You lost me with your example. What could the word center mean if the thing that all the other things orbit around in the solar system is not referred to as being in the center?
Orbits are influenced by gravity and momentum and are always changing as the objects pull on each other and are pulled on. It only appears to be stable because the scale is so immense and our lives are so short in comparison.
Depends on how many epicycles you add!
They orbit the earth in a different shape that is more complex than an ellipse.
For further reading, I like Early Wittgenstein, but warning, he is a meme for a reason, you will only understand 10%...
Imagine we have a table with black and white splotches. We could use a square fishnet with a fine enough resolution to accurately describe it. But why use a square fishnet? Why not use hexagons? They both can accurately describe it with a fine enough resolution.
All of science is built on this first step of choosing (squares or hexagons).
Maybe something easier than Wittgenstein, there is Waltz Theory of International Politics, specifically chapter 1. But that is more practical/applied than metaphysical. I find this a difficult topic to recommend a wikipedia article, as they are too specific to each type of knowledge and don't explain the general topic. Even the general topic gets a bit lost in the weeds. Maybe Karl Popper too.
Barycenter is a good candidate, and apparently it's often outside of the Sun[0].
[0] https://astronomy.stackexchange.com/questions/40782/where-is...