How does the above model comply with Newton's third law?

The above model is really a model for the motion of a single body in a field which has spherical symmetry. The second body of mass $M$ is completely ignored. However, if we have two bodies, which are connected by a symmetric force (which Newton's third law implies) any motion of the smaller body will be accompanied by a motion of the larger body. We will, however, prove that in many cases this motion of the larger body can be ignored. But we will also give several significant examples, where it can't be.