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Linet B.,CNRS Laboratory for Theoretical Physics | Teyssandier P.,CNRS Time Space Reference Systems
Classical and Quantum Gravity | Year: 2013

A new iterative method for calculating the travel time of a photon as a function of the spatial positions of the emitter and the receiver in the field of a static, spherically symmetric body is presented. The components of the metric are assumed to be expressible in power series in m/r, with m being half the Schwarzschild radius of the central body and r a radial coordinate. The procedure exclusively works for a light ray which may be described as a perturbation in powers of G of a Minkowskian null geodesic, with G being the Newtonian gravitational constant. It is shown that the expansion of the travel time of a photon along such a ray only involves elementary integrals whatever the order of approximation. An expansion of the impact parameter in power series of G is also obtained. The method is applied to explicitly calculate the perturbation expansions of the light travel time and the impact parameter up to the third order. The full expression yielding the terms of order G3 is new. This expression confirms the existence of a third-order enhanced term when the emitter and the receiver are in conjunction relative to the central body. This term is shown to be necessary for determining the post-Newtonian parameter γ at a level of accuracy of 10-8 with light rays grazing the Sun. © 2013 IOP Publishing Ltd. Source


Teyssandier P.,CNRS Time Space Reference Systems
Classical and Quantum Gravity | Year: 2012

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 finite distances 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. © 2012 IOP Publishing Ltd. Source


Lambert S.,CNRS Time Space Reference Systems
Astronomy and Astrophysics | Year: 2014

Aims. I checked the consistency of recent astrometric radio source catalogs obtained by geodetic very long baseline radio interferometry (VLBI) with the second realization of the International Celestial Reference Frame (ICRF2), released in 2009, which is the most accurate astrometric catalog currently available. Methods. The catalogs were compared to the ICRF2 in terms of radio source coordinates, global second-degree deformations, and error distribution. Results. All catalogs were found to be consistent with the ICRF2 within 20 μas. At high observational rates, the formal error is likely limited to the level of ~10 μas by correlated-noise errors. The comparison of offsets to ICRF2 against formal errors raised noise floors of the differences between 50 μas and 100 μas, and hence no improvement with respect to the ICRF2. Conclusions. The inconsistencies between catalogs result in differences significantly larger than the accuracy expected for the future realizations of the celestial reference frame. These inconsistencies have to be clarified in the near future in view of the next ICRF realization and accurate linking to reference frames at other frequencies. © 2014 ESO. Source


Bizouard C.,CNRS Time Space Reference Systems
Journal of Geodesy | Year: 2016

Because of its geophysical interpretation, Earth’s polar motion excitation is generally decomposed into prograde (counter-clockwise) and retrograde (clockwise) circular terms at fixed frequency. Yet, these later are commonly considered as specific to the frequency and to the underlying geophysical process, and no study has raised the possibility that they could share features independent from frequency. Complex Fourier Transform permits to determine retrograde and prograde circular terms of the observed excitation and of its atmospheric, oceanic and hydrological counterparts. The total prograde and retrograde parts of these excitations are reconstructed in time domain. Then, complex linear correlation between retrograde and conjugate prograde parts is observed for both the geodetic excitation and the matter term of the hydro-atmospheric excitation. In frequency domain, the ratio of the retrograde circular terms with their corresponding conjugate prograde terms favours specific values: the amplitude ratio follows a probabilistic gamma distribution centred around 1.5 (maximum for 1), and the argument ratio obeys a distribution close to a normal law centred around 2α=160∘. These frequency and time domain characteristics mean an elliptical polarisation towards α=∼80∘ East with an ellipticity of 0.8, mostly resulting from the matter term of the hydro-atmospheric excitation. Whatsoever the frequency band above 0.4 cpd, the hydro-atmospheric matter term tends to be maximal in the geographic areas surrounding the great meridian circle of longitude ∼80∘ or ∼260∘ East. The favoured retrograde/prograde amplitude ratio around 1.5 or equivalently the ellipticity of 0.8 can result from the amplification of pressure waves propagating towards the west by the normal atmospheric mode Ψ31 around 10 days. © 2015, Springer-Verlag Berlin Heidelberg. Source


Lambert S.,CNRS Time Space Reference Systems
Astronomy and Astrophysics | Year: 2013

Aims. I assess the astrometric stability of the 295 defining sources of the current best realization of the International Celestial Reference System (ICRS): the second realization of the International Celestial Reference Frame (ICRF2), constructed and published in 2009 after the analysis of millions of VLBI observations at 2 and 8 GHz between 1979.6 and 2009.2. I also assess the time evolution of the ICRF2 axis stability. Methods. I derived coordinate time series of hundreds of quasars monitored by the regular geodetic VLBI program of the International VLBI Service for Geodesy and Astrometry (IVS). The axis stability was studied by constructing annual reference frames based on the ICRF2 defining sources. The time variable frame stability was obtained by computing the deformation parameters that lead from one frame to the next. Results. I show that, although the astrometric stability of some of the ICRF2 defining sources has slightly degraded since 2009.2, the ensemble still constitutes a very stable reference frame. The current estimation of the axis stability over 1979.6-2013.1 remains at the same level as the one estimated over 1979.6-2009.2, i.e., on the order of 20 μas for each axis. © 2013 ESO. Source

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