Newtonian mechanics fails only at extreme scales as far as mass is concerned, to break it completely you need to solve it for the entire mass of the universe, o

Newtonian mechanics fails only at extreme scales as far as mass is concerned, to break it completely you need to solve it for the entire mass of the universe, or for a singularity (the latter breaks GR too). Newtonian mechanics is still the primary tool for astrophysics, and anything we do in space. In some cases PPN is used but no one is solving non linear equations outside of extreme cases which are usually theoretical.