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Propagation of light in the gravitational field of self-gravitating spinningbodies moving with arbitrary velocities is discussed. The gravitational fieldis assumed to be "weak" everywhere. Equations of motion of a light ray aresolved in the first post-Minkowskian approximation that is linear with respectto the universal gravitational constant $G$. We do not restrict ourselves withthe approximation of gravitational lens so that the solution of light geodesicsis applicable for arbitrary locations of source of light and observer. Thisformalism is applied for studying corrections to the Shapiro time delay inbinary pulsars caused by the rotation of pulsar and its companion. We alsoderive the correction to the light deflection angle caused by rotation ofgravitating bodies in the solar system (Sun, planets) or a gravitational lens.The gravitational shift of frequency due to the combined translational androtational motions of light-ray-deflecting bodies is analyzed as well. We givea general derivation of the formula describing the relativistic rotation of theplane of polarization of electromagnetic waves (Skrotskii effect). This formulais valid for arbitrary translational and rotational motion of gravitatingbodies and greatly extends the results of previous researchers. Finally, wediscuss the Skrotskii effect for gravitational waves emitted by localizedsources such as a binary system. The theoretical results of this paper can beapplied for studying various relativistic effects in microarcsecond spaceastrometry and developing corresponding algorithms for data processing in spaceastrometric missions such as FAME, SIM, and GAIA.Comment: 36 pages, 1 figure, submitted to Phys. Rev.

Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary-moving and spinning bodies