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This letter introduces an advanced novel theory for calculating non-linear Newtonian hydrostatic perturbations in the density, shape, and gravitational field of fluid stars and planets subjected to external tidal and rotational forces. The theory employs a Lie group approach using exponential mappings to derive exact differential equations for large gravitational field perturbations and the shape function, which describes the finite deformation of the body's figure. This approach lays the foundation for the precise analytic determination and numerical computation of the induced body's multipole moments and Love numbers with any desired degree of accuracy., Comment: 11 pages, no figures

We consider the orbital motion of a test particle in the gravitational field of a massive body (that might be a black hole) with mass $m$ placed on the expanding cosmological manifold described by the McVittie metric. We introduce the local coordinates attached to the massive body to eliminate nonphysical, coordinates-dependent effects associated with Hubble expansion. The resultant equation of motion of the test particle are analyzed by the method of osculating elements with application of time-averaging technique. We demonstrate that the orbit of the test particle is not subject to the cosmological expansion up to the terms of the second order in the Hubble parameter. However, the cosmological expansion causes the precession of the orbit of the test particle with time and changes the frequency of the mean orbital motion. We show that the direction of motion of the orbital precession depends on the Hubble parameter as well as the deceleration parameter of the universe. We give numeric estimates for the rate of the orbital precession with respect to time due to the cosmological expansion in case of several astrophysical systems., Comment: 31 pages, 1 figure and 2 tables (Updated for improvement.)

We introduce the general-relativistic definition of Lunar Coordinate Time (TCL) based on the IAU 2000 resolutions that provide a framework for relativistic reference systems. From this foundation, we derive a transformation equation that describes the relative rate of TCL with respect to Geocentric Coordinate Time (TCG) for various locations of the clock on lunar surface. This equation serves as the cornerstone for constructing a relativistic TCL--TCG time conversion algorithm. Using this algorithm, we can compute both secular and periodic variations in the rate of an atomic clock placed on the Moon, relative to an identical clock on Earth. The algorithm accounts for various effects, including time dilation caused by the Moon's orbital motion around Earth, gravitational potentials of both Earth and Moon, and direct and indirect time dilation effects due to tidal perturbations caused by the Sun and other major planets of the solar system. Our approach provides exquisite details of the TCL--TCG transformation, achieving a precision of several nanoseconds within the spatial volume dominated by the Earth's gravitational field known as the Hill sphere. This sphere extends from the Earth to a distance of approximately 1.5 million km, substantially encompassing the Moon's orbit. To validate our methodology for lunar coordinate time, we compare it with the mathematical formalism of local inertial frames applied to the Earth-Moon system and confirm their equivalence., Comment: 37 pages, 7 figures, 2 tables, appendix

This review paper discusses the science of astrometric catalogs, their current applications and future prospects for making progress in fundamental astronomy, astrophysics and gravitational physics. We discuss the concept of fundamental catalogs, their practical realizations, and future prospects. Particular attention is paid to the astrophysical implementations of the catalogs such as the measurement of the Oort constants, the secular aberration and parallax, and asteroseismology. We also consider the use of the fundamental catalogs in gravitational physics for testing general theory of relativity and detection of ultra-long gravitational waves of cosmological origin., Comment: 20 pages, 185 references, accepted to Frontiers in Astronomy and Space Sciences (Fundamental Astronomy Section)

The present paper derives the post-Newtonian Lagrangian of translational motion of N arbitrary-structured bodies with all mass and spin multipoles in a scalar-tensor theory of gravity. The multipoles depend on time and evolve in accordance with their own dynamic equations of motion. The Lagrangian is retrieved from the post-Newtonian equations of motion by solving the inverse problem of the Lagrangian mechanics and generalizes a well-known Lagrangian of pole-dipole-quadrupole massive particles to the particles of higher multipolarity. Analytic treatment of the higher-order multipole contributions is important for more rigorous computation of gravitational waveform of inspiralling compact binaries at the latest stage of their orbital evolution before merger when tidal and rotational deformations of stars are no longer small and rapidly change in time. The Lagrangian of an N-body system with arbitrary mass and spin multipoles is instrumental for formulation of the post-Newtonian conservation laws of energy, momenta and the integrals of the center of mass., Comment: 60 pages, no figures; new references added; typos fixed, accepted to Phys. Rev. D

