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Everything in the galaxy orbits the center of the combined mass of the entire galaxy. So could the center of the combined mass of the entire galaxy change if there were no external forces acting on that galaxy ? (By external I mean forces outside of the galaxy)

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Can you clarify a few points? By center do you mean the center of mass? Is the center (of mass) initially stationary? – BMS Aug 12 '14 at 0:14

I will assume you are talking about the center of mass.

If there's no external forces, the center of mass would conserve it's momentum. So, it would stay in constant speed, whatever what that speed is, with respect to whatever inertial frame of reference.

This happens because Newton's third law. In the summation of all forces, the internal forces will cancel out, leaving the external forces.

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The interesting thing about this result is that you can derive it with first year physics (even in a algebra/trig level class). Alas, most of my students look at me like I'm an idiot when I try to explain how wonderful and beautiful it is. – dmckee Aug 12 '14 at 1:07

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