I appreciate the comments from Michael Noonan. There is much that I have not taken into account, not actually being in the field. While I have worked with tensors in the past, it has been many years ago. Because I have not worked with that type of math for a long time, I could not do it any more, and other skills have taken its place. Nevertheless, the experience and knowledge in the past helps with my understanding today.

As far as dark matter is concerned, attraction increasing over a distance may account for observations that are currently attributed to dark matter. I am not saying that it would account for it, but I am stating that it is a real possibility worth considering.

Why does gravity start to increase beyond a certan distance? I do not know why. The model I have proposed just seems like a reasonable explanation for what is observed. The slowing down of our spacecraft seems to be a rather weak confirmation of the idea. It is strong enough to bring up the model as a possible answer, but I suppose it is far too weak to cite it as a confirmation of the model.

Thank you too, Jim Jast, for your comments. By "gravitational attraction" I actually ment simply "gravity" or "attraction".