A Practical Relativistic Model of Microarcsecond Astrometry in Space

Abstract

This paper is devoted to a practical model for relativistic reduction of positional observations with an accuracy of 1 \muas which is expected to be attained in the future space astrometry missions. All relativistic effects which are caused by the gravitational field of the Solar system and which are of practical importance for this accuracy level are thoroughly calculated and discussed. The model includes relativistic modeling of the motion of observer, modeling of relativistic aberration and gravitational light deflection as well as a relativistic treatment of parallax and proper motion suitable for the accuracy of 1 \muas. The model is formulated both for remote sources (stars, quasars, etc.) and for Solar system objects (asteroids, etc.). The suggested model is formulated within the framework of Parametrized Post-Newtonian Formalism with parameters $β$ and $γ$. However, for general relativity ($β=γ=1$) the model is fully compatible with the IAU Resolutions (2000) on relativity in celestial mechanics, astrometry and metrology. The model is presented in a form suitable for implementation in a software system for data processing or simulation. The changes which should be applied to the model to attain the accuracy of 0.1 \muas are reviewed. Potentially important relativistic effects caused by additional gravitational fields which are generated outside of the Solar system are also briefly discussed.