My question relates to Noether's theorem, which I've recently been reading about, and I couldn't find any good answers on the internet relating a conservation law to the symmetry between Newton's law of gravity and Coulomb's. Would it be something like the conservation of charge, or the conservation of angular momentum? Or both?
Also, is this an area of physics that's received much attention by researchers? I ask this because I can't seem to find any published papers on the subject and would really like to know the answer.