A practical relativistic model for microarcsecond astrometry in space

We develop a practical model for relativistic reduction of positional observations with an accuracy of 1 muas, which is expected to be attained in future space astrometry missions. All relativistic effects that are caused by the gravitational field of the solar system and are of practical importance for this accuracy level are thoroughly calculated and discussed. The model includes relativistic modeling of the motion of the observer and 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 the parameterized post-Newtonian formalism, with parameters beta and gamma. However, for general relativity (beta = gamma = 1) the model is fully compatible with the year 2000 IAU resolutions 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 that should be applied to the model to attain an accuracy of 0.1 muas are reviewed. Potentially important relativistic effects caused by additional gravitational fields that are generated outside of the solar system are also briefly discussed.