Mass distributions for the Kepler problem

TL;DR

This paper introduces a new formula based on a logarithmic integrality constraint on angular momentum to explain planetary and satellite mass distributions, providing a theoretical basis for observed regularities.

Contribution

It derives a general formula from a logarithmic integrality constraint, explaining orbital spacing and mass distributions without fitting, applied to planets and Jupiter's satellites.

Findings

The new formula accounts for the Titius-Bode law.

Applications to planetary and satellite systems show good agreement.

Provides a theoretical basis for orbital regularities.

Abstract

The regularities in the structure of the planetary system, expressed by the Titius-Bode law, can be accounted also by using a more general formula, derived not by fit but from a logarithmic integrality constraint on the angular momentum (areolar velocity). This work presents the elementary adiabatic invariant used in constraint, the new formula, and applications to the orbit spacing, numbering and mass distributions for planets and the Jupiter satellites.