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The Phi Nest on the Golden Number
on the
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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:

Solar system

    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...)

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