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

Abstract

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 {mu}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 quadrupolarmore » deflection of light is caused by the physical oblateness, J{sub 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{sub 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.« less

Authors:
;  [1];  [2]
  1. Department of Physics and Astronomy, University of Missouri-Columbia, Columbia, Missouri 65211 (United States)
  2. (United States)
Publication Date:
OSTI Identifier:
21020119
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.75.062002; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; COSMOLOGY; DIPOLES; DOPPLER EFFECT; EINSTEIN FIELD EQUATIONS; GENERAL RELATIVITY THEORY; GRAVITATION; GRAVITATIONAL FIELDS; IMPACT PARAMETER; INTERFEROMETERS; ITERATIVE METHODS; JUPITER PLANET; POTENTIALS; QUADRUPOLE MOMENTS; QUADRUPOLES; RELATIVISTIC RANGE; SOLAR SYSTEM; VISIBLE RADIATION

Citation Formats

Kopeikin, Sergei M., Makarov, Valeri V., and Michelson Science Center, California Technology Institute, Pasadena, California 91125. Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.062002.
Kopeikin, Sergei M., Makarov, Valeri V., & Michelson Science Center, California Technology Institute, Pasadena, California 91125. Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers. United States. doi:10.1103/PHYSREVD.75.062002.
Kopeikin, Sergei M., Makarov, Valeri V., and Michelson Science Center, California Technology Institute, Pasadena, California 91125. Thu . "Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers". United States. doi:10.1103/PHYSREVD.75.062002.
@article{osti_21020119,
title = {Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers},
author = {Kopeikin, Sergei M. and Makarov, Valeri V. and Michelson Science Center, California Technology Institute, Pasadena, California 91125},
abstractNote = {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 {mu}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{sub 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{sub 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.},
doi = {10.1103/PHYSREVD.75.062002},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}