A spectroscopic binary star is a binary star which cannot be resolved as a visual binary, even with telescopes of the highest existing resolving power. In such binaries the separation between the stars is usually very small, and the orbital velocity very high. Unless the plane of the orbit happens to be perpendicular to the line of sight, the orbital velocities will have components in the line of sight and the observed radial velocity of the system will vary periodically. Since radial velocity can be measured with a spectroscope by observing the Doppler shift of the stars' spectral lines, the binaries detected in this manner are known as spectroscopic binaries.
In some spectroscopic binaries the spectra of both stars are visible and the lines are alternately double and single. Such stars are known as double-line binaries. In others, the spectrum of only one of the stars is seen and the lines in the spectrum move periodically from blue to red and back again.
Determining the orbit of a spectroscopic binary is done by making a long series of observations of the radial velocity of one or more component of the binary. The observations are plotted against time, and from the resulting curve a period is determined. If the orbit is circular, then the curve will be a sine curve. If the orbit is elliptical, the shape of the curve will depend on the eccentricity of the ellipse and the orientation of the major axis with reference to the line of sight.
It is impossible to determine individually the semimajor axis a and the inclination of the orbit plane i. However, the product of the semimajor axis and the sine of the inclination (i.e., asin i) may be determined directly in linear units (eg, kilometers). If either a or i can be determined by other means, as in the case of eclipsing binaries, a complete solution for the orbit can be found.