Phi and the Solar System

Certain solar system orbital periods are related to phi

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:

 Curiously enough we find:

Ö Period of Venus * Phi = Distance of the Earth 

Ö 2.5490 * 1.6180339 = 1.5966 * 1.6180339 = 2.5833

In addition, Venus orbits the Sun in 224.695 days while Earth orbits the Sun in 365.242 days, creating a ratio of 8/13 (both Fibonacci numbers) or 0.615 (roughly phi.)  Thus 5 conjunctions of Earth and Venus occur every 8 orbits of the Earth around the Sun and every 13 orbits of Venus.

Mercury, on the other hand, orbits the Sun in 87.968 Earth days, creating a conjunction with the Earth every 115.88 days.  Thus there are 365.24/115.88 conjunctions in a year, or 22 conjunctions in 7 years, which is very close to Pi!

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:

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 Robert Bartlett.)

The shape of the Universe itself is a dodecahedron based on Phi

New findings in 2003 based on the study of data from NASA's Wilkinson Microwave Anisotropy Probe (WMAP) on cosmic background radiation reveal that the universe is finite and shaped like a dodecahedron, a geometric shape based on pentagons, which are based on phi.   The the Universe page for more.