quantum mechanics - Why do electrons orbit protons?

I was wondering why electrons orbited protons rather than protons orbiting electrons.

My first thought was that it was due to the small amount of gravitational attraction between them that would cause the orbit to be very close to the proton (or nucleus). The only other idea that I would have is that the strong interaction between protons and neutrons have something to due with this.

I have heard that the actual answer is due to something in QM, but haven't seen the actual explanation. The only relation to QM that I can think of is that due to a proton's spin and the fact that they are fermions, the atomic orbitals should be somewhat similar. Do protons have the same types of orbitals, that are just confined by the potential of the strong force?

A related question that came up while thinking of this being due to a gravitational interaction: do orbits between protons and electrons have a noticeable rotation between each other (as the sun orbits the earth just as the earth orbits the sun), or is any contribution this has essentially nullified by the uncertainty of the location of the electron (and possibly proton as well)?

Answer

Technically the electron and proton are both orbiting the barycenter of the system, both in classical and quantum mechanics, just as in gravitational systems.

You find the same dynamics for the system if you assume the proton and electron are moving independently about the barycenter, or if you convert to a one-body problem of a single "particle" with the reduced mass $$ \mu = \frac{m_p m_e}{m_p + m_e } \approx m_e \left(1 - \frac{m_e}{m_p}\right). $$ However, the proton is nearly 2000 times more massive than the electron. If we assume that the proton is fixed and infinitely massive, and model our atom using $\mu=m_e$, we introduce errors starting in the fourth decimal place. Usually that's good enough.