Statistics proved that many double stars are true partners, not coincidences
Two stars that look close in the sky might simply line up by chance, one near and one far away. In 1767 the English clergyman John Michell tested that idea mathematically. Studying the Pleiades, he calculated odds of about one in half a million for such a tight cluster arising by accident, and concluded gravity must bind them.
Michell's paper was the first application of statistics to the stars, and gave the first evidence that stars really do come in bound pairs and groups. Telescopes had already revealed plenty of doubles: Giovanni Battista Riccioli saw that Mizar in the Big Dipper was two stars in 1650, and the bright southern star Acrux was split in 1685. William Herschel then went hunting for pairs, hoping a near star beside a distant one would let him measure its distance through parallax. After tracking some for 25 years, he found instead that they were circling each other, and in 1802 he coined the term binary for such systems.
Astronomers now separate true binaries, which orbit a shared centre of mass, from optical doubles that merely appear side by side. The US Naval Observatory's catalogue listed over 100,000 double stars by 2017, yet orbits are known for only a few thousand, since many take centuries to complete a single circuit. Félix Savary computed the first orbit, for Xi Ursae Majoris, in 1827.
Most binaries are too close to see as two points of light, so other clues give them away. In spectroscopic binaries, each star's light shifts toward blue as it approaches and toward red as it recedes, revealing an orbit invisible to the eye. Eclipsing binaries, whose orbits lie edge-on to Earth, dim regularly as one star passes in front of the other; Algol in Perseus is the classic example. Rarely, about 40 known systems can be both seen as pairs and measured spectroscopically, making them especially valuable.
Binaries matter because they let astronomers weigh stars directly and test ideas about how stars age. Close pairs can distort each other's outer layers and even swap material, sending them down evolutionary paths a lone star could never take. Such partnerships give rise to novae and type Ia supernovae, and one famous binary, Cygnus X-1, contains a black hole.
Source: Binary star