The dimensions of the Earth and Moon are in Phi relationship, forming a Triangle based on 1.618.
The illustration shows the relative sizes of the Earth and the Moon to scale.
 Draw a radius of the Earth (1).
 Draw a line from the center point of the Earth to the center point of the Moon (square root of Phi).
 Draw a line to connect the two lines to form a Golden Triangle (Phi).
Using dimensions from Wikipedia and geometry’s classic Pythagorean Theorem, this is expressed mathematically as follows:
Dimension (km) 
Proportion (Earth=1) 
Mathematical Expression 

Radius of Earth  6,378.10  1.000  A 
Radius of Moon  1,735.97  0.272  
Earth + Moon  8,114.07  1.272  B 
Hypotenuse  10,320.77  1.618 (Φ)  C, where C²=A²+B², so C=√(A²+B²) 
Hypotenuse² / (Earth Radius + Moon Radius)² 
1.618 (Φ)  C²/B² 
Another way of looking at the relationship is to take 10320.77² / 8114.07², which is 106,518,293.39 / 65,838,131.96, which rounds to 1.618. The calculation to 6 significant digits is 1.61788…, which is different from 1.61803… by only 0.0009%.
This triangle is known as a Kepler triangle. This geometric construction is the same as that which appears to have been used in the construction of the Great Pyramid of Egypt.
Source: Hidden Nature by Alick Bartholomew. Thanks to Sathimantha Malalasekera for bringing this to my attention.
Certain solar system orbital periods are closely 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 reveals a golden ratio phi relationship in several of its dimensions
The diameter of Saturn is very close to a phi relationship with the diameter of its rings, as illustrated by the green lines. The inner ring division is in a relationship that is very close to phi with the diameter of the rings outside the sphere of the planet, as illustrated by the blue lines.The Cassini division in the rings of Saturn falls at the Golden Section of the width of the lighter outside section of the rings.
Note: Phi grid showing Golden Ratio lines provided by PhiMatrix software.
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 golden ratio 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:
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:
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 onethird 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.)
2005 unveiled the discovery of a 10th planet called 2003UB313. It was found at a distance of 97 times that of the Earth from the Sun. Its ratio to Pluto would thus be 2.47224, much higher than any previous planet to planet orbital distance ratio. Could it be that this is actually the 11th planet and the 10th planet will be found at an orbit whose ratio is 1.52793 times that of Pluto, preserving the phi average? Time will only tell, but if it happens remember that you heard it here first.
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. See the Universe page for more.
skilled says
This is just WOW!
Andrea says
Do you know golden point on earth!!
It is Holy Kaaba in Mecca ……watch it on youtube…!
Gary Meisner says
And see the article and discussion on it on this site at “The Golden Ratio Point of the Earth.”
EKIM says
Well if true it has moved. The North Pole is now over Russia land in Siberia and it has moved considerably. This means there is a new location for the Golden point on Earth, probably S.W. of Mecca I am sure someone has tracked it?
SYED MASUD ALI says
You mean our Earth is tilted more than it was ?
It is so small that even after centuries, the Golden Ratio Point will even be inside the circumference of the HOLY KAABA !
Gary B Meisner says
The pole is based on the axis of the Earth’s rotation, which is independent of the tilt of that axis from perpendicular to the Earth’s orbit.
Leo says
WHOA!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1111
Daviid says
http://tallbloke.wordpress.com/2013/02/20/aremarkablediscoveryallsolarsystemperiodsfitthefibonacciseriesandthegoldenratio/
behnam falamarzi says
I believe God created everything in order
Granger says
Very interesting. This challenges many materialistic views of science that claim the universe is an accidental happening
Harmen Mulder says
This is genius
Paykasa Bozdurma says
Do you know golden point on earth!!
Gary B Meisner says
Yes, I’ve investigated this topic. There are actually many golden ratio points depending on where you start. See https://www.goldennumber.net/goldenratioofearth/.
Rasheed Usman says
Makkah
Sabrina lock says
i agree good tune
Skeptic says
Your math is wrong. The hyporonuse of the triangle for the earth moon ratio is 10320 divided by 8114 is about 1.27 that’s .4 of from Phi.
You should really do the math here, and learn to see for yourself the wonders of this world.
Gary B Meisner says
Hello, Skeptic. The math is correct. The “about 1.27” you calculated represents the SQUARE ROOT of Phi, which is 1.2720 to four places. As the illustration shows, the 10320.77/8114.07 ratio corresponds to the hypotenuse of the triangle divided by its height. This is Phi divided by the square root of phi, which is the square root of phi, or 1.272.
