The Lorentz covariant theory of propagation of light in the ( weak ) gravitational fields of N-body systems consisting of arbitrarily moving point-like bodies with constant masses m _ { a } ( a = 1 , 2 , ... ,N ) is constructed .
The theory is based on the Liénard-Wiechert representation of the metric tensor which describes a retarded type solution of the gravitational field equations .
A new approach for integrating the equations of motion of light particles ( photons ) depending on the retarded time argument is invented .
Its application in the first post-Minkowskian approximation , which is linear with respect to the universal gravitational constant , G , makes it evident that the equations of light propagation admit to be integrated straightforwardly by quadratures .
Explicit expressions for the trajectory of light ray and its tangent vector are obtained in algebraically closed form in terms of functionals of the retarded time .
General expressions for the relativistic time delay , the angle of light deflection , and the gravitational shift of electromagnetic frequency are derived in the form of instantaneous functions of the retarded time .
They generalize previously known results for the case of static or uniformly moving bodies .
The most important applications of the theory to relativistic astrophysics and astrometry are given .
They include a discussion of the velocity dependent terms in the gravitational lens equation , the Shapiro time delay in binary pulsars , gravitational Doppler shift , and a precise theoretical formulation of the general relativistic algorithms of data processing of radio and optical astrometric measurements made in the non-stationary gravitational field of the solar system .
Finally , proposals for future theoretical work being important for astrophysical applications are formulated .