From the spectrum of a single star we can obtain an estimate of its surface temperature and also, from the width of the spectral lines, a crude estimate of the surface gravity. If we know the distance to the star, we can deduce its luminosity from its apparent magnitude and hence, by applying Stefan’s Radiation Law, an estimate of its radius. Having found the specific gravity and the radius, we can arrive at a crude estimate of the star’s mass.

If the star is in a binary system, we are in a much stronger position and have many more possibilities open to us than in the case of solitary stars. It is possible to deduce from observations of binary stars the masses of individual stars and also their radii. It is, in fact, solely because of the study of binary stars, that astronomers feel that they know the masses and sizes of stars with some confidence. Theoretical studies based on these data, for example stellar evolution, which is of central importance to astrophysics, have reasonably solid foundations.

Most known binary systems appear to us as a single point of light because they are too far away for the two stars to be resolved separately. Such stars fall into two categories. For spectroscopic binaries, the binary nature is inferred from periodic shifts of the wavelengths of the spectral lines caused by the Doppler effect as the stars swing round each other. For eclipsing binaries, the duplicity is inferred from the regular variation of the brightness of the system which is interpreted as the eclipsing of one star by the other in each orbit.
It is sometimes found that one star of a binary system is, in fact, a binary system in its own right and the system as a whole is then called a TRIPLE SYSTEM. For example, the star Milburn 377 (also known as Vyssotsky 2) was originally thought to be just a visual binary consisting of a 10.5-mag M2 dwarf and a 12.5-mag M4 dwarf with a period of about 320 years. However it was found later that the brighter star is itself an astrometric binary and revolves around an unseen companion once every 15.9 years

The two components of Mizar are both spectroscopic binaries and there is evidence that the fainter one may be a triple system. Mizar itself may be a quintuple system! Alcor travels along a path parallel to that of Mizar. If Alcor and Mizar form a wide binary system, the system is at least quintuple and possibly sextuple. Multiple systems appear to be stable only when they are formed in a hierarchical structure of binary systems, with each binary pair acting as a single component in an even larger binary system. For this reason we now turn our attention to binary systems. These stars are of consider¬able importance in astrophysics because it is possible to determine many properties, especially sizes and masses, that cannot be found for single stars. In view of their value to astrophysics we shall first show how the orbits of binary stars are analysed in order to deter¬mine the physical properties.

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