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Sergei Kopeikin

Publications and source records attributed to Sergei Kopeikin.

33 records · Page 2Linked to original sources

Post-Newtonian Reference Frames for Advanced Theory of the Lunar Motion and a New Generation of Lunar Laser Ranging

We construct a set of post-Newtonian reference frames for a comprehensive study of the orbital dynamics and rotational motion of the Moon and Earth by means of lunar laser ranging (LLR) with the precision of one millimeter. We also derive the post-Newtonian coordinate transformations between the frames and analyze the residual gauge freedom, which is used for removing spurious post-Newtonian effects from the equations of motion of the solar system bodies.

gr-qc↗

Millimeter Laser Ranging to the Moon: a comprehensive theoretical model for advanced data analysis

Lunar Laser Ranging (LLR) measurements are crucial for advanced exploration of the evolutionary history of the lunar orbit, the laws of fundamental gravitational physics, selenophysics and geophysics as well as for future human missions to the Moon. Current LLR technique measures distance to the Moon with a precision approaching one millimeter that 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/selenophysical processes and rely upon the most recent IAU standards in order to give us the opportunity to perform the most precise fundamental test of general relativity in the solar system in robust and physically-adequate way. The talk discusses new methods and approaches in developing such a mathematical model.

gr-qc↗

Astrodynamical Space Test of Relativity using Optical Devices I (ASTROD I) - A class-M fundamental physics mission proposal for Cosmic Vision 2015-2025

ASTROD I is a planned interplanetary space mission with multiple goals. The primary aims are: to test General Relativity with an improvement in sensitivity of over 3 orders of magnitude, improving our understanding of gravity and aiding the development of a new quantum gravity theory; to measure key solar system parameters with increased accuracy, advancing solar physics and our knowledge of the solar system and to measure the time rate of change of the gravitational constant with an order of magnitude improvement and the anomalous Pioneer acceleration, thereby probing dark matter and dark energy gravitationally. It is an international project, with major contributions from Europe and China and is envisaged as the first in a series of ASTROD missions. ASTROD I will consist of one spacecraft carrying a telescope, four lasers, two event timers and a clock. Two-way, two-wavelength laser pulse ranging will be used between the spacecraft in a solar orbit and deep space laser stations on Earth, to achieve the ASTROD I goals. A second mission, ASTROD II is envisaged as a three-spacecraft mission which would test General Relativity to one part per billion, enable detection of solar g-modes, measure the solar Lense-Thirring effect to 10 parts per million, and probe gravitational waves at frequencies below the LISA bandwidth. In the third phase (ASTROD III or Super-ASTROD), larger orbits could be implemented to map the outer solar system and to probe primordial gravitational-waves at frequencies below the ASTROD II bandwidth.

astro-ph↗

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.

gr-qc↗

Gravitational bending of light by planetary multipoles

General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived in the approximation of the linearized Einstein equations. All terms of order 1 microarcsecond are taken into account, parametrized, and classified in accordance with their physical origin. We discuss the observational capabilities of the near-future optical and radio interferometers for detecting the Doppler modulation of the radial deflection, and the dipolar and quadrupolar light-ray bendings by Jupiter and the Saturn.

gr-qc↗

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived. All terms of order 1 microarcsecond are taken into account, parametrized, and classified in accordance with their physical origin. We calculate the instantaneous patterns of the light-ray deflections caused by the monopole, the dipole and the quadrupole moments, and derive equations describing apparent motion of the deflected position of the star in the sky plane as the impact parameter of the light ray with respect to the planet changes due to its orbital motion. The present paper gives the physical interpretation of the observed light-ray deflections and discusses the observational capabilities of the near-future optical (SIM) and radio (SKA) interferometers for detecting the Doppler modulation of the radial deflection, and the dipolar and quadrupolar light-ray bendings by the Jupiter and the Saturn.

