Time transfer functions as a way to validate light propagation solutions for space astrometry

Given the extreme accuracy of modern space astrometry, a precise relativistic
modeling of observations is required. Concerning light propagation, the
standard procedure is the solution of the null-geodesic equations. However, another approach based on the time transfer functions (TTF) has demonstrated its capability to give access to key quantities such as the time of flight of a light signal between two point-events and the tangent vector to its null-geodesic in a weak gravitational field using an integral-based method. The availability of several models, formulated in different and independent ways, must not be considered like an oversized relativistic toolbox. Quite the contrary, they are needed as validation to put future experimental results on solid ground. The objective of this work is then twofold. First, we build the time of flight and tangent vectors in a closed form within the TTF formalism giving the case of a time-dependent metric. Second, we show how to use this new approach to obtain a comparison of the TTF with two existing modelings, namely the Gaia RElativistic Model (GREM) and the Relativistic Astrometric MODel (RAMOD). In this way, we highlight the mutual consistency of the three models, opening the basis for further links between all the approaches, which is mandatory for the interpretation of future space missions data. This will be illustrated through two recognized cases: a static gravitational field and a system of gravitational mass monopoles in uniform motion.