Would nature treat multiple body system as two body systems and ignore gravity between some bodies to keep the system together?
Yes, that’s the whole point. Nature is guiding the model. In the Sun Earth Moon system, nature is not ignoring anything, nor are they. Nature’s gravitational influence on the Earth moon interaction from the Sun is so small, that the model can accurately predict the earth moon rotations without it.
Then, nature treats the equivalent two body problem of the Earth-Moon’s center of mass with the Sun. This makes RE sense, given that the Earth and moon rotate around each other, and that center point orbits the Sun.
So you see, it isn’t that nature “ignores” anything. Sometimes things are just small in certain regimes. For example, we use a ruler to measure a table. Does nature “ignore” the size of atoms? No of course not, but the size of an atom is so small compared to a ruler, that we can safely get a good measurement for a table without worrying about atoms.
This is the analogous situation with orbits and multi-body central forces.
To be rather direct, if I may, the best avenue to attack RE theory is the failure of it to unify quantum mechanics with general relativity. This is its greatest weakness, and it is here you will find traction. If FET can address this weakness successfully then it will become instantly recognised. Scientists will have no choice in the matter.
The N-Body orbit and family galleries represent direct experimental evidence for possibilities under the laws of Newton, and which were created with great effort by researchers manually and via supercomputer.
Should we expect to see what you describe, with bodies of different masses and close enough approximations somewhere in these galleries? It seems that we have access to a vast amount of experimental evidence on the matter and we should be able to see it for ourselves to put the matter to bed.
Flat Earth Theory as the Grand Unified Theory would be a good topic to discuss. As I can see, Special Relativity was a flavor of relativity created to explain lack of horizontal motion (Michelson-Morley), and General Relativity was created to explain why the earth seems to be accelerating upwards. Perhaps you can help us on that topic.
It is difficult for me to identify what evidence will “put the matter to bed” for you, because I am uncertain a) how much is being understood from my expository replies, and b) the willingness of the FE community to adjust their stances on topics of relevance.
Now, verification of my claims regarding three body problems as detailed in my previous replies can be found in just about any upper division undergraduate text on classical mechanics. You will find no published research on this item because it is not researchable. It is too basic. Just like you can find no research on 1+1=2 (a silly example).
It is not my intention to frustrate your efforts here. Rather, due to my training I can identify several points of criticism of RET on these forums that are not viable avenues. These mostly appear to result from a lack of understanding of RE/traditional physics.
I recognize and appreciate the caution and reservation with which you would view my input.
My training permits me to contrast the rigor and formal address between FET and RET, and it is my conclusion that FET is vastly outmatched. I do see attempts made by e.g., Parsifal and Sandokhan, but these efforts are amateur, plagiarized, and contain errors.
My goal is to raise the standard of address for FET so that it can receive proper consideration. True science hides no idea. To the extend that I can make progress here, that is what I will do.
I am happy to guide efforts to position FET as a competitor to GUT.