Proper stellar directions and astronomicala berration

The general relativistic definition of astrometric measurement needs an appropriate use of the concept of reference frame, which should then be linked to the conventions of the IAU Resolutions (Soffel et al., 2003), which fix the celestial coordinate system. A consistent definition of the astrometric observables in the context of General Relativity is also essential to find uniquely the stellar coordinates and proper motion, this being the main physical task of the inverse ray tracing problem. 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 light direction to a star, an essential item for deducing the star coordinates and proper motion within the same level of measurement accuracy.