IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v30y2006i2p399-406.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906000464
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.01.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Estrada, Ernesto, 2007. "Graphs (networks) with golden spectral ratio," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1168-1182.
    2. Büyükkılıç, F. & Demirhan, D., 2009. "Cumulative growth with fibonacci approach, golden section and physics," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 24-32.
    3. Contreras-Reyes, Javier E., 2021. "Lerch distribution based on maximum nonsymmetric entropy principle: Application to Conway’s game of life cellular automaton," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Stakhov, Alexey, 2006. "The golden section, secrets of the Egyptian civilization and harmony mathematics," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 490-505.
    5. Falcón, Sergio & Plaza, Ángel, 2007. "The k-Fibonacci sequence and the Pascal 2-triangle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 38-49.
    6. El Naschie, M.S., 2006. "An elementary proof for the nine missing particles of the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1136-1138.
    7. El Naschie, M.S., 2006. "Is Einstein’s general field equation more fundamental than quantum field theory and particle physics?," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 525-531.
    8. Kocer, E. Gokcen & Tuglu, Naim & Stakhov, Alexey, 2009. "On the m-extension of the Fibonacci and Lucas p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1890-1906.
    9. Crasmareanu, Mircea & Hreţcanu, Cristina-Elena, 2008. "Golden differential geometry," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1229-1238.
    10. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    11. Buyukkilic, F. & Ok Bayrakdar, Z. & Demirhan, D., 2015. "Investigation of cumulative growth process via Fibonacci method and fractional calculus," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 237-244.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:30:y:2006:i:2:p:399-406. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.