Relativistic Reduction of Astrometric Measurements

2017 ◽  
pp. 197-225
Author(s):  
V. A. Brumberg
Keyword(s):  
Relativistic Reduction

scholarly journals Relativistic Reduction of Astrometric Observations at Points Level of Accuracy

1990 ◽  
Vol 141 ◽  
pp. 229-240
Author(s):  
V. A. Brumberg ◽  
S. A. Klioner ◽  
S. M. Kopejkin
Keyword(s):  
Gravitational Field ◽  
Flat Space ◽  
Satellite System ◽  
Relativity Theory ◽  
Position Vector ◽  
Geometric Optics ◽  
General Relativity Theory ◽  
Isotropic Geodesic ◽  
Stationary Gravitational Field ◽  
Relativistic Reduction

The framework of general relativity theory (GRT) is applied to the problem of reduction of high precision astrometric observations of the order of one microarcsecond. The equations of geometric optics for the non-stationary gravitational field of the Solar system have been deduced. Integration of the equations of geometric optics results in the isotropic geodesic line connecting the source of emission (a star, a quasar) and an observer. This permits to calculate the effects of relativistic aberration of light due to monopole and quadrupole components of the gravitational field of the Sun and the planets taking into account their motions and rotation. Transformations between the reference systems are used to calculate the light aberration occurring when passing from the satellite system to the geocentric system and from the geocentric system to the baryecntric system. The baryecntric components of the observed position vector reduced to the flat space-time are corrected, if necessary, for parallax and proper motion of a celestial object using the classical techniques of Euclidean geometry.

Studies on the retarded interaction between neutral atoms - I. Three-body London-van der Waals interaction of neutral atoms

1960 ◽  
Vol 257 (1291) ◽  
pp. 464-476 ◽  
Keyword(s):  
Interaction Energy ◽  
Quantum Electrodynamics ◽  
Dipole Approximation ◽  
Neutral Atoms ◽  
Approximation Result ◽  
Atomic Transitions ◽  
Body Interaction ◽  
Three Body ◽  
Dipole Energy ◽  
Relativistic Reduction

An expression for the non-additive, three-body interaction energy of three neutral atoms is deduced, by the methods of quantum electrodynamics. Non-relativistic reduction and dipole approximation result in an expression which for interatomic separations R small compared to the wavelengths of typical atomic transitions reduces to the triple-dipole energy varying as R –9 (Axilrod & Teller), whereas at distances large compared with these wavelengths, the three-body interaction energy becomes proportional to R –10 , owing to the influence of retardation.

scholarly journals Non-relativistic reduction of spinors, new currents and their algebra

2020 ◽  
Vol 954 ◽  
pp. 114994
Author(s):  
Rabin Banerjee ◽  
Debashis Chatterjee
Keyword(s):  
Relativistic Reduction

scholarly journals Relativistic Reduction of Astrometric Observations

1986 ◽  
Vol 109 ◽  
pp. 19-42 ◽  
Author(s):  
V. A. Brumberg
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Satellite Observations ◽  
List Type ◽  
Type Number ◽  
General Technique ◽  
Two Body Problem ◽  
The One ◽  
Relative Measurements ◽  
Relativistic Reduction

The nonuniqueness of the quasi-Galilean coordinates of general relativity leads to the emergence of unmeasurable coordinate-dependent quantities in astronomical practice. One may offer three possible ways to overcome the related difficulties: 1.developing theoretical conclusions only in terms of measurable quantities2.using arbitrary coordinates and developing an unambiguous procedure for comparing measurable and calculated quantities3.agreement to utilize one and only one coordinate system.In this paper we prefer the second way. After formulating the heliocentric planetary and geocentric satellite equations of motion, the general technique for relativistic reduction in astrometry and geodynamics is developed. Specific algorithms for the reduction of absolute and relative measurements are derived for the one- and the two- body problem. For illustration, the relativistic reduction of stellar parallaxes, Doppler satellite observations, navigation measurements with the aid of satellites and radiointerferometric measurements are presented in detail.

scholarly journals Possible Relativistic Definitions of Parallax, Proper Motion and Radial Velocity

2000 ◽  
Vol 180 ◽  
pp. 308-313 ◽  
Author(s):  
S. Klioner
Keyword(s):  
Radial Velocity ◽  
Observational Data ◽  
Proper Motion ◽  
Relativistic Reduction

AbstractIt is argued that the relativistic definitions of parallax, proper motion and radial velocity consistent with an accuracy of 1 μas should be considered only within a well-defined algorithm of relativistic reduction of observational data. Such an algorithm is formulated and the corresponding definitions of astrometric parameters are discussed.

scholarly journals Relativistic Reduction of Astronomical Measurements and Reference Frames

1980 ◽  
Vol 56 ◽  
pp. 283-294
Author(s):  
V. A. Brumberg
Keyword(s):  
Light Propagation ◽  
Reference Frames ◽  
Relativistic Effects ◽  
Propagation Characteristics ◽  
Lunar Laser Ranging ◽  
Schwarzschild Metric ◽  
The Earth ◽  
Lunar Laser ◽  
Relativistic Treatment ◽  
Relativistic Reduction

AbstractWith the accuracy of modern observations the relativistic treatment of the basic astronomical reference frames only requires the consideration of comparatively simple types of metrics such as heliocentric Schwarzschild metric, geocentric Schwarzschild metric and metric of the Earth-Sun system. Dynamical (related to the motion of the bodies) and kinematical (related to the light propagation) characteristics of these metrics enable one to perform the accurate relativistic reduction of astronomical measurements. In this reduction, the choice of specific quasi-Galilean coordinates may remain arbitrary. This paper presents expressions for the main relativistic terms in coordinates of the principal planets and Moon using the PPN formalism parameters β, γ and coordinate parameter α. General formulae for the reduction of radar, radio-interferometric and astrometric observations of planets and for the interpretation of lunar laser ranging are given. For estimating the actual magnitude of relativistic effects, the ephemeris data should be expressed in terms of physically measurable quantities.

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