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Given the high-precision modern space mission, a precise relativisticmodeling of observations is required. By solving the eikonal equation with thepost-Newtonian approximation, the light propagation is determined by theiterative method in the gravitational field of an isolated, gravitationallybound N-body system. Different from the traditional $N$ bodies that areindependent with each other in the system, our system includes the velocities,accelerations, gravitational interactions and tidal deformations of thegravitational bodies. The light delays of these factors then are preciselydetermined by the analytical solutions. These delays are significant and arelikely to reach a detectable level for the \emph{strong} gravitational fields,such as binary pulsars and some gravitational wave sources. The result'sapplication in the vicinity of the Earth provides a relativistic framework formodern space missions. From the relativistic analysis in the TianQin mission,we find the possible tests for the alternative gravitational theories, such asa possible determination for the post-Newtonian parameter $\gamma$ in the levelof some scalar-tensor theories of gravity.

Light propagation in the field of the N-body system and the application in the TianQin mission