This paper presents the analytical solution of the inverse ray tracing
problem for photons emitted by a star and collected by an observer located in
the gravitational field of the Solar System. This solution has been conceived
to suit the accuracy achievable by the ESA Gaia satellite (launched on December
19, 2013) consistently with the measurement protocol in General relativity
adopted within the RAMOD framework. Aim of this study is to provide a general
relativistic tool for the science exploitation of such a revolutionary mission,
whose main goal is to trace back star directions from within our local curved
space-time, therefore providing a three-dimensional map of our Galaxy. The
results are useful for a thorough comparison and cross-checking validation of
what already exists in the field of Relativistic Astrometry. Moreover, the
analytical solutions presented here can be extended to model other measurements
that require the same order of accuracy expected for Gaia.Comment: 29 pages, 1 figur
