A barycenter (also spelled barycentre) is the center of mass of two or more bodies that are gravitationally bound to one another. When two or more objects orbit under mutual gravitational influence, they do not orbit a fixed point within the larger body but rather orbit their common center of mass. The term derives from the Greek barys (heavy) and kentron (center). The concept applies at all scales, from binary star systems to galaxy clusters, but is most commonly discussed in the context of planetary systems, including the Solar System.

The barycenter of a two-body system is located along the line connecting the two bodies, at a distance from each body inversely proportional to their masses. For the Earth-Moon system, the barycenter lies approximately 4,671 km from Earth's center - well within Earth's radius of roughly 6,371 km - meaning the Moon technically orbits a point inside the Earth, and both bodies wobble around that shared center. For the Sun-Jupiter system, the barycenter lies just outside the Sun's surface, at roughly 1.07 solar radii from the Sun's center. When all planetary masses are considered together, the Solar System's barycenter moves in a complex, irregular path that can be as far as two solar radii from the Sun's center.

The position of the barycenter r from the first body is given by:

r = (m₂ · d) / (m₁ + m₂)

where m₁ and m₂ are the masses of the two bodies and d is the distance between them. Both bodies orbit the barycenter with the same orbital period, but with orbital radii inversely proportional to their masses.

Keplerian orbital mechanics, as formalized by Johannes Kepler in the early 17th century, described planetary orbits as ellipses with the Sun at one focus. Isaac Newton's later reformulation in the Principia Mathematica (1687) established that it is more precisely the barycenter of a two-body system that occupies the focus of each body's elliptical orbit. For most practical purposes in the Solar System, the Sun's mass so dominates that the Sun-barycenter offset introduces only small corrections. However, in precision applications - including spacecraft navigation, pulsar timing, and gravitational wave astronomy - barycentric coordinates are essential.

The distinction between heliocentric and barycentric reference frames is relevant to certain technical and philosophical debates about the nature of Solar System motion. A heliocentric model places the Sun at the center; a strictly barycentric description places no single body at the center of the system. See Heliocentrism and Heliocentrism - Scientific Consensus for related discussion.

The barycentric wobble of a star induced by an orbiting planet is one of the primary methods of exoplanet detection. As a planet orbits the system barycenter, the host star undergoes a corresponding reflex motion. Two detection techniques exploit this effect:

• Radial velocity (Doppler spectroscopy): The component of the star's barycentric motion along the line of sight produces a periodic Doppler shift in the star's spectral lines.
• Astrometry: The star's transverse motion across the sky can be measured directly if the instrumentation is precise enough.

Both methods are most sensitive to massive planets orbiting close to their host stars, which produce the largest barycentric displacement.

The physics of barycentric motion is part of classical mechanics and is not a subject of scientific dispute. Its application within heliocentric Solar System models is addressed in Heliocentrism - Scientific Consensus.

There are no significant scientific viewpoints disputing the existence or mechanics of barycenters. Disagreements that invoke barycenters tend to arise in adjacent contexts:

• Some critics of conventional heliocentric descriptions argue that because the Solar System's true center of motion is the barycenter rather than the Sun, the label “heliocentric” is technically imprecise. See Heliocentrism - Barycentric Correction Viewpoint.
• Geocentric and other alternative cosmological frameworks sometimes appeal to barycentric mechanics selectively. See Geocentrism.

• Barycenter - History
• Heliocentrism
• Heliocentrism - Scientific Consensus
• Geocentrism
• Orbital Mechanics
• Exoplanet Detection
• Newton's Law of Universal Gravitation

[(1»Newton, Isaac. Philosophiæ Naturalis Principia Mathematica. London: Royal Society, 1687. Book I, Section XI.)] [(2»Murray, C. D., and S. F. Dermott. Solar System Dynamics. Cambridge: Cambridge University Press, 1999. pp. 8-10.)] [(3»Standish, E. M. “Barycentric coordinates.” In Explanatory Supplement to the Astronomical Almanac, 3rd ed., edited by Sean E. Urban and P. Kenneth Seidelmann. Mill Valley, CA: University Science Books, 2013.)] [(4»Mayor, Michel, and Didier Queloz. “A Jupiter-mass companion to a solar-type star.” Nature 378 (1995): 355-359. doi:10.1038/378355a0.)] [(5»Perryman, Michael. The Exoplanet Handbook. 2nd ed. Cambridge: Cambridge University Press, 2018. Chapter 2.)]