Relativistic theory of astronomical reference systems in closed form

Klioner, S. A.; Voinov, A. V.

doi:10.1103/physrevd.48.1451

Cited by 46 publications

(67 citation statements)

References 16 publications

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“…However, after the structure of the PPN coordinate transformation is found the domain of applicability of the local coordinates can be stretched out up to much larger distances (see text below after Eq. (7.3.12) and papers [47,61,105] for more detail).…”

Section: Preliminary Remarksmentioning

confidence: 99%

“…instantaneous orientation of the barycentric coordinates fixed by the position of the vernal equinox as it was located on the sky in 2000AD or 1950AD). Post-Newtonian coordinate transformation from the local to global frame is an inalienable part in the procedure of derivation of the general relativistic equations of motion of test and/or extended bodies in the solar system [1,41,42,43,45,56,57,58,59,60,61,69,70,105,106] as well as compact relativistic stars in binary systems emitting gravitational waves [67,79,95,96,107,108]. It is widely accepted that scalar fields must exist since they provide elegant explanation for various effects and phenomena encountered by modern theoretical physics of fundamental particle interactions, gravitation and cosmology [109].…”

Section: Preliminary Remarksmentioning

confidence: 99%

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

2004

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Section: Preliminary Remarksmentioning

confidence: 99%

Section: Preliminary Remarksmentioning

confidence: 99%

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

2004

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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%

“…x 0 x cos ÿ y sin ; y 0 x sin y cos : (57) In the new coordinates, the dipolar mapping transformation is deduced from Eq. (52) and is given by (58) where p rL=X.…”

Section: Dynamic Patternsmentioning

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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“…Not going into complicated details of constructing the global and local reference systems (see, e.g., Brumberg, Kopejkin (1989); Kopejkin (1988); Damour, Soffel, Xu (1991); Klioner, Voinov (1993) for details), let us write down the generic form of the metric tensor which is valid for both the BRS and the GRS…”

Section: Relativistic Reference Systemsmentioning

confidence: 99%

Angular velocity of rotation of extended bodies in general relativity

Klioner

1996

Symp. - Int. Astron. Union

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Abstract. We consider rotational motion of an arbitrarily composed and shaped, deformable weakly self-gravitating body being a member of a system of Ν arbitrarily composed and shaped, deformable weakly selfgravitating bodies in the post-Newtonian approximation of general relativity. Considering importance of the notion of angular velocity of the body (Earth, pulsar) for adequate modelling of modern astronomical observations, we are aimed at introducing a post-Newtonian-accurate definition of angular velocity. Not attempting to introduce a relativistic notion of rigid body (which is well known to be ill-defined even at the first post-Newtonian approximation) we consider bodies to be deformable and introduce the postNewtonian generalizations of the Tisserand axes and the principal axes of inertia.

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Relativistic theory of astronomical reference systems in closed form

Cited by 46 publications

References 16 publications

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

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

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

Angular velocity of rotation of extended bodies in general relativity

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