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Given the extreme accuracy of modern space astrometry, a precise relativisticmodeling of observations is required. Concerning light propagation, thestandard procedure is the solution of the null-geodesic equations. However,another approach based on the Time Transfer Functions (TTF) has demonstratedits capability to give access to key quantities such as the time of flight of alight signal between two point-events and the tangent vector to itsnull-geodesic in a weak gravitational field using an integral-based method. Theavailability of several models, formulated in different and independent ways,must not be considered like an oversized relativistic toolbox. Quite thecontrary, they are needed as validation to put future experimental results onsolid ground. The objective of this work is then twofold. First, we build thetime of flight and tangent vectors in a closed form within the TTF formalismgiving the case of a time dependent metric. Second, we show how to use this newapproach to obtain a comparison of the TTF with two existing modelings, namelyGREM and RAMOD. In this way, we evidentiate the mutual consistency of the threemodels, opening the basis for further links between all the approaches, whichis mandatory for the interpretation of future space missions data. This will beillustrated through two recognized cases: a static gravitational field and asystem of monopoles in uniform motion.

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