The solar system mimics a hydrogen atom

The solar system and the hydrogen atom are two well known systems on different scales and look unrelated: The former is a classical system on the scale of about billions of kilometers and the latter a quantum system of about tens of picometers. Here we show a connection between them. Specifically, we find that the orbital radii of the planets mimic the mean radii of the energy levels of a quantum system under the Coulomb-like potential. This connection might be explained by very light dark matter which manifests quantum behavior in the solar system, thereby hinting at a dark matter mass around $8 \times 10^{-14}$ electron-volts.