Solar system, commensurability

Message, P.J. (1999) Orbits of Saturn s satellites some aspects of commensurabilities and periodic orbits. In Steves, B., and Archie Roy, A.E., editors, The Dynamics of Small Bodies in the Solar System A Major Key to Solar System Studies (The Proceedings of the N.A. T. O. Advanced Study Institute, in Acquafredda di Maratea, Calabria, Italy, 1997.), pages 207-225. 

Roy, A.E., and Ovenden, M.W.(1955) On the Occurrence of Commensurable Mean Motions in the Solar System. Monthly Notices of the Royal Astronomical Society, vol. 115, pages 296-309. 

By assuming that the dynamic variables follow the same rules as for hydrogen in many-electron atoms, there was the expectation that the periodic table of the elements could be reduced to the Schrodinger solution for hydrogen. Apart from a superficial correlation, which is commonly assumed to vindicate this expectation, it has now been shown that the neglect of general-relativistic curvature of space-time prevents such reduction. Once this defect has been rectified the atomic model will be used to investigate commensurability in the self-similar solar system. 

Until the parallel between number and cosmos is demonstrated to be an illusion we shall use this idea to model the universe. The power of this approach lies therein that all regularities in the physical world can be reduced to the same mathematical rules as the commensurable relationships in the solar system. The same mathematics that optimizes the distribution of matter in spiral galaxies and solar systems, shapes the growth of nautilus shells and sunflower heads. This ubiquitous symmetry, known as self-similarity is... 

---