Parametrized post-Newtonian theory of reference frames, multipolar expansions and equations of motion in the N-body problem

Kopeikin, Sergei M.; Vlasov, Igor

doi:10.1016/j.physrep.2004.08.004

Cited by 111 publications

(258 citation statements)

References 129 publications

(458 reference statements)

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“…Local harmonic coordinates were introduced to gravitational physics by Thorne and Hartle [52]. The law of transformation between the local harmonic coordinates extends the linear Lorentz transformation to the class of harmonic polynomials that are solutions of the homogeneous wave equation [53][54][55][56][57][58]. They have a great practical value for modern fundamental astronomy [59,60].…”

Section: A the Field Equationsmentioning

confidence: 99%

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

2007

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General-relativistic deflection of light by mass, dipole, and quadrupole moments of the 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 as are taken into account, parametrized, and classified in accordance with their physical origin. The monopolar light-ray deflection, modulated by the radial Doppler effect, is associated with the total mass and radial velocity of the gravitating body. It displaces the apparent positions of stars in the sky plane radially away from the origin of the celestial coordinates associated with the planet. The dipolar deflection of light is due to a translational mismatch of the center of mass of the planet and the origin of the planetary coordinates caused by the inaccuracy of planetary ephemeris. It can also originate from the difference between the null cone for light and that for gravity that is not allowed in general relativity but can exist in some of the alternative theories of gravity. The dipolar gravity field pulls the apparent position of a star in the plane of the sky in both radial and orthoradial directions with respect to the origin of the coordinates. The quadrupolar deflection of light is caused by the physical oblateness, J 2 , of the planet, but in any practical experiment it will have an admixture of the translation-dependent quadrupole due to inaccuracy of planetary ephemeris. This leads to a bias in the estimated value of J 2 that should be minimized by applying an iterative data reduction method designed to disentangle the different multipole moments and to fit out the translation-dependent dipolar and quadrupolar components of light deflection. The method of microarcsecond interferometric astrometry has the potential of greatly improving the planetary ephemerides, getting unbiased measurements of planetary quadrupoles, and of thoroughly testing the null-cone structure of the gravitational field and the speed of its propagation in the near-zone of the solar system. 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. We discuss 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 Jupiter and Saturn.

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Section: A the Field Equationsmentioning

confidence: 99%

“…Equations (16) and (17) approximate more precise, post-Newtonian definitions of the multipole moments used in the relativistic celestial mechanics of the N-body system [58]. However, the post-Newtonian corrections to Eqs.…”

Section: B the Gravitational Multipolesmentioning

confidence: 99%

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

2007

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“…It means that the equations of motion for the fluid and the scalar field are decoupled, and we can calculate their evolution separately. In other words, the Lagrangian of the ideal fluid and that of the scalar field depend only on their own field variables.The tensor of energy-momentum of matter of the localized astronomical system is not specified in agreement with the approach adopted in the post-Newtonian approximation scheme developed in the asymptotically-flat spacetime [23,57]. This allows us to generate all possible types of cosmological perturbations: scalar, vector and tensor modes.…”

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confidence: 99%

Post-Newtonian celestial dynamics in cosmology: Field equations

Kopeikin

Петров

2013

Phys. Rev. D

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Post-Newtonian celestial dynamics is a relativistic theory of motion of massive bodies and test particles under the influence of relatively weak gravitational forces. Standard approach for development of this theory relies upon the key concept of the isolated astronomical system supplemented by the assumption that the background space-time is flat. The standard post-Newtonian theory of motion was instrumental in explanation of the existing experimental data on binary pulsars, satellite and lunar laser ranging, and in building precise ephemerides of planets in the solar system. Recent studies of the formation of large-scale structure in our universe indicate that the standard post-Newtonian mechanics fails to describe more subtle dynamical effects in motion of the bodies comprising the astronomical systems of larger size -galaxies and clusters of galaxies -where the Riemann curvature of the expanding FLRW universe interacts with the local gravitational field of the astronomical system and, as such, can not be ignored.The present paper outlines theoretical principles of the post-Newtonian mechanics in the expanding universe. It is based upon the gauge-invariant theory of the Lagrangian perturbations of cosmological manifold caused by an isolated astronomical N-body system (the solar system, a binary star, a galaxy, a cluster of galaxies). We postulate that the geometric properties of the background manifold are described by a homogeneous and isotropic Friedman-Lemaître-Robertson-Walker (FLRW) metric governed by two primary components -the dark matter and the dark energy. The dark matter is treated as an ideal fluid with the Lagrangian taken in the form of pressure along with the scalar Clebsch potential as a dynamic variable. The dark energy is associated with a single scalar field with a potential which is hold unspecified as long as the theory permits. Both the Lagrangians of the dark matter and the scalar field are formulated in terms of the field variables which play a role of generalized coordinates in the Lagrangian formalism. It allows us to implement the powerful methods of variational calculus to derive the gauge-invariant field equations of the post-Newtonian celestial mechanics of an isolated astronomical system in an expanding universe. These equations generalize the field equations of the post-Newtonian theory in asymptotically-flat spacetime by taking into account the cosmological effects explicitly and in a self-consistent manner without assuming the principle of liner superposition of the fields or a vacuole model of the isolated system, etc. The field equations for matter dynamic variables and gravitational field perturbations are coupled in the most general case of arbitrary equation of state of matter of the background universe.We introduce a new cosmological gauge which generalizes the de Donder (harmonic) gauge of the post-Newtonian theory in asymptotically flat spacetime. This gauge significantly simplifies the gravitational field equations and allows to find out the approximations where the ...

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“…Only the terms in the equations of motion, which can not be eliminated by the gauge transformation to the local inertial frame can be physically interpreted. The analysis of the gauge freedom in the three body-problem had been done in [30,31,32]. It proves that all non-tidal and V -dependent terms, including the first term in the right side of Eq.…”

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confidence: 90%

The Gravitomagnetic Influence on Earth-Orbiting Spacecrafts and on the Lunar Orbit

Kopeikin

2010

Astrophysics and Space Science Library

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Gravitomagnetic field is covariantly split in the intrinsic and extrinsic parts, which are generated by rotational and translational currents of matter respectively. The intrinsic component has been recently discovered in the LAGEOS spacecraft experiment. We discuss the method of detection of the 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 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. Detection of gravitomagnetic components as predicted by Einstein's theory of general relativity is one of the primary goals of experimental gravitational physics. The paper [1] states that the gravitomagnetic interaction plays a part in shaping the lunar orbit readily obervable by LLR. The authors picked up a "gravitomagnetic" term from the parameterized post-Newtonian (PPN) equation of motion of massive bodies [2] and proved that it correctly reproduces the Lense-Thirring precession of the GP-B gyroscope. The paper [1] argues that the very same term in the equations of motion of the Moon, derived in the solar-system barycentric (SSB) frame, perturbs the lunar orbit with a radial amplitude ≃ 6 meters that was observed with the lunar laser ranging (LLR). We have explained [3] and confirm in more detail in the present paper that the gauge freedom of the relativistic three-body problem suppresses the gravitomagnetic effects in the lunar motion, that depend on the Earth's velocity V around the Sun, to the level ≤ 1 centimeter. It makes LLR currently insensitive to

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Parametrized post-Newtonian theory of reference frames, multipolar expansions and equations of motion in the N-body problem

Cited by 111 publications

References 129 publications

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

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

Post-Newtonian celestial dynamics in cosmology: Field equations

The Gravitomagnetic Influence on Earth-Orbiting Spacecrafts and on the Lunar Orbit

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