Gravitational Bending of Light with Frequency Shifts

Non-static gravitational fields generally introduce frequency shifts when bending light. In this paper, I discuss the frequency shifts induced in the bending of light by moving masses. As examples, I treat the recently discovered high-velocity pulsar PSR 2224+65 and a typical Einstein ring. PACS Numbers: 97.60Gb, 97.60Jd The four Jupiter probes Pioneers 10, 11 and Voyagers 1,2 have all reached solar system escape velocities by the employment of the ”sling-shot” effect. This effect involved sending the spacecraft in a trajectory such that it received a gravitational boost from Jupiter’s motion. One can say that during the time of the satellite’s proximity to Jupiter, Jupiter carried the craft along its orbit. An equivalent view is to treat the satellite-Jupiter encounter as a two-body scattering event with the spacecraft leaving with additional kinetic energy at Jupiter’s expense. The analogous situation will occur for light: