Many people believe that the Centre of Mass Theorem is a powerful and useful tool in Newtonian Mechanics. In fact it is a farce. (1) It is trivially true at distances in which the massive object is virtually a point-mass, such as between distant stars. (2) It is completely incoherent and self-contradictory at distances in which the size of the object(s) approachs 1/20 the distance between them. Try it yourself. I'll post the simple proof that it is nonsense after a few people try to guess what is wrong.