The Ray Tracing Analytical Solution within the RAMOD framework. The case of a Gaia-like observer

摘要

This paper presents the analytical solution of the inverse ray tracingproblem for photons emitted by a star and collected by an observer located inthe gravitational field of the Solar System. This solution has been conceivedto suit the accuracy achievable by the ESA Gaia satellite (launched on December19, 2013) consistently with the measurement protocol in General relativityadopted within the RAMOD framework. Aim of this study is to provide a generalrelativistic tool for the science exploitation of such a revolutionary mission,whose main goal is to trace back star directions from within our local curvedspace-time, therefore providing a three-dimensional map of our Galaxy. Theresults are useful for a thorough comparison and cross-checking validation ofwhat already exists in the field of Relativistic Astrometry. Moreover, theanalytical solutions presented here can be extended to model other measurementsthat require the same order of accuracy expected for Gaia.