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Wed like to examine the motion of two particles. Heres particle 1. And heres particle 2. And each particle can have some motion. In between them is the center of mass. And what wed like to do is figure out how to describe the motion of each of these particles with respect to the center of mass. So lets choose some coordinate system. Origin down here. Heres our particle r1. Heres our particle r2. And here is our center of mass. Now in the reference frame of the center of mass, we have position vector r1 prime. And we have position vector r2 prime. And what wed like to do is find expressions for r2 prime and r2 prime in terms of the positions of r1 and r2. Now we call that the position of the center of mass for this two body problem is given by m2 m1 r1 plus m2 r2 divided by the total mass. And here we use the vector triangle that r1 prime equals r1 minus center of mass. Now remember this vector is equal to this vector minus that vector. Sometimes people like to say the vector r