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

TL;DR

This paper derives an analytical inverse ray tracing solution within the RAMOD framework tailored for Gaia-like observations, enabling precise star position measurements in the Solar System's curved spacetime for galactic mapping.

Contribution

It provides the first analytical solution for inverse ray tracing in the RAMOD framework, specifically designed for Gaia's measurement accuracy in relativistic astrometry.

Findings

Analytical solution compatible with Gaia's measurement protocol

Validation tool for relativistic astrometry methods

Extension potential for other high-precision measurements

Abstract

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.