Recent article "Revisiting the 2PN Pericenter Precession in View of Possible Future Measurements" published by Iorio (Universe, 2020) argues that calculations of the secular 2PN precession of the orbital pericenter of a binary system accomplished by Damour and Schaefer (Nuovo Cim. B, 1988) and by Kopeikin and Potapov (Astron. Rep., 1994) with different mathematical techniques are inconsistent, differ from each other and do not agree with the result obtained by Iorio (Universe, 2020). The purpose of this communication is to demonstrate that the article by Iorio is erroneous, suffers from misconceptions and cannot be trusted., Comment: 8 pages, typos removed

The ability to make independent detections of the signatures of exoplanets with complementary telescopes and instruments brings a new potential for robust identification of exoplanets and precision characterization. We introduce PEXO, a package for Precise EXOplanetology to facilitate the efficient modeling of timing, astrometry, and radial velocity data, which will benefit not only exoplanet science but also various astrophysical studies in general. PEXO is general enough to account for binary motion and stellar reflex motions induced by planetary companions and is precise enough to treat various relativistic effects both in the solar system and in the target system. We also model the post-Newtonian barycentric motion for future tests of general relativity in extrasolar systems. We benchmark PEXO with the pulsar timing package TEMPO2 and find that PEXO produces numerically similar results with timing precision of about 1 ns, space-based astrometry to a precision of 1 $\mu$as, and radial velocity of 1 $\mu$m/s and improves on TEMPO2 for decade-long timing data of nearby targets, due to its consideration of third-order terms of Roemer delay. PEXO is able to avoid the bias introduced by decoupling the target system and the solar system and to account for the atmospheric effects which set a practical limit for ground-based radial velocities close to 1 cm/s. Considering the various caveats in barycentric correction and ancillary data required to realize cm/s modeling, we recommend the preservation of original observational data. The PEXO modeling package is available at GitHub (https://github.com/phillippro/pexo)., Comment: 54 pages, 2 tables, 19 figures; PEXO is available at https://github.com/phillippro/pexo

The present paper studies the post-Newtonian dynamics of N bodies in general relativity. We derive covariant equations of translational and rotational motion of N extended bodies having arbitrary distribution of mass and velocity of matter by employing the set of global and local coordinate charts on curved spacetime manifold of N-body system along with the mathematical apparatus of the Cartesian STF tensors and Blanchet-Damour multipole formalism. We separate the self-field effects of the bodies from the external gravitational environment and construct the effective background spacetime manifold by making use of the asymptotic matching technique. We make worldline of the center of mass of each body identical with that of the origin of the body-adapted local coordinates by the appropriate choice of the dipole moments. The covariant equations of motion are obtained by applying the Einstein principle of equivalence and the Fermi-Walker law of transportation of the linear momentum and spin of each body. Our approach significantly extends the Mathisson-Papapetrou-Dixon covariant equations of motion beyond the spin-dipole particle approximation by accounting for the entire infinite set of the internal multipoles of the bodies which are gravitationally coupled with the curvature tensor of the background manifold and its covariant derivatives. The results of our study can be used for much more accurate prediction of orbital dynamics of extended bodies in inspiraling binary systems and construction of templates of gravitational waves at the merger stage when the strong gravitational interaction between the higher-order multipoles of the bodies play a dominant role. The covariant theory of the post-Newtonian equations of motion beyond the spin-dipole approximation is a solid foundation for future improvements in long-term accuracy of relativistic celestial ephemerides of the solar system bodies., Comment: 36 pages, no figures, typos fixed. arXiv admin note: substantial text overlap with arXiv:1810.11713

