Given current high-precision modern space missions, a precise relativistic modeling of observations is required. By solving the eikonal equation within the post-Newtonian approximation, we use an iterative method to determine light propagation in the gravitational field of an isolated, gravitationally bound $N$-body system. Different from traditional $N$ bodies that are independent of each other within a system, our system includes the velocities, accelerations, gravitational interactions, and tidal deformations of the gravitational bodies. The light delays of these factors are then precisely determined by the analytical solutions. These delays are significant and are likely to reach a detectable level for strong gravitational fields, such as binary pulsars and some gravitational-wave sources. The result’s application in the vicinity of the Earth provides a relativistic framework for modern space missions. From the relativistic analysis in the TianQin mission, we find possible tests for alternative gravitational theories, such as a possible determination of the post-Newtonian parameter $\gamma$ at the level of some scalar-tensor theories of gravity.

• Received 16 May 2019

DOI:https://doi.org/10.1103/PhysRevD.100.064063