The so called Solar System is a mathematically chaotic, unpredictable system. the problem of finding the "center of gravity" in a 3-body system is mathematically unsolvable. and when it's extended to a more complex system like the solar system with 100+ bodies (8 planets, 1 star, 100+ satellites), is much more complicated and even more so unsolvable. and there is no way to predict the future states of such a system using this model.

we say a mathematical model describes a natural phenomena, only if the model is properly predictable. but this simply is not possible in the solar system model, proving that we don't live in such a system. mathematicians like Newton, Laplace, Euler, Poincare have tried to solve this problem for centuries, and only succeeded in coming up with ideal solutions that are nowhere near the current complicated solar system that is proposed.