Introduction

The fundamental equations, relationships, and definitions that we considered in Chapter 2 can be applied directly to interpretation of observational data on binary stars from four types of experiments. The first is spectroscopy, which yields measurements of line-of-sight (or radial) velocities, followed by derivation of the elements of the orbits from those observed velocities. These data furnish the quantities related to the absolute sizes of the orbits and to the masses of the stars in binary systems. The second is pulse timing: measurements of the times of arrival of short pulses of radiation from x-ray and radio pulsars that are found to be members of binary systems, followed by derivation of the relevant orbital elements. Nature has been kind enough to provide us with the kinds of binary stars that will permit both of these independent types of observations to be carried out, with the result that quite complete descriptions of the systems are possible, and observational astronomy can yield directly determined masses for the intriguing end states of stellar evolution: neutron stars and black holes. The third experiment is astrometry: accurate determination of the positions of the components of resolved binaries, both relative to each other and relative to a fundamental astrometric reference frame over the whole sky. Once again, we find some binary systems for which both astrometric data and radial-velocity data are available, so that complete descriptions can be established.