Precision Measuring of Velocities via the Relativistic Doppler effect

Just as the ordinary Doppler effect serves as a tool to measure radial velocities of celestial objects, so can the relativistic Doppler effect be implemented to measure a combination of radial and transverse velocities by using recent improvements in observing techniques. A key element that makes a further use of this combination feasible is the periodicity in changes of the orbital velocity direction for the source. Two cases are considered: (i) a binary star; and (ii) a solitary star with the planetary companion. It is shown that, in case (i), several precision Doppler measurements employing the gas absorption cell technique would determine both the total orbital velocity and the inclination angle of the binary orbit disentangled from the peculiar velocity of the system. The necessary condition for that is the measured, at least with a modest precision, proper motion and distance to the system.