General relativistic satellite astrometry I. A non-perturbative approach to data reduction

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 μarcsec 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 μarcsec (as expected for V' 16 mag stars), repeated over an observing period of only one year can be modeled to yield ∼ 20 μarcsec 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.