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I have a three body system of point masses that represent mercury, earth and the sun. I want them to orbit about a common centre of mass, but I think the centre of mass will move. I need the centre of mass to always remain at the origin.

If I move the bodies a certain amount, find the new position of the centre of mass and subtract it from the new positions of the planets, does that mean the centre of mass is still at the origin? Or do I also need to do some calculation using the velocity of the centre of mass?

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  • $\begingroup$ The center of mass of a closed system of masses will follow an inertial trajectory, so it's possible to choose a reference frame in which it does not and will never move. $\endgroup$
    – Brionius
    Dec 4, 2015 at 23:53
  • $\begingroup$ Once I did the very same exercise and had the same problem. I simply calculated the total momentum of the system, divided it by the total mass and got the velocity of the center of mass. Then I substracted that velocity to every body of the system. Done: the system is equivalent and the center of mass has velocity 0. $\endgroup$
    – rodrigo
    Dec 5, 2015 at 0:05

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