system
Given the following post, respond as if you're commenting on Reddit:
human
Can two objects orbit each other because of Coulomb's law?

Both Newton's universal law of gravitation and Coulomb's law are inverse square laws, so is this possible?
gpt
According to the simple inverse square laws: yes, absolutely.  They are mathematically governed the same (just with different constants) and so orbits should be possible in both.

Classically speaking, this is what we believed, and indeed it is a good approximation of the truth for nonrelativistic speeds.

Relativity puts a dent in the classical picture though, and both gravitational and electric orbits actually emit waves due to the accelerating reference frames that cause them to lose energy and spiral inwards.

This effect is usually quite small for gravity.

Of course, quantum mechanics also puts a dent in the classical picture, so if we are talking about a proton and an electron then quantum mechanical effects would dominate and no it wouldn't make sense to describe the electron as orbiting the proton.