348 research outputs found
Light Propagation in the Gravitational Field of Moving Bodies by means of Lorentz Transformation. I. Mass monopoles moving with constant velocities
We show how to derive the equations of light propagation in the gravitational
field of uniformly moving mass monopoles without formulating and integrating
the differential equations of light propagation in that field. The well-known
equations of light propagation in the gravitational field of a motionless mass
monopole are combined with a suitable Lorentz transformation. The possibility
to generalize this technique for the more complicated case of uniformly moving
body of arbitrary multipole structure is discussed.Comment: 10 page
Numerical versus analytical accuracy of the formulas for light propagation
Numerical integration of the differential equations of light propagation in
the Schwarzschild metric shows that in some situations relevant for practical
observations the well-known post-Newtonian solution for light propagation has
an error up to 16 microarcsecond. The aim of this work is to demonstrate this
fact, identify the reason for this error and to derive an analytical formula
accurate at the level of 1 microarcsecond as needed for high-accuracy
astrometric projects (e.g., Gaia).
An analytical post-post-Newtonian solution for the light propagation for both
Cauchy and boundary problems is given for the Schwarzschild metric augmented by
the PPN and post-linear parameters , and . Using
analytical upper estimates of each term we investigate which
post-post-Newtonian terms may play a role for an observer in the solar system
at the level of 1 microarcsecond and conclude that only one post-post-Newtonian
term remains important for this numerical accuracy. In this way, an analytical
solution for the boundary problem for light propagation is derived. That
solution contains terms of both post-Newtonian and post-post-Newtonian order,
but is valid for the given numerical level of 1 microarcsecond. The derived
analytical solution has been verified using the results of a high-accuracy
numerical integration of differential equations of light propagation and found
to be correct at the level well below 1 microarcsecond for arbitrary observer
situated within the solar system. Furthermore, the origin of the
post-post-Newtonian terms relevant for the microarcsecond accuracy is
elucidated. We demonstrate that these terms result from an inadequate choice of
the impact parameter in the standard post-Newtonian formulas
A generalized lens equation for light deflection in weak gravitational fields
A generalized lens equation for weak gravitational fields in Schwarzschild
metric and valid for finite distances of source and observer from the light
deflecting body is suggested. The magnitude of neglected terms in the
generalized lens equation is estimated to be smaller than or equal to 15 Pi/4
(m/d')^2, where m is the Schwarzschild radius of massive body and d' is
Chandrasekhar's impact parameter. The main applications of this generalized
lens equation are extreme astrometrical configurations, where 'Standard
post-Newtonian approach' as well as 'Classical lens equation' cannot be
applied. It is shown that in the appropriate limits the proposed lens equation
yields the known post-Newtonian terms, 'enhanced' post-post-Newtonian terms and
the Classical lens equation, thus provides a link between these both essential
approaches for determining the light deflection.Comment: 11 pages, 3 figure
Relativistic Celestial Mechanics with PPN Parameters
Starting from the global parametrized post-Newtonian (PPN) reference system
with two PPN parameters and we consider a space-bounded
subsystem of matter and construct a local reference system for that subsystem
in which the influence of external masses reduces to tidal effects. Both the
metric tensor of the local PPN reference system in the first post-Newtonian
approximation as well as the coordinate transformations between the global PPN
reference system and the local one are constructed in explicit form. The terms
proportional to reflecting a violation of the
equivalence principle are discussed in detail. We suggest an empirical
definition of multipole moments which are intended to play the same role in PPN
celestial mechanics as the Blanchet-Damour moments in General Relativity.
