General Relativistic Satellite Astrometry (original) (raw)
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General relativistic satellite astrometry: II. Modeling parallax and proper motion
Astronomy & Astrophysics, 2001
The non-perturbative general relativistic approach to global astrometry introduced by de Felice et al. (1998) is here extended to account for the star motions on the Schwarzschild celestial sphere. A new expression of the observables, i.e. angular distances among stars, is provided, which takes into account the effects of parallax and proper motions. This dynamical model is then tested on an end-to-end simulation of the global astrometry mission GAIA. The results confirm the findings of our earlier work, which applied to the case of a static (angular coordinates only) sphere. In particular, measurements of large arcs among stars (each measurement good to ∼100 µarcsec, as expected for V ∼ 17 mag stars) repeated over an observing period comparable to the mission lifetime foreseen for GAIA, can be modeled to yield estimates of positions, parallaxes, and annual proper motions good to ∼15 µarcsec. This second round of experiments confirms, within the limitations of the simulation and the assumptions of the current relativistic model, that the space-born global astrometry initiated with Hipparcos can be pushed down to the 10 −5 arcsec accuracy level proposed with the GAIA mission. Finally, the simplified case we have solved can be used as reference for testing the limiting behavior of more realistic models as they become available.
General relativistic satellite astrometry. I. A non-perturbative approach to data reduction
Astronomy & Astrophysics, 1998
A general relativistic scenario is utilized to build a non-perturbative model, in Schwarzschild metric, for the representation of observed angles among star pairs. This model is then applied to an end-to-end simulation of the GAIA satellite, a concept for global astrometry within the 2000+ scientific program of the European Space Agency. GAIA is expected to measure positions, parallaxes, and annual proper motions to better than 20 mu arcsec for more than 50 million stars brighter than V =~ 16 mag. This first attempt at modeling global astrometric data within the framework of general relativity considers a static sphere, namely, only Schwarzschild azimuth and colatitude are estimated, locating stars on the Schwarzschild sphere centered at the Sun. The results show that measurements of large arcs among stars, each measurement good to ~ 100 mu arcsec (as expected for V =~ 16 mag stars), repeated over an observing period of only one year can be modeled to yield ~ 20 mu arcsec errors on the estimated relativistic parameters. Although it remains to be established if the non-perturbative approach can be extended to a more realistic observing scenario (including the oblate and rotating Sun, and the other planets of the solar system), these results provide strong evidence that the lessons learned with Hipparcos apply to the 10(-5) arcsec regime of the GAIA mission.
Some Aspects of Relativistic Astrometry from Within the Solar System
Celestial Mechanics & Dynamical Astronomy, 2003
In this article we outline the structure of a general relativistic astrometric model which has been developed to deduce the position and proper motion of stars from 1 µarcsecond optical observations made by an astrometric satellite orbiting around the Sun. The basic assumption of our model is that the Solar System is the only source of gravity, hence we show how we modeled the satellite observations in a many-body perturbative approach limiting ourselves to the order of accuracy of (v/c)2. The microarcsecond observing scenario outlined is that for the GAIA astrometric mission.
Gaia relativistic astrometric models
Astronomy and Astrophysics, 2010
The high accuracy achievable by modern space astrometry requires the use of General Relativity to model the stellar light propagation through the gravitational field encountered from a source to a given observer inside the Solar System. The general relativistic definition of an astrometric measurement needs an appropriate use of the concept of reference frame, which should then be linked to the conventions of the IAU resolutions. On the other hand, a definition of the astrometric observables in the context of General Relativity is also essential for finding the stellar coordinates and proper motion uniquely, this being the main physical task of the inverse raytracing problem. The aim of this work is to set the level of reciprocal consistency of two relativistic models, GREM and RAMOD (Gaia, ESA mission), in order to guarantee a physically correct definition of the light's local direction to a star and deduce the star coordinates and proper motions at the level of accuracy required by these models consistently with the IAU's adopted reference systems.
Physical Review D
With the launch of the Gaia mission, general relativity (GR) is now at the very core of astrometry. Given the high level of accuracy of the measurements, the development of a suitable relativistic model for carrying out the correct data processing and analysis has become a critical necessity; its primary goal is to have a consistent set of stellar astrometric parameters by which to map a relativistic kinematic of a large portion of the Milky Way and, therefore, taking the first step of the cosmic distance ladder to higher accuracy. To trace light trajectories back to the emitting stars requires an appropriate treatment of local gravity and a relativistic definition of the observable, according to the measurement protocol of GR, so that astrometry cannot be set apart from fundamental physics. Consequently, the final Gaia outputs, following completion of its operational life, will have important new implications and an overwhelming potential for astrophysical phenomena requiring the highest precision. In this regard, the present work establishes the background GR procedure to treat such relativistic measurements from within the weak gravitational field of the Solar System. In particular, we make the method explicit in the framework of the RAMOD relativistic models, consistent with the IAU (standard) resolutions and, therefore, suitable for validating the GREM approach baselined for Gaia.
