Microarcsecond astrometry in space - Relativistic effects and reduction of observations

Klioner, S. A.; Kopeikin, Sergei M.

doi:10.1086/116284

Cited by 96 publications

(229 citation statements)

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“…which exactly coincides with the previously known formula for a stationary rotating gravitational lens (see, e.g., the leading terms of equation (6.28) in [58]) derived using a different mathematical technique. One can also recast (72) in a simpler gradient form…”

Section: B Deflection Of Light In Gravitational Lenses and By The Sosupporting

confidence: 90%

Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary-moving and spinning bodies

2002

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Section: B Deflection Of Light In Gravitational Lenses and By The Sosupporting

confidence: 90%

Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary-moving and spinning bodies

2002

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“…in accordance with the results form the literature (e.g., Klioner & Kopeikin 1992;Bertone et al 2014). …”

Section: C1 a Single Gravitating Body At Restsupporting

confidence: 93%

“…The time delay (36) has the same form as (C-29) of Appendix C for the case of the body A moving with a constant velocity (Kopeikin 1997;Klioner & Kopeikin 1992). Klioner (1991) has estimated the effects from the translational motion of gravitating bodies.…”

Section: Mass-monopoles To 1pn Order In Motionmentioning

confidence: 99%

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Advanced relativistic VLBI model for geodesy

Söffel

Kopeikin

Han

2016

J Geod

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Abstract:Our present relativistic part of the geodetic VLBI model for Earthbound antennas is a consensus model which is considered as a standard for processing high-precision VLBI observations. It was created as a compromise between a variety of relativistic VLBI models proposed by different authors as documented in the IERS Conventions 2010. The accuracy of the consensus model is in the picosecond range for the group delay but this is not sufficient for current geodetic pur-poses. This paper provides a fully documented derivation of a new relativistic model having an accuracy substantially higher than one picosecond and based upon a well accepted formalism of relativistic celestial mechanics, astrometry and geodesy. Our new model fully confirms the consensus model at the picosecond level and in several respects goes to a great extent beyond it. More specifically, terms related to the acceleration of the geocenter are considered and kept in the model, the gravitational time-delay due to a massive body (planet, Sun, etc.) with arbitrary mass and spin-multipole moments is derived taking into account the motion of the body, and a new formalism for the time-delay problem of radio sources located at finite distance from VLBI stations is presented. Thus, the paper presents a substantially elaborated theoretical justification of the consensus model and its significant extension that allows researchers to make concrete estimates of the magnitude of residual terms of this model for any conceivable configuration of the source of light, massive bodies, and VLBI stations. The largest terms in the relativistic time delay which can affect the current VLBI observations are from the quadrupole and the angular momentum of the gravitating bodies that are known from the literature. These terms should be included in the new geodetic VLBI model for improving its consistency.

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“…Without any restriction on the ratio of the impact parameter d of the light-ray trajectory to the distance r 1 from the origin of the coordinate system to observer, the total angle of the gravitational deflection of light in the plane of the sky is given by a vector [2,36] …”

Section: B the Null-cone Integration Techniquementioning

confidence: 99%

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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Microarcsecond astrometry in space - Relativistic effects and reduction of observations

Cited by 96 publications

References 0 publications

Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary-moving and spinning bodies

Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary-moving and spinning bodies

Advanced relativistic VLBI model for geodesy

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

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