Self-organizing systems in planetary physics:  
Harmonic resonances of planet

and moon orbits

Paper published in New Astronomy, Volume 58, January 2018, Pages 107-123
Link to article at


  • Evidence for quantized (low-harmonic) planet orbit period ratios.
  • Harmonic orbit resonances are a physical model of the empirical Titius–Bode law.
  • Exo-planet observations from KEPLER provide statistical tests of model.
  • The harmonic orbit resonance model is a self-organization process.

The geometric arrangement of planet and moon orbits into a regularly spaced pattern of distances is the result of a self-organizing system. The positive feedback mechanism that operates a self-organizing system is accomplished by harmonic orbit resonances, leading to long-term stable planet and moon orbits in solar or stellar systems. The distance pattern of planets was originally described by the empirical Titius–Bode law, and by a generalized version with a constant geometric progression factor (corresponding to logarithmic spacing). Read More...

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