Light propagation in 2PN approximation in the field of one moving monopole: I. Initial value problem

In this investigation the light propagation in the gravitational field of one arbitrarily moving body with monopole structure is considered in the second post-Newtonian approximation. It is found that the light trajectory depends on the acceleration of the body. Some of these acceleration terms are important in order to get well-defined logarithmic functions with dimensionless arguments, while all the other acceleration terms are negligible on the pico-second level of accuracy in time-delay measurements. The expressions of the observables total light deflection and time delay are determined.