Mass distributions for the Kepler problem.

The regularities in the structure of the planetary system, expressed by the Titius-Bode law, resembling a quantum condition, can be retrieved 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.