This paper employs the post-Newtonian approximations of scalar-tensor theory of gravity along with the Cartesian STF tensors and the Blanchet-Damour multipole formalism to derive translational and rotational equations of motion of N extended bodies with arbitrary distribution of mass and velocity. We assume that spacetime can be covered by a global coordinate chart which is Minkowskian at infinity. We also introduce N local coordinate charts adapted to each body and covering a finite domain of space around the body. Gravitational field of each body is parametrized by an infinite set of the body's mass and spin multipoles and tidal multipoles of external N-1 bodies. The origin of the local coordinates is set moving along accelerated worldline of the center of mass of the body by an appropriate choice of the internal and external dipole moments of its gravitational field. Translational and rotational equations of motion are derived by integrating microscopic equations of matter and applying the method of asymptotic matching. The matching is also used for separating the post-Newtonian self-field effects from the external gravitational environment and for constructing the effective background spacetime manifold. It allows us to present the equations of translational and rotational motion of each body in covariant form by making use of the Einstein principle of equivalence. Our approach significantly generalizes the Mathisson-Papapetrou-Dixon covariant equations of motion with regard to the number of body's multipoles and the post-Newtonian terms taken into account. The equations of translational and rotational motion derived in the present paper include the infinite set of mass and spin multipoles of the bodies and can be used for much more accurate prediction of orbital dynamics of extended bodies in inspiraling binary systems before they merge., Comment: 121 pages, 1 figure, accepted to Phys. Rev. D

We compare the Vinti integral of the classic celestial mechanics with a conserved Carter-like integral of motion for an axially-symmetric body in the Newtonian theory that has been recently found by Clifford Will. We demonstrate that the integrals are identical. It sheds new light on the Newtonian limit of the Kerr geometry., Comment: 2 pages

Modern geodesy is subject to a dramatic change from the Newtonian paradigm to Einstein's theory of general relativity. This is motivated by the ongoing advance in development of quantum sensors for applications in geodesy including quantum gravimeters and gradientometers, atomic clocks and fiber optics for making ultra-precise measurements of the geoid and multipolar structure of the Earth's gravitational field. At the same time, VLBI, SLR, and GNSS have achieved an unprecedented level of accuracy in measuring coordinates of the reference points of the ITRF and the world height system. The main geodetic reference standard is a normal gravity field represented in the Newtonian gravity by the field of a Maclaurin ellipsoid. The present paper extends the concept of the normal gravity field to the realm of general relativity. We focus our attention on the calculation of the first post-Newtonian approximation of the normal field that is sufficient for applications. We show that in general relativity the level surface of the uniformly rotating fluid is no longer described by the Maclaurin ellipsoid but is an axisymmetric spheroid of the forth order. We parametrize the mass density distribution and derive the post-Newtonian normal gravity field of the rotating spheroid which is given in a closed form by a finite number of the ellipsoidal harmonics. We employ transformation from the ellipsoidal to spherical coordinates to deduce the post-Newtonian multipolar expansion of the metric tensor given in terms of scalar and vector gravitational potentials of the rotating spheroid. We compare these expansions with that of the normal gravity field generated by the Kerr metric and demonstrate that the Kerr metric has a fairly limited application in relativistic geodesy. Finally, we derive the post-Newtonian generalization of the Somigliana formula for the gravity field on the reference ellipsoid., Comment: 39 pages, no figures, accepted to Physical Review D

Time measured by an ideal clock crucially depends on the gravitational potential and velocity of the clock according to general relativity. Technological advances in manufacturing high-precision atomic clocks have rapidly improved their accuracy and stability over the last decade that approached the level of 10$^{-18}$. Based on a fully relativistic description of the background gravitational physics, we discuss the impact of those highly-precise clocks on the realization of reference frames and time scales used in geodesy. We discuss the current definitions of basic geodetic concepts and come to the conclusion that the advances in clocks and other metrological technologies will soon require the re-definition of time scales or, at least, clarification to ensure their continuity and consistent use in practice. The relative frequency shift between two clocks is directly related to the difference in the values of the gravity potential at the points of clock's localization. According to general relativity the relative accuracy of clocks in 10$^{-18}$ is equivalent to measuring the gravitational red shift effect between two clocks with the height difference amounting to 1 cm. We show how clock measurements can provide geopotential numbers for the realization of gravity-field-related height systems and can resolve discrepancies in classically-determined height systems as well as between national height systems. Another application of clocks is the direct use of observed potential differences for the improved recovery of regional gravity field solutions. Finally, clock measurements for space-borne gravimetry are analyzed along with closely-related deficiencies of this method like an extra-ordinary knowledge of the spacecraft velocity, etc. For all these applications besides the near-future prospects, we also discuss the challenges that are related to using those novel clock data in geodesy., Comment: Will be published in Space Science Reviews as special issue on High Performance Clocks which is organized by ISSI

