The advanced fluid physics module: A technical description

Pletser, Vladimir; Gonfalone, A.; Verga, Antonio; Raimondo, F.; Defilippi, V.; Gily, A.

doi:10.1016/0273-1177(91)90268-o

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“…Noting early on that the original Titius-Bode law breaks down for the most extremal planets (Mercury at the inner side, and Neptune and Pluto at the outer side), numerous modifications were proposed: such as a 4-parameter polynomial (Blagg 1913;Brodetsky 1914); the Schrödinger-Bohr atomic model with a scaling of R n ∝ n(n + 1), where the quantum-mechanical number n is substituted by the planet number (Wylie 1931;Louise 1982;Scardigli 2007a,b); a geometric progression by a constant factor (Blagg 1913;Nieto 1970;Dermott 1968Dermott , 1973Armellini 1921;Munini and Armellini 1978;Badolati 1982;Rawal 1986Rawal , 1989; see compilation in Table 1); fitting an exponential distance law (Pletser 1986(Pletser , 1988; the introduction of additional planets (Basano and Hughes 1979), applying a symmetry correction to the Jupiter-Sun system (Ragnarsson 1995); tests of random statistics (Dole 1970;Lecar 1973;Dworak and Kopacz 1997;Hayes and Tremaine 1998;Lynch 2003;Neslusan 2004;Cresson 2011;Pletser 2017); self-organization of atomic patterns (Prisniakov 2001), standing waves in the solar system formation (Smirnov 2015), or the Four Poisson-Laplace theory of gravitation (Nyambuya 2015).…”

Section: Introductionmentioning

confidence: 99%

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

Aschwanden

2018

New Astronomy

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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 T i and planet distances R i from the Sun are not consistent with logarithmic spacing, but rather follow the quantized scaling (R i+1 /R i ) = (T i+1 /T i ) 2/3 = (H i+1 /H i ) 2/3 , where the harmonic ratios are given by five dominant resonances, namely (H i+1 : H i ) = (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 quasiregular 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 ≈ 10 resonant zones that can be occupied with planets (or moons) in long-term stable orbits.Subject headings: planetary systems -planets and satellites: general -stars: individual 1.

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Section: Introductionmentioning

confidence: 99%

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

Aschwanden

2018

New Astronomy

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show abstract

The advanced fluid physics module: A technical description

Cited by 1 publication

References 1 publication

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

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

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