  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.
