Self-Organizing Systems in Planetary Physics: Harmonic Resonances of Planet and Moon orbits
Markus J. Aschwanden Submitted: 2017-01-27 12:58
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).
We find that the orbital periods Ti and planet distances Ri from
the Sun are not consistent with
logarithmic spacing, but rather follow the quantized scaling
(Ri+1/Ri) = (Ti+1/Ti)2/3 = (Hi+1/Hi)2/3, where
the harmonic ratios are given by five dominant resonances, namely
(Hi+1 : Hi) = (3:2), (5:3), (2:1), (5:2), (3:1).
We find that the orbital period ratios tend to follow the quantized harmonic
ratios in increasing order. We apply this harmonic orbit resonance model
to the planets and moons in our solar system, and to the exo-planets
of 55 Cnc and HD 10180 planetary systems.
The model allows us a prediction of missing planets
in each planetary system, based on the quasi-regular self-organizing
pattern of harmonic orbit resonance zones. We predict 7 (and 4) missing
exo-planets around the star 55 Cnc (and HD 10180).
The accuracy of the predicted planet and moon distances amounts
to a few percents. All analyzed systems are found to have
approx 10 resonant zones that can be occupied with planets
(or moons) in long-term stable orbits.
Authors: Markus J. Aschwanden
Publication Status: 2018, New Astronomy 58C, 107-123
Last Modified: 2017-09-25 09:16