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# Phi and the Solar System

### Certain solar system orbital periods are related to phi

Certain planets of our solar system seem to exhibit a relationship to phi, as shown by the following table of the time it takes to orbit around the Sun:

 Mercury Venus Earth Jupiter Saturn Power of Phi -3 -1 0 5 7 Decimal Result 0.24 0.62 1.0 11.1 29.0 Actual Period 0.24 0.62 1.0 11.9 29.5

### Saturn's rings are divided at two phi points

The Cassini division in the rings of Saturn falls at the Golden Section of the width of the ring.
A closer look at Saturn's rings reveals a darker inner ring which exhibits the same  golden section proportion as the brighter outer ring.

### Venus and Earth reveal a phi relationship

Venus and the Earth are linked in an unusual relationship involving phi.  Start by letting Mercury represent the basic unit of orbital distance and period in the solar system:

 Planet Distance from the sun in km (000) Distance where Mercury equals 1 Period where Mercury equals 1 Mercury 57,910 1.0000 1.0000 Venus 108,200 1.8684 2.5490 Earth 149,600 2.5833 4.1521

Curiously enough we find:

Φ Period of Venus * Phi = Distance of the Earth

Φ 2.5490 * 1.6180339 = 1.5966 * 1.6180339 = 2.5833

See more relationships at the Solar Geometry site.

### Relative planetary distances average to Phi

The average of the mean orbital distances of each successive planet in relation to the one before it approximates phi:

 Planet Mean distance in million kilometers per NASA Relative mean distance where Mercury=1 Mercury 57.91 1.00000 Venus 108.21 1.86859 Earth 149.60 1.38250 Mars 227.92 1.52353 Ceres 413.79 1.81552 Jupiter 778.57 1.88154 Saturn 1,433.53 1.84123 Uranus 2,872.46 2.00377 Neptune 4,495.06 1.56488 Pluto 5,869.66 1.30580 Total 16.18736 Average 1.61874 Phi 1.61803 Degree of variance (0.00043)

Note:  We sometimes forget about the asteroids when thinking of the planets in our solar system.  Ceres, the largest asteroid, is nearly spherical, comprises over one-third the total mass of all the asteroids and is thus the best of these minor planets to represent the asteroid belt.  (Insight on mean orbital distances contributed by Bartau.)

Phi - The Golden Number
A source to some of Net's "phi-nest" information on the
Golden Section / Mean / Proportion / Ratio / Number,
Divine Proportion, Fibonacci Series and Phi (1.6180339887...)