Astrometric tests of General Relativity in the Solar system
Journal of Physics: Conference Series, 2014
We review the mathematical models available for relativistic astrometry, discussing the different approaches and their accuracies in the context of the modern experiments from space like Gaia and GAME, and we show how these models can be applied to the real world, and their consequences from the mathematical and numerical point of view, with specific reference to the case of Gaia, whose launch is due before the end of the year.
Application of time transfer functions toGaia’s global astrometry
Astronomy & Astrophysics, 2017
Context. A key objective of the ESA Gaia satellite is the realization of a quasi-inertial reference frame at visual wavelengths by means of global astrometric techniques. This requires accurate mathematical and numerical modeling of relativistic light propagation, as well as double-blind-like procedures for the internal validation of the results, before they are released to the scientific community at large. Aims. We aim to specialize the time transfer functions (TTF) formalism to the case of the Gaia observer and prove its applicability to the task of global sphere reconstruction (GSR), in anticipation of its inclusion in the GSR system, already featuring the Relativistic Astrometric MODel (RAMOD) suite, as an additional semi-external validation of the forthcoming Gaia baseline astrometric solutions. Methods. We extended the current GSR framework and software infrastructure (GSR2) to include TTF relativistic observation equations compatible with Gaia's operations. We used simulated data generated by the Gaia Data Processing and Analysis Consortium (DPAC) to obtain different least-squares estimations of the full (five-parameter) stellar spheres and gauge results. These were compared to analogous solutions obtained with the current RAMOD model in GSR2 (RAMOD@GSR2) and to the catalog generated with the Gaia RElativistic Model (GREM), the model baselined for Gaia and used to generate the DPAC synthetic data. Results. Linearized least-squares TTF solutions are based on spheres of about 132 000 primary stars uniformly distributed on the sky and simulated observations spanning the entire 5 yr range of Gaia's nominal operational lifetime. The statistical properties of the results compare well with those of GREM. Finally, comparisons to RAMOD@GSR2 solutions confirmed the known lower accuracy of that model and allowed us to establish firm limits on the quality of the linearization point outside of which an iteration for nonlinearity is required for its proper convergence. This has proved invaluable as RAMOD@GSR2 is prepared to go into operations on real satellite data.
Journal of Physics: Conference Series, 2014
We review the mathematical models available for relativistic astrometry, discussing the different approaches and their accuracies in the context of the modern experiments from space like Gaia and GAME, and we show how these models can be applied to the real world, and their consequences from the mathematical and numerical point of view, with specific reference to the case of Gaia, whose launch is due before the end of the year.
2000
The accuracy of astrometric observations conducted via a space-borne optical interferometer orbiting the Earth is expected to approach a few microarcseconds. Data processing of such extremely high-precision measurements requires access to a rigorous relativistic model of light ray propagation developed in the framework of General Relativity. The data-processing of the space interferometric observations must rely upon the theory of generalrelativistic transformations between the spacecraft, geocentric, and solar barycentric reference systems allowing unique and unambiguous interpretation of the stellar aberration and parallax effects. On the other hand, the algorithm must also include physically adequate treatment of the relativistic effect of light deflection caused by the spherically-symmetric (monopoledependent) part of the gravitational field of the Sun and planets as well as the quadrupoleand spin-dependent counterparts of it. In some particular cases the gravitomagnetic field induced by the translational motion of the Sun and planets should be also taken into account for unambigious prediction of the light-ray deflection angle. In the present paper we describe the corresponding software program for taking into account all classical (proper motion, parallax, etc.) and relativistic (aberration, deflection of light) effects up to the microarcsecond threshold and demonstrate, using numerical simulations, how observations of stars and/or quasars conducted on board a space optical interferometer orbiting the Earth can be processed and disentangled. For doing numerical simulations the spacecraft orbital parameters and the telescope optical-system-characteristics have been taken to be similar to those in the HIPPARCOS mission. The performed numerical data analysis verifies that the relativistic algorithm chosen for data processing is convergent and can be used in practice for determining astronomical coordinates and proper motions of stars (quasars) with the required microarcsecond precision. Results shown in the paper have been obtained with the rather small number of stars (a few thousand). Simulations which are based on a much larger number of stars taken, e.g., from the Guide Star Catalogue used for modelling original observations are to give more complete information about potential abilities of the space astrometric missions.