barus = [Greek] heavy The barycenter is the same as the center of mass It is spelled barycentre in British English
The center of mass of a system of bodies, such as the solar system When a comet, for example, is well outside the orbit of Neptune (the farthest major planet), it sees the sun and major planets essentially as a single object of summed mass, and the center of this mass (called the barycenter of the solar system) is offset somewhat from the sun; "original" and "future" orbits of long-period comets are computed for this barycenter, while perturbed, osculating orbits of currently-observed objects in the inner solar system are computed for heliocentric orbits
From physics, this is the center of mass: the point at which a mass (body) can be considered as being concentrated without altering the effect of the attraction that the earth has upon it This is the average position ({x^i}) of particles, weighted by their masses ({m_i}): Sum_i{m_i x^i}/Sum_i{m_i} In mathematical programming, this is usually used to mean the simple average of the extreme points of a polytope: Sum_i{x^i}/m, where {x^i} = {x^1, , x^m} is the set of extreme points More generally, this could be a weighted average