barycentrum

A barycenter, or barycentre, is the center of mass of two or more bodies around which they orbit under mutual gravity. In a two-body system the barycenter lies on the line connecting the bodies and moves with them; with more than two bodies it is the mass-weighted average position of all bodies in the system. If the bodies have masses m1, m2, … and position vectors r1, r2, …, the barycenter is at R_cm = (m1 r1 + m2 r2 + …) / (m1 + m2 + …). For a two-body system with separation a, the distances from the barycenter to the bodies satisfy r1 = a m2/(m1 + m2) and r2 = a m1/(m1 + m2).

Observationally, the barycenter explains the apparent motion of stars in star–planet systems. The star orbits the barycenter as the planet orbits, producing reflex motion detectable by radial-velocity measurements or astrometry. If the planet is small compared with the star, the barycenter lies well inside the star; for massive planets, the barycenter can lie near or outside the stellar surface. In the Solar System, the solar barycenter is the center of mass of the Sun, planets, and other bodies; its position relative to the Sun changes with the planetary configuration and can lie outside the Sun’s radius at times, mainly due to Jupiter’s influence.

In astronomy, barycentric coordinates and reference frames, such as the Barycentric Celestial Reference System (BCRS), are used to specify positions and motions relative to the barycenter, providing a natural framework for high-precision celestial mechanics and astrometry.