Scaling Analogies Between Atomic and Planetary Systems: Energy and Orbital Families Across Scales

This preregistered work explores an analogy between atomic systems (electron orbital structures) and planetary systems (multi-body orbital dynamics).
The core hypothesis – hereafter referred to as the Danteverse Hypothesis – is that both scales may exhibit families of orbital ratios and energy emission patterns that follow similar clustering laws.

Key elements:

1. Data sources:

   • Atomic spectra (focus on sodium, fluorine, and comparative elements).

   • Exoplanetary systems from NASA Exoplanet Archive and Solar System reference data.

2. Method:

   • Period ratios $R = P_{\text{out}}/P_{\text{in}}$ computed for planetary systems.

   • Orbital/energy level ratios computed for atomic electron shells.

   • Clustering tests to identify families of ratios at both scales.

3. Preliminary findings:

   • Both atomic and planetary data show clustering into three main families of ratios.

   • Energy scales differ by orders of magnitude, but mapping through normalized dimensionless ratios suggests a possible structural similarity.

4. Implications:

   • If confirmed, this analogy could provide a new framework for linking micro (quantum) and macro (celestial mechanics) dynamics.

   • The hypothesis remains testable: predictions can be falsified through further atomic spectroscopy and exoplanet orbital analysis.

Blind registration:

This document is preregistered and time-locked for 1 year. The content cannot be modified until embargo expiry. After release, results will be openly compared against new datasets to assess validity.