On the Speed of Gravity and Relativistic v/c Corrections to the Shapiro Time Delay

Recent papers by Samuel declared that the linearized post-Newtonian v/c effects are too small to have been measured in the recent experiment involving Jupiter and quasar J0842+1845 that was used to measure the ultimate speed of gravity defined as a fundamental constant entering in front of each time derivative of the metric tensor in the Einstein gravity field equations. We describe our Lorentz-invariant formulation of the Jovian deflection experiment and confirm that v/c effects are do observed, as contrasted to the erroneous claim by Samuel, and that they vanish if and only if the speed of gravity is infinite.Comment: 7 pages. Final version published in Physics Letters

Gravimagnetic effect of the barycentric motion of the Sun and determination of the post-Newtonian parameter gamma in the Cassini experiment

The most precise test of the post-Newtonian gamma parameter in the solar system has been achieved in measurement of the frequency shift of radio waves to and from the Cassini spacecraft as they passed near the Sun. The test relies upon the JPL model of radiowave propagation that includes, but does not explicitly parametrize, the impact of the non-stationary component of the gravitational field of the Sun, generated by its barycentric orbital motion, on the Shapiro delay. This non-stationary gravitational field of the Sun is associated with the Lorentz transformation of the metric tensor and the affine connection from the heliocentric to the barycentric frame of the solar system and can be treated as gravimagnetic field. The gravimagnetic field perturbs the propagation of a radio wave and contributes to its frequency shift at the level up to 4 10^{-13} that may affect the precise measurement of the parameter gamma in the Cassini experiment to about one part in 10,000. Our analysis suggests that the translational gravimagnetic field of the Sun can be extracted from the Cassini data, and its effect is separable from the space curvature characterized by the parameter gamma.Comment: 12 pages, 1 figure, accepted to Physical Letters

Light Propagation in the Gravitational Field of Moving Bodies by means of Lorentz Transformation. I. Mass monopoles moving with constant velocities

We show how to derive the equations of light propagation in the gravitational field of uniformly moving mass monopoles without formulating and integrating the differential equations of light propagation in that field. The well-known equations of light propagation in the gravitational field of a motionless mass monopole are combined with a suitable Lorentz transformation. The possibility to generalize this technique for the more complicated case of uniformly moving body of arbitrary multipole structure is discussed.Comment: 10 page

Post-Newtonian limitations on measurement of the PPN parameters caused by motion of gravitating bodies

We derive explicit Lorentz-invariant solution of the Einstein and null geodesic equations for data processing of the time delay and ranging experiments in gravitational field of moving gravitating bodies of the solar system - the Sun and major planets. We discuss general-relativistic interpretation of these experiments and the limitations imposed by motion of the massive bodies on measurement of the parameters gamma_{PPN}, beta_{PPN} and delta_{PPN} of the parameterized post-Newtonian formalism.Comment: 17 pages, 1 figure; accepted for publication to MNRA

On the two approaches to the data analysis of the Cassini interplanetary relativity experiment

We compare two theoretical approaches to the data analysis of the Cassini relativity experiment based on the Doppler tracking and the time delay technique that were published correspondingly by Kopeikin et al in Phys. Lett. A 367, 276 (2007) and by Bertotti et al in Class. Quant. Grav. 25, 045013 (2008). Bertotti et al believed that they found a discrepancy with our paper and claimed that our analysis was erroneous. The present paper elucidates, however, that the discrepancy is illusory and does not exist. The two techniques give the same result making it evident that the numerical value of the PPN parameter 'gamma' measured in the Cassini experiment is indeed affected by the orbital motion of the Sun around the barycenter of the solar system.Comment: 6 pages, no figures. Accepted for publication to Physics Letters

Relativistic Reference Frames for Astrometry and Navigation in the Solar System

Astrophysical space missions deliver invaluable information about our universe, stellar dynamics of our galaxy, and motion of celestial bodies in the solar system. Astrometric space missions SIM and Gaia will determine distances to stars and cosmological objects as well as their physical characteristics and positions on the celestial sphere with microarcsecond precision. These and other space missions dedicated to exploration of the solar system are invaluable for experimental testing of general relativity. Permanently growing accuracy of space and ground-based astronomical observations require corresponding development of relativistic theory of reference frames, motion of celestial bodies, and propagation of light/radio signals from a source of light/radio to observer. Such theory must be based on Einstein's general relativity and account for various relativistic effects both in the solar system and outside of its boundary. We describe a hierarchy of the relativistic frames adopted by the International Astronomical Union in 2000, and outline directions for its theoretical and practical extentions by matching the IAU 2000 reference frames in the solar system to the cosmological Friedman-Robertson-Walker reference frame and to the frames used in the parametrized post-Newtonian formalism.Comment: 16 pages, bugs in equations removed, minor changes in text, to appear in Proc. of the ASTROCON 2006 meeting (Princeton University, Princeton, NJ, USA) http://www.andrew.cmu.edu/user/jarrieta/blog/astrocon2006.shtm

The gravitomagnetic influence on Earth-orbiting spacecrafts and on the lunar orbit

Gravitomagnetic field is covariantly split in the {\it intrinsic} and {\it extrinsic} parts, which are generated by rotational and translational currents of matter respectively. The {\it intrinsic} component has been recently discovered in the LAGEOS spacecraft experiment. We discuss the method of detection of the {\it extrinsic} tidal component with the lunar laser ranging (LLR) technique. Analysis of the gauge residual freedom in the relativistic theory of three-body problem demonstrates that LLR is currently not capable to detect the {\it extrinsic} gravitomagnetic effects which are at the ranging level of few millimeters. Its detection requires further advances in the LLR technique that are coming in the next 5-10 years.Comment: 9 pages, a contributed paper to the book in memory of J.A. Wheeler, (ed.) I. Ciufolin