The ray tracing analytical solution within the RAMOD framework. The case of a Gaia-like observer

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 19 December 2013) consistently with the measurement protocol in General Relativity adopted within the RAMOD framework. The 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 calculations are performed assuming that the massive bodies of the Solar System move uniformly and have monopole and quadrupole structures. 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 as that expected for Gaia.