Determination of Phase-Space Areas of the Body Motion in the Solar System Deduced from the Bohr-Sommerfeld Atomic Theory and Approximate Invariance of Their Ratios for the Pairs of Planets and Satellites

Abstract

Energy-time and momentum-position phase spaces defined by the electron orbits in the hydrogen-like atom exhibit special properties of equivalence. It is demonstrated that equivalence of the same kind can be obtained for the phase-space areas defined by the orbit pairs of planets, or satellites, which compose the solar system. In the choice of the examined areas it is useful to be guided by the Bohr-Sommerfeld atomic theory.