Applying the recently developed dynamical perturbation formalism on cosmological background to scalar-tensor theory, we provide a solid theoretical basis and a rigorous justification for phenomenological models of orbital dynamics that are currently used to interpret experimental measurements of the time-dependent gravitational constant. We derive the field equations for the scalar-tensor perturbations and study their gauge freedom associated with the cosmological expansion. We find a new gauge eliminating a prohibitive number of gauge modes in the field equations and significantly simplifying post-Newtonian equations of motion for localized astronomical systems in the universe with time-dependent gravitational constant. We identify several new post-Newtonian terms and calculate their effect on secular cosmological evolution of the osculating orbital elements., Comment: 7 pages, no figures; supplemental materials added: "Derivation of the wave equations for perturbations", 27 pages, no figures

We discuss a field-theoretical approach based on variational principle to derive the field and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter. The total Lagrangian is expanded in an asymptotic Taylor series around the background manifold defined as a solution of Einstein's equations in the form of the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein's equations and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of the baryonic matter., Comment: 62 pages, no figures. Accepted to the Annals of Physics

We study physical consequences of the Einstein equivalence principle (EEP) for a Hubble observer in FLRW universe. We introduce the local inertial coordinates with the help of a special conformal transformation. The local inertial metric is Minkowski-flat and materialized by a congruence of time-like geodesics of static observers. The static observers are equipped with the ideal clocks measuring the proper time that is synchronized with the clocks of the Hubble observer. The local inertial metric is used for physical measurements of spacetime intervals with the ideal clocks and rulers. The special conformal transformation preserves null geodesics but does not keep invariant time-like geodesics. Moreover, it makes the rate of the local time coordinate dependent on velocity of the particle which makes impossible to rich the uniform parameterization of the world lines of static observers and light geodesics with a single parameter - they differ by the conformal factor of FLRW metric. It tells us that the metric on the light cone is not Minkowski-flat but depends on the scale factor of FLRW universe and it can be interpreted as a weak violation of EEP for photons. The importance of this violation for gravitational physics is that some of local experiments conducted with freely-propagating electromagnetic waves may be sensitive to the Hubble expansion. We show that the Hubble constant H can be measured within the solar system by means of high-precision spacecraft Doppler tracking as a blue shift of frequency of radio waves circulating in the Earth-spacecraft radio link. We also analyze the behavior of the standing wave in a microwave resonator and show that the standing wave is insensitive to the Hubble expansion., Comment: 52 pages, no figures, references added

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 - beta and gamma; (3) embedding the post-Newtonian barycentric reference system to the Friedman-Robertson-Walker cosmological model., Comment: 9 pages, no figures, submitted to the proceedings of the IAU 261 Symposium "Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis"", Virginia Beach, USA; May 2009

Lunar Laser Ranging (LLR) measurements are crucial for advanced exploration of the laws of fundamental gravitational physics and geophysics. Current LLR technology allows us to measure distances to the Moon with a precision approaching 1 millimeter. As NASA pursues the vision of taking humans back to the Moon, new, more precise laser ranging applications will be demanded, including continuous tracking from more sites on Earth, placing new CCR arrays on the Moon, and possibly installing other devices such as transponders, etc. Successful achievement of this goal strongly demands further significant improvement of the theoretical model of the orbital and rotational dynamics of the Earth-Moon system. This model should inevitably be based on the theory of general relativity, fully incorporate the relevant geophysical processes, lunar librations, tides, and should rely upon the most recent standards and recommendations of the IAU for data analysis. This paper discusses methods and problems in developing such a mathematical model. The model will take into account all the classical and relativistic effects in the orbital and rotational motion of the Moon and Earth at the sub-centimeter level. The new model will allow us to navigate a spacecraft precisely to a location on the Moon. It will also greatly improve our understanding of the structure of the lunar interior and the nature of the physical interaction at the core-mantle interface layer. The new theory and upcoming millimeter LLR will give us the means to perform one of the most precise fundamental tests of general relativity in the solar system., Comment: 26 pages, submitted to Proc. of ASTROCON-IV conference (Princeton Univ., NJ, 2007)

Analysis of the gauge residual freedom in the relativistic theory of lunar motion demonstrates that lunar laser ranging (LLR) is not currently capable to detect gravitomagnetic effects., Comment: 1 page, accepted to Physical Review Letters

