Post-Newtonian and Post-post-Newtonian effects in the theory of light propagation for high-precision astrometry

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The ESA astrometry missions Hipparcos (1989-1993) and Gaia (2013-2022) have established a new area in astrometric science, based on wide-field astrometry realized by global astrometric instruments which are designed to measure large angles on the sky. In particular, the Hipparcos final catalogue provides positions, proper motions, and parallaxes of stars up to 1 milli-arcsecond in angular accuracies, while the Gaia mission aims at precisions up to 5 micro-arcseconds in determining positions, proper motions, and parallaxes of stellar objects. The impressive progress made during the realization of these both cornerstone missions of ESA has encouraged the astrometric science to further proceed in nearest future. Among several astrometry missions proposed to ESA we mention the recent M-5 mission proposals Theia, NEAT, and Gaia-NIR, all of which are aiming at the sub-microarcsecond and even nano-arcsecond level of precision. Such unprecedented accuracies necessitate corresponding advancements in the theory of light propagation in the Solar system. Especially, at such level of precision it is necessary to describe the propagation of a light signal in the gravitational field of $N$ arbitrarily moving Solar system bodies having arbitrary shape, inner structure, oscillations and rotational motion. Such a general solution for light trajectories has been determined in the post-Newtonian approximation (1PN and 1.5PN) during the previous period of this DFG project. Also the problem of light propagation in the field of one arbitrarily moving point-like body in the 2PN approximation has been solved. However, there are further aspects of the theory of light propagation which are of decisive importance in order to gain the sub-microarcsecond level of astrometric precision, as there are: (1) treatment of the finite speed of gravitational action (retardation), (2) development of a highly efficient algorithm for real astrometric data reduction, (3) taking into account further 2PN effects of extended bodies, (4) transformation of the light trajectory in the reference system of a space-based observer. These investigations are in line with recent statements of the Senior-Survey-Committee (SSC) of ESA which in response of the selection of science themes for space-based astrometry missions have underlined the importance of proper modeling of light propagation in the Solar system within the general-relativistic framework as fundamental prerequisite for high-precision astrometry in near future. The envisaged project is devoted to these fundamental problems.