
A binary star is a system of two stars orbiting around a common center of mass.A binary star is a system of two stars orbiting a common center of mass. Periods can range from hours to millions of years. Such pairs are often born together from a single gas cloud, becoming true twins. Their dance allows direct determination of stellar masses—a fundamental characteristic governing stellar evolution. Binaries come in visual (seen separately), spectroscopic (detected by Doppler shift—the change in light frequency due to motion), eclipsing (when one star periodically blocks the other), and astrometric (an invisible companion revealed by wobbles of the visible star).
The duality of Mizar was first recorded by Riccioli in 1650. In the late 18th century, William Herschel began systematic searches for binaries and proved their orbital motion. The 19th century brought computations of the first orbits. In the 20th century, spectroscopy unveiled invisible duets, and space telescopes allowed us to discern pairs in other galaxies. Today, the Gaia mission is building a three-dimensional map of billions of stars, revealing the architecture of binary systems in the Milky Way.
Motion follows Newtonian mechanics (or general relativity for compact objects). Period and distance yield total mass. If the orbital plane lies along the line of sight, eclipses are observed with characteristic light curves. When the Roche lobe is filled, matter streams onto the accretor, forming a disk and a hot spot. This process explains cataclysmic variables, X-ray pulsars, and Type Ia supernovae. Mergers of neutron stars and black holes are detected by LIGO and Virgo detectors via gravitational-wave bursts. Kepler's third law plus spectroscopy unveil the masses of exoplanets in binary systems.
Binary stars serve as cosmic scales, allowing measurement of stellar masses and discovery of invisible objects like black holes. Their mergers generate gravitational waves and supernovae—forges of heavy elements.
The North Star, famously a guiding beacon, is itself a triple system: the bright supergiant is accompanied by two small companions.
| q | variable | Mass ratio of the binary system — mass ratio |
| m_2 | variable | Mass of the secondary component — mass kilogram |
| m_1 | variable | Mass of the primary component — mass kilogram |
| R_L | variable | Roche lobe radius — radius metre |
| a | variable | orbital separation — length metre |
| q | variable | mass ratio (M1/M2) — mass ratio |
| ln | operator | natural logarithm — natural logarithm |
| E_orb | variable | Total orbital energy of the binary system — orbital energy joule |
| M_1 | variable | Mass of the first body — mass kilogram |
| M_2 | variable | Mass of the second body — mass kilogram |
| a | variable | Semi-major axis of the relative orbit — length metre |
| G | constant | Newtonian gravitational constant, quantifying the strength of gravity — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| r_H | variable | Hill sphere radius — length metre |
| a | variable | semi-major axis — length metre |
| m | variable | mass of the smaller body — mass kilogram |
| M | variable | mass of the central body — mass kilogram |
| ∛ | operator | cube root operation — cube root |

























