and aspects of strong-field general relativity. During the coming decades, tests of general relativity in new regimes may be possible. Laser interferometric gravitational-wave observatories on Earth and in space may provide new tests via precise measurements of the properties of gravitational waves. Future efforts using X-ray, infrared, gamma-ray and gravitational-wave astronomy may one day test general relativity in the strong-field regime near black holes and neutron stars.

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.

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.

Using the radio telescopes in Chinese VLBI Network and the K5/VSSP32 VLBI system of NICT in Japan, we have developed algorithms that can extract open loop Doppler information from the Chang'E-1 and Mars Express radio tracking data. Our latest results indicate the Doppler accuracy of open loop three-way Doppler is about 1mm/s in 1 second integration time, relative to a 8.4GHz carrier. In the forthcoming joint Russian-Chinese Martian mission in 2009, the current software algorithms and hardware performance will be improved, and we will attempt to use the high precision Doppler shift and phase information to test gravitation theories.

Pulsar timing has proven to be a wonderful tool with which to study neutron stars, providing insights into their ages, distances, proper motions, magnetic field strengths, internal structure, binary histories and evolution, and for tests of General Relativity. Here I describe how to optimise strategies for millisecond pulsar timing to enable the highest timing precision.

Binary pulsars are a valuable laboratory for gravitational experiments. Double-neutron-star systems such as the double pulsar provide the most stringent tests of strong-field gravity available to date, while pulsars with white-dwarf companions constrain departures from general relativity based on the difference in gravitational binding energies in the two stars. Future observations may open up entirely new tests of the predictions of general relativity.

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.

Gravitational wave detection can be done by precision timing of millisecond pulsars, and (with less likelihood) by precision astrometry on distant objects whose light or radio waves pass through gravitational waves on their way to our observatories. Underlying both of these is the relatively simple theory of light propagation in spacetimes with gravitational waves, which is also the basis of interferometric gravitational wave detectors. I review this theory and apply it to the timing and astrometric methods of detection. While pulsar timing might even be the first way that we directly detect gravitational waves, light deflection by gravitational waves seems out of reach.

The gravitational wave detectors that are operating now are looking for several kinds of gravitational wave signals at frequencies of tens of Hertz to kilohertz. One of these is mergers of roughly 10 M⊙ BH binaries. Sometime between now and about 8 years from now, it is likely that signals of this kind will be observed. The result will be strong tests of the dynamical predictions of general relativity in the high field regime. However, observations at frequencies below 1 Hz will have to wait until the launch of the Laser Interferometer Space Antenna (LISA), hopefully only a few years later. LISA will have 3 main objectives, all involving massive BHs. The first is observations of mergers of pairs of intermediate mass (100 to 105M⊙) and higher mass BHs at redshifts out to roughly z=10. This will provide new information on the initial formation and growth of BHs such as those found in most galaxies, and the relation between BH growth and the evolution of galactic structure. The second objective is observations of roughly 10 M⊙ BHs, neutron stars, and white dwarfs spiraling into much more massive BHs in galactic nuclei. Such events will provide detailed information on the populations of such compact objects in the regions around galactic centers. And the third objective is the use of the first two types of observations for testing general relativity even more strongly than ground based detectors will. As an example, an extreme mass ratio event such as a 10 M⊙ BH spiraling into a galactic center BH can give roughly 105 observable cycles during about the last year before merger, with a mean relative velocity of 1/3 to 1/2 the speed of light, and the frequencies of periapsis precession and Lense-Thirring precession will be high. The LISA Pathfinder mission to prepare for LISA is scheduled for launch in 2011.