
The gravitational and orbital interactions between pairs of stars, including effects on dark matter and planetary ejection.Binary star dynamics is the study of how two stars orbit each other under gravity, and how that orbital dance shapes their evolution, their surroundings, and even the fate of any planets they host. Most stars in the Milky Way are in binary or multiple systems, so understanding these interactions is essential for explaining phenomena like stellar mergers, X-ray binaries, and the production of gravitational waves. The gravitational pull of a companion can distort a star's shape, drive mass transfer, and dramatically alter the star's rotation and magnetic activity.
The study began with William Herschel's discovery of binary stars in 1802, and the first orbit calculation was done by Félix Savary in 1827. Modern understanding of mass transfer and Roche lobe overflow was developed in the 1960s by researchers like Bohdan Paczyński.
The dynamics are governed by Newtonian gravity, with corrections from general relativity when the stars are compact or close. The two stars orbit their common center of mass, and their mutual tides can synchronize rotation and circularize the orbit over time. When a third body — like a planet — is present, the binary's gravitational perturbations can excite eccentricity in the planet's orbit, sometimes ejecting it entirely. In close binaries, one star can overflow its Roche lobe, spilling gas onto the companion, which can ignite nova eruptions or, if the accretor is a neutron star or black hole, produce bright X-ray emission.
Binary star dynamics is used to detect exoplanets in binary systems, to predict gravitational wave sources for detectors like LIGO, and to calibrate stellar evolution models by measuring precise masses and radii.
In a binary system, a planet can be ejected at speeds exceeding the escape velocity of the galaxy, becoming a free-floating 'rogue planet' that wanders interstellar space.
| 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 |