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 A

We introduce a linearized bi-metric theory of gravity with two metrics. The metric g_{ab} describes null hypersurfaces of the gravitational field while light moves on null hypersurfaces of the optical metric \bar{g}_{ab}. Bi-metrism naturally arises in vector-tensor theories with matter being non-minimally coupled to gravity via long-range vector field. We derive explicit Lorentz-invariant solution for a light ray propagating in space-time of the bi-metric theory and disentangle relativistic effects associated with the two metrics. This anlysis can be valuable for future spaceborne laser missions ASTROD and LATOR dedicated to map various relativistic gravity parameters in the solar system to unparalleled degree of accuracy., Comment: 6 pages, figure and text improved. To appear in: Proceedings of the 359th WE-Heraeus Seminar on "Lasers, Clocks, and Drag-Free: Technologies for Future Exploration in Space and Tests of Gravity"}, ZARM, Bremen, Germany, May 30-June 1, 2005

A prolonged timing of millisecond pulsars has revealed low-frequency uncorrelated noise, presumably of astrophysical origin, in the pulse arrival time (PAT) residuals for some of them. In most cases, pulsars in globular clusters show a low-frequency modulation of their rotational phase and spin rate. The relativistic time delay of the pulsar signal in the curved space time of randomly distributed and moving globular cluster stars (the Shapiro effect) is suggested as a possible cause of this modulation. Given the smallness of the aberration corrections that arise from the nonstationarity of the gravitational field of the randomly distributed ensemble of stars under consideration, a formula is derived for the Shapiro effect for a pulsar in a globular cluster. The derived formula is used to calculate the autocorrelation function of the low-frequency pulsar noise, the slope of its power spectrum, and the behavior of the $\sigma_z$ statistic that characterizes the spectral properties of this noise in the form of a time function. The Shapiro effect under discussion is shown to manifest itself for large impact parameters as a low-frequency noise of the pulsar spin rate with a spectral index of n=-1.8 that depends weakly on the specific model distribution of stars in the globular cluster. For small impact parameters, the spectral index of the noise is n=-1.5., Comment: 23 pages, 6 figures

Experimental verification of the existence of gravimagnetic fields generated by currents of matter is important for a complete understanding and formulation of gravitational physics. Although the rotational `intrinsic' gravimagnetic field has been extensively studied and is now being measured by the Gravity Probe B, the `extrinsic' gravimagnetic field generated by the translational current of matter is less well studied. The present paper uses the post-Newtonian parametrized Einstein and light geodesics equations to show that the `extrinsic' gravimagnetic field generated by the translational current of matter can be measured by observing the relativistic time delay and/or light deflection caused by the moving mass. We prove that the `extrinsic' gravimagnetic field is generated by the relativistic effect of the aberration of the gravity force caused by the Lorentz transformation of the metric tensor and the Levi-Civita connection. We show that the Lorentz transformation of the gravity field variables is equivalent to the technique of the retarded Lienard-Wiechert gravitational potentials predicting that a light particle is deflected by gravitational field of a moving body from its retarded position so that both general-relativistic phenomena -- the aberration and the retardation of gravity -- are tightly connected and observing the aberration of gravity proves that gravity has a causal nature. We explain in this framework the 2002 deflection experiment of a quasar by Jupiter where the aberration of gravity from its orbital motion was measured with accuracy 20%. We describe a theory of VLBI experiment to measure the gravitational deflection of radio waves from a quasar by the Sun, as viewed by a moving observer from the geocentric frame, to improve the measurement accuracy of the aberration of gravity to a few percent., Comment: 44 pages including references, 7 figures, 1 table; accepted for publication in General Relativity and Gravitation

