QED, I recall giving references to experimental evidence that a three body problem with a sun that that a planet that had a moon was not possible and did not exist in the n-body families. They all required at least two bodies of equal masses, and were in configurations that looked nothing like heliocentric orbits. You appeared to agree that there were no numerical solutions with such a configuration in the galleries or the studies and told me that we could cheat by treating it as a two body problem and considering the earth and moon as one, because that is what students do.
If this were true and Newton's gravity worked based on approximations then we should expect to see those configurations in the three body problem galleries.
It is my opinion that experimental evidence from Newtonian gravity simulators > "We can fudge a little" and "it's close enough"
I remember you providing references that detailed investigations into analytical solutions for n=3 bodys. You expressed concern that this was problematic because for these analytical solutions, two of the three had equal mass, which is not the case for the Sun moon earth system.
In response, I explained that n body problems lacking an analytical solution is not a constraint on the physical model, but instead a constraint on mathematical techniques. Numerically, the solutions exist and undergraduates find them. In other words - they are COMMON. I also explained that their commonality is why you cannot find research on them - because we research unknown things....
I also explained how we use Newtonian dynamics to solve for orbits in our solar system. I explained that in the earth moon sun system, the equations decouple, and we solve this by considering the equivalent 2 body systems. Indeed, the force on the moon from the earth >> the force on the moon from the sun. It is in most textbooks how one completes the calculations.
That the equations decouple is not a fudging...it is what happens to some differential equations, and is rather commonly found, in fact.
What you refer to as “loopholes” or “cheats” are what scientists call: mathematical methods, and those methods are pretty basic as applied to central force problems.
If you wish to learn how to do this, then take a physics class! The reason you don’t see these methods in “galleries” is the same reason why you don’t see investigations of 1+1=2 in galleries: because it is basic and understood.
Tom, I wish I could get you to see this. You are not presenting valid criticisms of central force problems. Continued denial of what I am explaining to you looks foolish, not because I have any agenda, or wish to be hurtful, but because any undergraduate physics student can immediately see your mistake - and as a zetetic council member, the mistake represents the FE community as an uninformed and scientifically juvenile movement.
I promise that I am trying to guide your efforts in a productive direction.