In this thread I would like to discuss aspects of this separate from some recent related threads. In particular, I prefer that proposing that mathematical results of differential geometry and well known results in GR are wrong please not occur. I have a disussion question at the end of this summary. From information provided by Sam Gralla, Bcrowell, and the links they provided (in other threads), I can see that my attempts (so far) to propose some geodesic conclusion for the two body problem were misguided. A few points I now undersstand: 1) It is exceedingly difficult to even pose the question of geodesic motion for two massive co-orbiting bodies in a meaningful way. a) However one might define it, the center of mass of body will be inside a region where the stress-energy tensor is nonzero. A geodesic in this region would seem to be saying more about the internal stresses of the object than about the overall motion of the object. It would be a complete coincidence if some COM definition followed this geodesic, and if somehow it did, the meaning would unclear. b) Trying to get around this by asking about the geodesics passing through a surface just outside one of the bodies, at some initial hypersurface, with similar motion to the body, fails because these geodesics simply represent the motion of co-moving test particles falling into the body. 2) The type of limiting argument used in the Elhers and Geroch paper to show geodesic motion from the field equations for 'test bodies' does not generalize in any obvious way to the (massive) two body problem. As I understand it, all issues with singular representations of mass points were sidestepped by a limiting regime where mass and size were decreased together, subject to reasonable energy conditions, leading to a rigorous result in the limit. However, the whole point of the massive two body problem is to incorporate radiation, so decreasing the mass will eliminate (completely, in the limit) that which we want to model. Finally my question: Can anyone propose some limiting regime in which we can even meaningfully pose the following question: whether or not two (non-spinning?) massive 'pointlike' masses in co-orbit follow geodesics of the exact two body solution (including, of course the gravitational radiaiton)? If there isn't even a way to pose this question, we are done (and I am suspicious, now, there is no reasonable way to pose this).