astro-ph↗

The Effacing Principle in the Post-Newtonian Celestial Mechanics

First post-Newtonian (PN) approximation of the scalar-tensor theory of gravity is used to discuss the effacing principle in N-body system, that is dependence of equations of motion of spherically-symmetric bodies comprising the system on their internal structure. We demonstrate that the effacing principle is violated by terms which are proportional to the second order rotational moment of inertia of each body coupled with β-1, where βis the measure of non-linearity of gravitational field. In case of general relativity, where β=1, the effacing principle is violated by terms being proportional to the rotational moment of inertia of the forth order. For systems made of neutron stars (NS) and/or black holes (BH) these terms contribute to the orbital equations of motion at the level of the third and fifth PN approximation respectively.

gr-qc↗

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.

astro-ph↗

Parametrized Post-Newtonian Theory of Reference Frames, Multipolar Expansions and Equations of Motion in the N-body Problem

We discuss a covariant generalization of the parametrized post-Newtonian (PPN) formalism in a class of scalar-tensor theories of gravity. It includes an exact construction of a set of global and local (Fermi-like) references frames for an isolated N-body astronomical system as well as PPN multipolar decomposition of gravitational field in these frames. We derive PPN equations of translational and rotational motion of extended bodies taking into account all gravitational multipoles and analyze the body finite-size effects in relativistic dynamics that can be important at the latest stages of orbital evolution of coalescing binary systems. We also reconcile the IAU 2000 resolutions on the general relativistic reference frames in the solar system with the PPN equations of motion of the solar system bodies used in JPL ephemerides.

gr-qc↗

Propagation of Light in the Field of Stationary and Radiative Gravitational Multipoles

Extremely high precision of near-future radio/optical interferometric observatories like SKA, Gaia, SIM and the unparalleled sensitivity of LIGO/LISA gravitational-wave detectors demands more deep theoretical treatment of relativistic effects in the propagation of electromagnetic signals through variable gravitational fields of the solar system, oscillating and precessing neutron stars, coalescing binary systems, exploding supernova, and colliding galaxies. Especially important for future gravitational-wave observatories is the problem of propagation of light rays in the field of multipolar gravitational waves emitted by a localized source of gravitational radiation. Present paper suggests physically-adequate and consistent mathematical solution of this problem in the first post-Minkowskian approximation of General Relativity which accounts for all time-dependent multipole moments of an isolated astronomical system.

gr-qc↗

Note on the relationship between the speed of light and gravity in the bi-metric theory of gravity

Relationship between the speed of gravity c_g and the speed of light c_e in the bi-metric theory of gravity is discussed. We reveal that the speed of light is a function of the speed of gravity which is a primary fundamental constant. Thus, experimental measurement of relativistic bending of light propagating in time-dependent gravitational field directly compares the speed of gravity versus the speed of light and tests if there is any aether associated with the gravitational field considered as a transparent `medium' with the constant refraction index.

gr-qc↗

General relativistic model for experimental measurement of the speed of propagation of gravity by VLBI

A relativistic sub-picosecond model of gravitational time delay in radio astronomical observations is worked out and a new experimental test of general relativity is discussed in which the effect of retardation of gravity associated with its finite speed can be observed. As a consequence, the speed of gravity can be measured by differential VLBI observations. Retardation in propagation of gravity is a central part of the Einstein theory of general relativity which has not been tested directly so far. The idea of the proposed gravitational experiment is based on the fact that gravity in general relativity propagates with finite speed so that the deflection of light caused by the body must be sensitive to the ratio of the body's velocity to the speed of gravity. The interferometric experiment can be performed, for example, during the very close angular passage of a quasar by Jupiter. Due to the finite speed of gravity and orbital motion of Jupiter, the variation in its gravitational field reaches observer on Earth not instantaneously but at the retarded instant of time and should appear as a velocity-dependent excess time delay in addition to the well-known Shapiro delay, caused by the static part of the Jupiter's gravitational field. Such Jupiter-QSO encounter events take place once in a decade. The next such event will occur on September 8, 2002 when Jupiter will pass by quasar J0842+1835 at the angular distance 3.7 arcminutes. If radio interferometric measurement of the quasar coordinates in the sky are done with the precision of a few picoseconds (about 5 microarcseconds) the effect of retardation of gravity and its speed of propagation may be measured with an accuracy about 10%.

