"It means that the system is a product of *all* bodies in the system, and that it doesn't matter what coordinate system you..."
The question is do *you* understand what that means. I'm betting that you philosophically adopt a severely-restricted definition and ignore the greater.
"No matter what coordinate system you use, you will notice that the behavior can be explained by the same set of equations, based on the gravitation pull of the two objects in question."
Not quite.
Strictly speaking, it's not the 'gravitational pull' but the 'laws of gravity'. This might seem trivial but is an important difference.
In addition, gravity is not understood and the laws of gravity are observed to operate differently between the solar system and intergalactic space. That's what 'dark matter' is all about.
'Dark matter' is an invisible entity that is invoked to explain anomalous behavior of galactic objects.
Ah yes, “dark matter”… does this actually exist? Higgs (or the force exchange particle) should have shown up when the atom-smashing energy levels reached ~.8 TeV. We are beyond that now… It’s turtles all the way down when you start invoking a heavier mass in smaller particles, quark-gluon plasma, mini-black holes from heavy ion collisions, etc…
It's the dynamic interaction of the mass of the two bodies. Which is what I just said. :-)
All of which brings up the point -- this is evidence of a helio-centric solar system . . .