A Missing Phase in Optimization - Physical Modeling

The term, physical modeling, refers to the activity identifying unknown physical relationship of/within the system of interest.

When we describe satellites’ motion in Newton mechanics, we accept the absolute time-space assumptions implicitly. However, wrong results are obtained. We can establish a model using mathematical languages, enumerating all (obviously) known relations of the the system straightforwardly.

But, can any behavior that should be considered can be derived from this model?

This question looks like to ask can the * relativity * be derived from Newton mechanics?