Radial velocity spectrometers. What they measure

This report provides the theoretical analysis, within the framework of special relativity, for the information content of a radial velocity spectrometer. This device is an automated telescope photometer spectrometer combination. It measures the displacement between a Doppler shifted set of spectral lines and its at-rest version. Thus, it provides a measurement of radial velocity. Exactly what kinematical content is revealed by such a measurement within the solar system is brought out herein. The discussion is couched in terms of a satellite-based sensor observing another orbiting body. Both objects are presumed to orbit about the Earth. Sufficient generality is presented to treat any other case also. In the specific case of interest, both the topocentric distance and the topocentric radial velocity are present in the measured quality.