Gravitational analog of Bohr’s theory for the solar system

Abstract

In this paper, the gravitational analog of Bohr’s theory for the Solar System is presented by deriving explicit expressions for the gravitational analog of Bohr’s quantum condition on angular momentum of a secondary (planet or satellite) revolving around its primary (the Sun or a planet) and Planck’s constant , in terms of known physical quantities of the System (the Solar or a Satellite System). The correspondence principle connecting atomic theory and gravitational theory is stated. It turns out that the ground state orbit of an electron in an atom corresponds to the Roche limit of the primary (defined in the text) in the gravitational case. The gravitational Planck’s constant  when taken into atomic scale via the Correspondence principle gives an expression for the Planck’s constant of the atomic scale. It has shown here that a one-to-one correspondence exists between the Planetary Distance Law and the Electron Orbital Distance Law.