In a recent paper published in Classical and Quantum Gravity, 2004, vol. 21, p. 3803 Carlip used a vector-tensor theory of gravity to calculate the Shapiro time delay by a moving gravitational lens. He claimed that the relativistic correction of the order of v/c beyond the static part of the Shapiro delay depends on the speed of light c and, hence, the Fomalont-Kopeikin experiment is not sensitive to the speed of gravity c_g. In this letter we analyze Carlip's calculation and demonstrate that it implies a gravitodynamic (non-metric) system of units based on the principle of the constancy of the speed of gravity but it is disconnected from the practical method of measurement of astronomical distances based on the principle of the constancy of the speed of light and the SI metric (electrodynamic) system of units. Re-adjustment of theoretically-admissible but practically unmeasurable Carlip's coordinates to the SI metric system of units used in JPL ephemeris, reveals that the velocity-dependent correction to the static part of the Shapiro time delay does depend on the speed of gravity c_g as shown by Kopeikin in Classical and Quantum Gravity, 2004, vol. 21, p. 1. This analysis elucidates the importance of employing the metric system of units for physically meaningful interpretation of gravitational experiments., Comment: 8 pages, no figures, accepted to Classical and Quantum Gravity

One of the main endeavors of fundamental astrometry is to establish a practical realization of an inertial reference frame anchored to celestial objects whose positions are defined in the barycentric coordinates of the solar system. The development of astrometric facilities operating from space at a microarcsecond level of precision makes the non-uniformity of the galactic motion of the barycenter an observable effect that violates the inertiality of the barycentric frame. Most of the observable effect is caused by secular acceleration of the barycenter with respect to the center of the Galaxy. The acceleration results in a pattern of secular aberration which is observable astrometrically as a systematic vector field of the proper motions of distant quasars. We employ the vector spherical harmonics to describe the predicted field of the proper motions and evaluate its amplitude at each point on the celestial sphere. It is shown that the pattern of secular aberration is fully represented by three low-order electric-type vector harmonics, and hence, it is easily distinguishable from the residual rotations of the reference frame and other possible effects, such as the hypothetical long-period gravitational waves. Comprehensive numerical simulations of the grid astrometry with SIM PlanetQuest are conducted. The full covariance matrix of the simulated grid solution is used to evaluate the covariances of the three electric harmonic coefficients, representing the secular aberration pattern of proper motions. We conclude that the grid astrometry with SIM PlanetQuest will be sensitive to the main galactocentric component of secular acceleration, while the peculiar acceleration of the Sun with respect to LSR is expected to be too small to be detected with this astrometric space interferometer., Comment: 21 pages, 4 figures

Experimental discovery of the gravitomagnetic fields generated by translational and/or rotational currents of matter is one of primary goals of modern gravitational physics. The rotational (intrinsic) gravitomagnetic field of the Earth is currently measured by the Gravity Probe B. The present paper makes use of a parametrized post-Newtonian (PN) expansion of the Einstein equations to demonstrate how the extrinsic gravitomagnetic field generated by the translational current of matter can be measured by observing the relativistic time delay caused by a moving gravitational lens. We prove that measuring the extrinsic gravitomagnetic field is equivalent to testing relativistic effect of the aberration of gravity caused by the Lorentz transformation of the gravitational field. We unfold that the recent Jovian deflection experiment is a null-type experiment testing the Lorentz invariance of the gravitational field (aberration of gravity), thus, confirming existence of the extrinsic gravitomagnetic field associated with orbital motion of Jupiter with accuracy 20%. We comment on erroneous interpretations of the Jovian deflection experiment given by a number of researchers who are not familiar with modern VLBI technique and subtleties of JPL ephemeris. We propose to measure the aberration of gravity effect more accurately by observing gravitational deflection of light by the Sun and processing VLBI observations in the geocentric frame with respect to which the Sun is moving with velocity 30 km/s., Comment: 16 pages, no figures

Recent review article by S. Samuel "On the speed of gravity and the Jupiter/Quasar measurement" published in the International Journal of Modern Physics D13, 1753 (2004) provides the reader with a misleading "theory" of the relativistic time delay in general theory of relativity. Furthermore, it misquotes original publications by Kopeikin and Fomalont & Kopeikin related to the measurement of the speed of gravity by VLBI. We summarize the general relativistic principles of the Lorentz-invariant theory of propagation of light in time-dependent gravitational field, derive Lorentz-invariant expression for the relativistic time delay, and finally explain why Samuel's "theory" is conceptually incorrect and confuses the speed of gravity with the speed of light., Comment: 14 pages, one figure, text improved, references added

