I followed your logic pretty well and what I find is that the element of gravity which Newton found necessary does really remain in your transformed (simplified perhaps) though you have managed to bury it within "constants".
Can we start by recalling the inadequacy of our mathematics? We, at best, deal in approximations knowing that, at some point, math, which is only a language after all, will fail us. Usually by that time a satisfactory conclusion is reached so no matter.
Gravity does not require motion, relative or not, to remain a force. An object in space may be seen as a singularity but only when something else is there as well. Space is a "field" then upon which the singularity of this object has an effect just by being there. The difference between the field in ambience and the field where the object is is measurable. We call this gravity. Again no motion is necessary for this "force" which is only the result of other things to exist. Now we add motion, complex motions in spite of or in addition to or because of gravity and find a way to predict behavior without the considerations of gravity? I feel that "G" is present in your model proportions, indeed that it is foundational to those relationships especially as regards geometric ratios.
Gravity has existed since the smallest elementary particles popped into being. It was the friction through resistance to gravity when particles began interacting with each other that was responsible for ionization and the start up of charged particles. Then also electromagnetism added to the mix bringing a largely resultant force to bear upon, or with, an originating one. Now move up to planets and suns and moons and all the variables involved and devise a way to accurately solve celestial mechanics using geometry, albeit a dynamic one, alone? I think a mistake is evident. I'd like to take a closer look but at this point I am pretty well convinced that "G" is only in disguise. The place I will look is inside of your constants especially velocity. That seems the logical beginning.
What do you think?
edit on 8-10-2010 by trailertrash because: (no reason given)