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

欧空局的“希巴谷”（1989-1993）和“盖亚”（2013-2022）天文测量任务建立了天体测量科学的一个新领域，其基础是利用设计用于测量天空大角度的全球天体测量仪器实现的宽视场天体测量。特别是，依巴谷望远镜的最终目录提供的恒星位置、固有运动和视差的角精度可达1毫角秒，而盖亚任务的目标是确定恒星物体的位置、固有运动和视差的精度可达5微角秒。欧空局在实现这两项基石任务期间取得的令人印象深刻的进展，鼓励了天体测量科学在不久的将来进一步发展。在向欧空局提出的几个天体测量任务中，我们提到了最近的M-5任务提案Theia， NEAT和Gaia-NIR，它们的目标都是亚微弧秒甚至纳弧秒级别的精度。如此空前的精确度要求光在太阳系中的传播理论有相应的进步。特别是，在这样的精度水平上，有必要描述光信号在具有任意形状、内部结构、振荡和旋转运动的任意移动的太阳系物体的引力场中的传播。在此DFG项目的前期工作中，已经在后牛顿近似（1PN和1.5PN）中确定了光轨迹的一般解。同时也解决了任意移动的点状体在2PN近似下的光在场中的传播问题。然而，为了获得亚微弧秒级别的天文测量精度，光传播理论的其他方面也具有决定性的重要性，如：(1)处理引力作用的有限速度（延迟）；(2)开发一种高效的实际天体测量数据约简算法；(3)进一步考虑扩展体的2PN效应；(4)天基观测者参考系统中的光轨迹变换。这些研究与欧空局高级调查委员会（SSC）最近的声明是一致的，该委员会在回应天基天体测量任务的科学主题选择时强调了在广义相对论框架内对太阳系中的光传播进行适当建模的重要性，这是在不久的将来高精度天体测量的基本先决条件。设想的项目致力于解决这些基本问题。

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.