This paper discusses spectral sensitivity of solitary and binary pulsars to a low-frequency (colored) noise. It is a third paper in a series of papers devoted to analysis of the low-frequency noise in pulsar timing observations and its impact on observable fitting parameters of timing model., Comment: 25 pages, 3 figures, accepted to MNRAS

We describe our explicit Lorentz-invariant solution of the Einstein and null geodesic equations for the deflection experiment of 2002 September 8 when a massive moving body, Jupiter, passed within 3.7' of a line-of-sight to a distant quasar. We develop a general relativistic framework which shows that our measurement of the retarded position of a moving light-ray deflecting body (Jupiter) by making use of the gravitational time delay of quasar's radio wave is equivalent to comparison of the relativistic laws of the Lorentz transformation for gravity and light. Because, according to Einstein, the Lorentz transformation of gravity field variables must depend on a fundamental speed $c$, its measurement through the retarded position of Jupiter in the gravitational time delay allows us to study the causal nature of gravity and to set an upper limit on the speed of propagation of gravity in the near zone of the solar system as contrasted to the speed of the radio waves. We discuss the misconceptions which have inhibited the acceptance of this interpretation of the experiment. We also comment on other interpretations of this experiment by Asada, Will, Samuel, Pascual-Sanchez, and Carlip and show that their `speed of light' interpretations confuse the Lorentz transformation for gravity with that for light, and the fundamental speed of gravity with the physical speed of light from the quasar., Comment: 26 pages, 3 figures, physics improved, accepted to Foundations of Physics

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 A

Recent measurements of the propagation of the quasar's radio signal past Jupiter are directly sensitive to the time-dependent effect from the geometric sector of general relativity which is proportional to the speed of propagation of gravity but not the speed of light. It provides a first confirmative measurement of the fundamental speed of the Einstein general principle of relativity for gravitational field., Comment: 45 pages, 6 figures, published

This paper discusses the IAU Resolutions B1.3, B1.4, B1.5 and B1.9 (2000) that were adopted during the 24th General Assembly in Manchester, 2000 and provides details and explanations for these Resolutions. It is explained why they present significant progress over the corresponding IAU 1991 Resolutions and why they are necessary in the light of present accuracies in astrometry, celestial mechanics and metrology. In fact most of these Resolutions are consistent with astronomical models and software already in use. The metric tensors and gravitational potentials of both the Barycentric Celestial Reference System and Geocentric Celestial Reference System are defined and discussed. The necessity and relevance of the two celestial reference systems are explained. The transformations of coordinates and gravitational potentials are discussed. Potential coefficients parameterizing the post-Newtonian gravitational potentials are expounded. Simplified versions of the time transformations suitable for modern clock accuracies are elucidated. Various approximations used in the Resolutions are explicated and justified. Some models (e.g. for higher spin moments) that serve the purpose for estimating orders of magnitude have actually never been published before., Comment: 45 pages, 1 figure, submitted to Astronomical Journal

Equations of light, propagating from quasar to observer on earth, are integrated in the time-dependent gravitational field of the solar system by making use of either retarded or advanced solutions of the Einstein field equations. This technique allows to separate explicitly the effects associated with the propagation of gravity from those associated with light in the integral expression for the relativistic time delay of light. We prove that the relativistic correction to the Shapiro time delay discovered by Kopeikin (ApJ, 556, L1, 2001) changes sign if one retains direction of the light propagation but replaces retarded with advanced solution of the gravitational field equations. Hence, this correction is due to the propagation of gravity and allows to measure its speed. Relativistic VLBI experiment conducted by Fomalont and Kopeikin in September 2002 proves that the propagation of gravitational field is characterized by the retarded potentials., Comment: 14 pages, 1 figure

We have determined the relativistic light deflection of the quasar J0842+1835 as Jupiter passed within 3.7' on 2002 September 8, by measuring the time delay using the VLBA and Effelsberg radio telescopes at 8.4 GHz. At closest approach, General Relativity (GR) predicts a radial (static) deflection of 1190 microarcsec, and tangential (retarded) deflection in the direction of Jupiter's motion of 51 microarcsec. Our experiment achieved an rms position error of <10 microarcsec, and measured this retarded deflection to be 0.98 +/- 0.19 (rms error) times that predicted by GR. The increase positional accuracy for this VLBI phase referencing experiment was achieved by using two calibrator sources. Comments on the interpretation of this experiment are given.