General relativistic observable for gravitational astrometry in the context of the Gaia mission and beyond

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.