Planetary golden spiral

Fig. 12 Simulation of planetary orbits by golden-spiral optimization. With the mean orbital radius of Jupiter as unit, the outer planets are on orbits defined by integral multiples thereof. On the same scale, the asteroid belt is at a distance x from the sun and the inner planets have orbital radii of t/ . For clarity, the inner planets are shown on a larger self-similar scale...

As recently shown (Boeyens, 2009) the Bode -Titius law, which hints at some harmonious regular organization of planetary motion in the solar system, is dictated by a more general self-similar symmetry that applies from subatomic systems to galactic spirals. The common parameter is the golden ratio, r = 0.61803. Any such cosmic symmetry should be dictated by a successful cosmological model. 

Figure 7.3 A set of logarithmic spirals, such as the golden, planetary spiral with divergence angle 2t, may serve as a model of Godd s compass of inertia, going through an odd number of involutions...

The mean orbits of all planets, including Ceres, the largest asteroid, are correctly predicted [13] by the relative distances from the spiral center. With the orbital radii expressed as rational fractions, a quantized distribution of major planets, as numbered, is revealed. On this scale the orbit of Ceres measures r and those of the inner planets are rational fractions of the golden ratio. The same pattern was shown to repeat itself for the orbital motion of planetary moons and rings. 

Cosmic self-similarity has been documented and discussed many times with reference to atomic nuclei, atomic structure, the periodicity of matter, covalence, molecular conformation [26], biological structures, planetary and solar systems [27], spiral galaxies and galactic clusters [28]. The prominent role of the golden ratio in all cases can only mean that it must be a topological feature of space-time structure. 

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