Barycenter (astronomy)

The distance from a body's center of mass to the barycenter can be calculated as a two-body problem.

In a simple two-body case, the distance from the center of the primary to the barycenter, r1, is given by: where : The semi-major axis of the secondary's orbit, r2, is given by r2 = a − r1.

But all celestial orbits are elliptical, and the distance between the bodies varies between the apses, depending on the eccentricity, e. Hence, the position of the barycenter varies too, and it is possible in some systems for the barycenter to be sometimes inside and sometimes outside the more massive body.

In classical mechanics (Newtonian gravitation), this definition simplifies calculations and introduces no known problems.

In general relativity (Einsteinian gravitation), complications arise because, while it is possible, within reasonable approximations, to define the barycenter, we find that the associated coordinate system does not fully reflect the inequality of clock rates at different locations.

Brumberg explains how to set up barycentric coordinates in general relativity.

Individual clocks of similar construction will not agree with this standard, because they are subject to differing gravitational potentials or move at various velocities, so the world-time must be synchronized with some ideal clock that is assumed to be very far from the whole self-gravitating system.