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

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  • de Oliveira Neto, Marçal

Abstract

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.

Suggested Citation

  • de Oliveira Neto, Marçal, 2006. "Pythagoras’ celestial spheres in the context of a simple model for quantization of planetary orbits," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 399-406.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:2:p:399-406
    DOI: 10.1016/j.chaos.2006.01.014
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    1. Stakhov, Alexey, 2006. "Fundamentals of a new kind of mathematics based on the Golden Section," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1124-1146.
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    Cited by:

    1. Pintr, P. & Peřinová, V. & Lukš, A., 2008. "Allowed planetary orbits in the solar system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1273-1282.
    2. Krot, Alexander M., 2009. "A statistical approach to investigate the formation of the solar system," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1481-1500.
    3. Giné, Jaume, 2007. "On the origin of the gravitational quantization: The Titius–Bode law," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 363-369.
    4. de Oliveira Neto, Marçal, 2007. "On a mass independent approach leading to planetary orbit discretization," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 740-747.

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