  Given the high-precision modern space mission, a precise relativistic
modeling of observations is required. By solving the eikonal equation with the
post-Newtonian approximation, the light propagation is determined by the
iterative method in the gravitational field of an isolated, gravitationally
bound N-body system. Different from the traditional $N$ bodies that are
independent with each other in the system, our system includes the velocities,
accelerations, gravitational interactions and tidal deformations of the
gravitational bodies. The light delays of these factors then are precisely
determined by the analytical solutions. These delays are significant and are
likely to reach a detectable level for the \emph{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 the possible tests for the alternative gravitational theories, such as
a possible determination for the post-Newtonian parameter $\gamma$ in the level
of some scalar-tensor theories of gravity.
