Pythagoras’ celestial spheres in the context of a simple model for quantization of planetary orbits

In the present article we attempt to search for a correlation between Pythagoras and Kepler’s ideas on harmony of the celestial spheres through simple quantization procedure to describe planetary orbits in our solar system. It is reasoned that starting from a Bohr-like atomic model, planetary mean radii and periods of revolution can be obtained from a set of small integers and just one input parameter given by the mean planetary radius of Mercury. It is also shown that the mean planetary distances can be calculated with the help of a Schrödinger-type equation considering the flatness of the solar system. An attempt to obtain planetary radii using both gravitational and electrostatic approaches linked by Newton’s dimensionless constant of gravity is presented.