Starting with the metric tensor in the local PPN reference system we derive
translational equations of motion of a test particle in that system. The
translational and rotational equations of motion for center of mass and spin of
each of extended massive bodies possessing arbitrary multipole structure
are derived. As an application of the general equations of motion a
monopole-spin dipole model is considered and the known PPN equations of motion
of mass monopoles with spins are rederived.Comment: 71 page
Direction of light propagation to order G^2 in static, spherically symmetric spacetimes: a new derivation
A procedure avoiding any integration of the null geodesic equations is used
to derive the direction of light propagation in a three-parameter family of
static, spherically symmetric spacetimes within the post-post-Minkowskian
approximation. Quasi-Cartesian isotropic coordinates adapted to the symmetries
of spacetime are systematically used. It is found that the expression of the
angle formed by two light rays as measured by a static observer staying at a
given point is remarkably simple in these coordinates. The attention is mainly
focused on the null geodesic paths that we call the "quasi-Minkowskian light
rays". The vector-like functions characterizing the direction of propagation of
such light rays at their points of emission and reception are firstly obtained
in the generic case where these points are both located at a finite distance
from the centre of symmetry. The direction of propagation of the
quasi-Minkowskian light rays emitted at infinity is then straightforwardly
deduced. An intrinsic definition of the gravitational deflection angle relative
to a static observer located at a finite distance is proposed for these rays.
The expression inferred from this definition extends the formula currently used
in VLBI astrometry up to the second order in the gravitational constant G.Comment: 19 pages; revised introduction; added references for introduction;
corrected typos; published in Class. Quantum Gra
Gaia Early Data Release 3 : The celestial reference frame (Gaia-CRF3)
Publisher Copyright: ©Context. Gaia-CRF3 is the celestial reference frame for positions and proper motions in the third release of data from the Gaia mission, Gaia DR3 (and for the early third release, Gaia EDR3, which contains identical astrometric results). The reference frame is defined by the positions and proper motions at epoch 2016.0 for a specific set of extragalactic sources in the (E)DR3 catalogue. Aims. We describe the construction of Gaia-CRF3 and its properties in terms of the distributions in magnitude, colour, and astrometric quality. Methods. Compact extragalactic sources in Gaia DR3 were identified by positional cross-matching with 17 external catalogues of quasi-stellar objects (QSO) and active galactic nuclei (AGN), followed by astrometric filtering designed to remove stellar contaminants. Selecting a clean sample was favoured over including a higher number of extragalactic sources. For the final sample, the random and systematic errors in the proper motions are analysed, as well as the radio-optical offsets in position for sources in the third realisation of the International Celestial Reference Frame (ICRF3). Results. Gaia-CRF3 comprises about 1.6 million QSO-like sources, of which 1.2 million have five-parameter astrometric solutions in Gaia DR3 and 0.4 million have six-parameter solutions. The sources span the magnitude range G = 13-21 with a peak density at 20.6 mag, at which the typical positional uncertainty is about 1 mas. The proper motions show systematic errors on the level of 12 μas yr-1 on angular scales greater than 15 deg. For the 3142 optical counterparts of ICRF3 sources in the S/X frequency bands, the median offset from the radio positions is about 0.5 mas, but it exceeds 4 mas in either coordinate for 127 sources. We outline the future of Gaia-CRF in the next Gaia data releases. Appendices give further details on the external catalogues used, how to extract information about the Gaia-CRF3 sources, potential (Galactic) confusion sources, and the estimation of the spin and orientation of an astrometric solution.Peer reviewe
Tracing a relativistic Milky Way within the RAMOD measurement protocol
Advancement in astronomical observations and technical instrumentation
implies taking into account the general relativistic effects due the
gravitational fields encountered by the light while propagating from the star
to the observer. Therefore, data exploitation for Gaia-like space astrometric
mission (ESA, launch 2013) requires a fully relativistic interpretation of the
inverse ray-tracing problem, namely the development of a highly accurate
astrometric models in accordance with the geometrical environment affecting
light propagation itself and the precepts of the theory of measurement. This
could open a new rendition of the stellar distances and proper motions, or even
an alternative detection perspective of many subtle relativistic effects
suffered by light while it is propagating and subsequently recorded in the
physical measurements.Comment: Proceeding for "Relativity and Gravitation, 100 Years after Einstein
in Prague" to be published by Edition Open Access, revised versio
Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers
General relativistic deflection of light by mass, dipole, and quadrupole
moments of gravitational field of a moving massive planet in the Solar system
is derived. All terms of order 1 microarcsecond are taken into account,
parametrized, and classified in accordance with their physical origin. 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. The present paper gives the physical
interpretation of the observed light-ray deflections and discusses 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 the Jupiter and the
Saturn.Comment: 33 pages, 10 figures, accepted to Phys. Rev.
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