gr-qc↗

Gravitomagnetic Effects in the Propagation of Electromagnetic Waves in Variable Gravitational Fields of Arbitrary-Moving and Spinning Bodies

Propagation of light in the gravitational field of self-gravitating spinning bodies moving with arbitrary velocities is discussed. The gravitational field is assumed to be "weak" everywhere. Equations of motion of a light ray are solved in the first post-Minkowskian approximation that is linear with respect to the universal gravitational constant $G$. We do not restrict ourselves with the approximation of gravitational lens so that the solution of light geodesics is applicable for arbitrary locations of source of light and observer. This formalism is applied for studying corrections to the Shapiro time delay in binary pulsars caused by the rotation of pulsar and its companion. We also derive the correction to the light deflection angle caused by rotation of gravitating bodies in the solar system (Sun, planets) or a gravitational lens. The gravitational shift of frequency due to the combined translational and rotational motions of light-ray-deflecting bodies is analyzed as well. We give a general derivation of the formula describing the relativistic rotation of the plane of polarization of electromagnetic waves (Skrotskii effect). This formula is valid for arbitrary translational and rotational motion of gravitating bodies and greatly extends the results of previous researchers. Finally, we discuss the Skrotskii effect for gravitational waves emitted by localized sources such as a binary system. The theoretical results of this paper can be applied for studying various relativistic effects in microarcsecond space astrometry and developing corresponding algorithms for data processing in space astrometric missions such as FAME, SIM, and GAIA.

gr-qc↗

Gravitational Radiation Theory and Light Propagation

The paper gives an introduction to the gravitational radiation theory of isolated sources and to the propagation properties of light rays in radiative gravitational fields. It presents a theoretical study of the generation, propagation, back-reaction, and detection of gravitational waves from astrophysical sources. After reviewing the various quadrupole-moment laws for gravitational radiation in the Newtonian approximation, we show how to incorporate post-Newtonian corrections into the source multipole moments, the radiative multipole moments at infinity, and the back-reaction potentials. We further treat the light propagation in the linearized gravitational field outside a gravitational wave emitting source. The effects of time delay, bending of light, and moving source frequency shift are presented in terms of the gravitational lens potential. Time delay results are applied in the description of the procedure of the detection of gravitational waves.

gr-qc↗

RELATIVISTIC EFFECT OF GRAVITATIONAL DEFLECTION OF LIGHT IN BINARY PULSARS

An improved formula for the timing of binary pulsars that accounts for the relativistic deflection of light in the gravitational field of the pulsar's companion is presented, and the measurability of this effect together with its variance estimates are discussed. The deflection of the pulsar's beam trajectory in the gravitational field of its companion leads to variation in the pulsar's rotational phase. This variation appears as the narrow sharp growth of the magnitude of the post-fit pulsar timing residuals in the vicinity of the moment of the superior conjunction of the pulsar with its companion. In contrast to the relativistic Shapiro effect the amplitude of the effect of gravitational deflection of the pulsar radio beam has two peaks with opposite signs, which become sharper as the inclination $i$ of the pulsar's orbit approaches 90$^{\circ}$. The effect under consideration influences the estimation of parameters of the relativistic Shapiro effect in the binary pulsars with nearly edgewise orbits. Its inclusion in the fitting procedure provide more careful measurement of sine of the orbital inclination $i$ as well as the masses of the pulsar $m_p$ and its companion $m_c$. This permits an improved testing of alternative theories of gravity in the strong field regime. Moreover, the measurement of this effect permits independent geometric constraints on the position of the pulsar rotational axis in space. The effect of the gravitational deflection of light has been numerically investigated for binary pulsars with nearly edgewise orbits. It is shown that the effect is observed in general only when $\cos i\leq 0.003.$ This estimate becomes less restrictive as the pulsar's spin axis approaches the line of the sight.

astro-ph↗