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all right what i want to look at here is the period of a binary system what i want to show is that when youve got two bodies well call this one four m1 and well call this one m1 when youve got two bodies rotating about each other you should know already that they rotate about the center of mass which ill put just there but what i want to just show here is that the period for the rotation is the same for both of them might seem uh trivial and obvious but lets just show that that it is so so center of mass is there i know that you all can do the center of mass calculation thats the one where you do the x equals m1 x1 plus m2 x2 all over m1 plus m2 if you do that youll find that the center of mass here and well call this distance out to this one r1 and well call this distance r2 youll find that r1 is one quarter of r2 or four r1s equal r2 or r1s equal r2 now theres a centripetal force acting to make each of those masses go around this center of mass and the centripetal force