# Is the barycenter always at the same position?

I am currently preoccupied with the Two Body Problem and I was wondering whether the barycenter, or center of mass, is a static point or if it is moving, and how to calculate its position.

• It might help if you specify moving with respect to what? – enumaris Dec 11 '18 at 17:24
• In respect to the inertial frame of the initial position – Ian Ronk Dec 11 '18 at 18:29

If the barycenter does move, then it will satisfy the newtonian equation of motion \begin{align} \frac{\mathrm d}{\mathrm dt}\mathbf R(t) = \frac1m \mathbf P(t) \\ \frac{\mathrm d}{\mathrm dt}\mathbf P(t) = \mathbf F(t), \end{align} with $$\mathbf P(t)$$ the total momentum of the system and $$\mathbf F(t)$$ the total external force acting on the system.