A binary star system is a star system with two stars orbiting around each other. Multiple star systems, such as trinaries, etc., are also usually categorized using the same term. Star systems with as many as seven mutually orbiting bodies have been classified.
It is thought that binary star systems are quite common in the universe, and may in fact be in the majority. This is because the dust cloud that collapses to form stars often has more than one center of gravity. If these are small clumps, they form planets or brown dwarfs, if large they form stars. Binary stars are said to be companion stars of one another.
Binary star systems are very important in astronomy, because mapping their mutual orbits allows one to estimate their mass. Estimating mass is useful for contrasting it against the temperature and apparent luminosity, helping us determine absolute luminosity and distance. Eclipsing binaries, where stars in a binary system eclipse each other periodically from our point of view, are especially useful. The way they mutually eclipse one another can be used to estimate their size, density, luminosity, and distance. Eclipsing binaries have been used to measure the distance to other galaxies, such as the Andromeda Galaxy and Triangulum Galaxy, with an error factor of less than 5%.
The closest star system, Alpha Centauri, is a binary star system, consisting of two closely orbiting Sun-sized stars orbited in turn by a red dwarf. The two center stars have an elliptical orbit around each other, coming as close as 11 AU and separating as far as 35 AU, and making a complete cycle every 80 years. Because of the chaotic dynamics of such a system, there is no true "habitable zone" where surface temperatures stay roughly constant. Surface temperature changes from year to year.