The solar system mimics a hydrogen atom

TL;DR

This paper reveals a surprising analogy between the orbital radii of planets in the solar system and the energy levels of a hydrogen atom, suggesting a potential link involving light dark matter.

Contribution

It demonstrates a novel connection between classical planetary orbits and quantum energy levels, proposing a dark matter explanation for this similarity.

Findings

Planetary orbital radii mimic hydrogen atom energy levels

Potential dark matter mass around 8 x 10^-14 eV

Quantum behavior may manifest at solar system scale

Abstract

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.