A barycenter is the point between two objects where they balance each other out and their combined gravitational pull is equal. In the case of two masses orbiting, the barycenter is the point around which they both revolve.
The two masses will exert a gravitational force on each other, causing them to orbit around the barycenter. The larger the masses and the closer they are to each other, the stronger the force and the faster they will orbit.
Yes, the barycenter can be located outside of either mass if one mass is significantly larger than the other. In this case, the barycenter will be closer to the larger mass.
The distance between two masses will affect the strength of their gravitational force and the speed at which they orbit. The closer the masses are to each other, the stronger the force and the faster the orbit. Conversely, the farther apart they are, the weaker the force and the slower the orbit.
The stability of two masses orbiting their barycenter depends on the masses of the objects, their distance from each other, and their relative velocities. If these factors are balanced, the orbit will be stable. However, if one of these factors changes significantly, it can disrupt the stability of the orbit.