Another way of looking at the relationship is to take 10320.77² / 8114.07², which is 106,518,293.39 / 65,838,131.96, which is 1.618.
I read a good quote recently. It said, “You should really do the math here, and learn to see for yourself the wonders of this world.” 🙂
Vonnwolf says
You guys have no idea just how extensive the Φ ratio permeates the natural physical world! You’ve only scratched the surface with the mainstream information on that ratio.
Things start getting real interesting when you combine the 9 code with the Φ code!
For example:
When one performs the classic “squaring of the circle” exercise, you end up with the moon in a 3×3 box. The square of it’s diagonal = 3²+3², or 9+9. This of course is the number 18; which by the way = (Φ^6 + ¹/Φ^6)
Now you have everything you need to calculate six types of moon cycles and and one earth cycle to the typical accuracy of about 00.001% on most, a little larger margin on a few. (18, Φ≈1. 618, φ≈0.618)
Soros ≈ 18 years: (Φ^6 + ¹/Φ^6)
Node precession ≈ 18+φ years
Eclipse on same date ≈ 18+Φφ years
Eclipse year ≈ (18+φ)² days. ( 18+φ days short of a solar year).
12 full Moons ≈ (18+φ) (18+Φφ) days.
1 Solar Year ≈ (18+φ) (18+Φ) days.
13 full Moons ≈ (18+φ) (18+Φ²) days ( 18+φ days over a Solar year)
Gary B Meisner says
Those are some very interesting relationships, Vonnwolf. Keep them coming.
raz says
HOLY WOW.
thanks man, as an engineer, and math/physics/astronomy buff you have no idea how much this appeals to my spiritual side also.
Vonnwolf says
Here’s another one you might find interesting:
We’re all familiar with how the Fibonocci Sequence approaches the Phi ratio with greater and greater precision as the sequence progresses, but did you know it’s embedded with the 9 code, and it’s on a numerical resonance frequencies of 24 with a half frequency demarcation at 12 (such as the twelve steps of Horus at day/night for a 24 hour day)? Example:
If you where to write out the Fibonocci Sequence from left to right, then right the numeric summation of each sequence under each sequence (just like you do for Gemotria); you’ll notice the number 9 only appears at every twelfth position, and the sequence of totals repeat themselves every twentyfour positions.
But now guess what? If you reright the summation sequence again under the first summation sequence, but shift the sequence by twelve positions and begin with sequence thirteen, you’ll
find that when you ad the top and bottom summation sequences to each other they all total to 9, every single one! you’ll just have a long row of never ending nines!
But what’s really interesting is that in reality all this is born out of the simple square; the Phi ratio, the sizes of all the rocky planets / moon, and much more.
Gary B Meisner says
Thanks. I cover this one at the Fibonacci 24 Repeating Pattern page.
Vonnwolf says
Here’s a simple one. We all know that the mean tilt of the earth’s axis is approximately 23.3°, wobbling in sync with the Sun’s Sunspot Cycles ± 1.2°(going from memory) with our current angle at about 23.4°. Well, did you know that the Phi ratio is encoded in that too?
The earth’s axis mean tilt angle ≈ tan¯¹(Φ²+Φ¯²/Φ⁴+Φ¯⁴) = tan¯¹(3/7) ≈ 23.2°
And if you’re familiar with the “Squaring of the Circle” exsercise, You’ll recognize the significance of those right angle numbers with 7 being the distance between the moon and earth, and 3
being the diameter of the moon.
Gary B Meisner says
Interesting, and creative. We need a standard though by which to determine what qualifies as a meaningful relationship based on phi versus a creative way to get to a desired result. One of the unique qualities of phi is that Phi raised to any even integer plus the reciprocal of that number will result in an integer. That allows one to say that any integer in this series is related to Phi. Does that mean that the Earth’s axis tilt is actually based on Phi, or does it just mean that we can develop a formula to approximate that value using Phi?
As an analogy, we can divide 360° by Phi to get two sections of 222.5° and 137.5°. It’s said that plants arrange their leaves by this angle. The rationale is that this pattern results in the most sunshine to all leaves. Is there a rationale that would explain why the Earth’s tilt would be actually related to Phi as you’ve described? That would make it much more scientific and compelling as an explanation.
It would seem that the simpler and more obvious golden ratios in nature would be more meaningful than those that involve more complex formulas, wouldn’t you agree?
BigJBigL says
Dont forget the fine structure constant is 1/137 😉
Paykasa Bozdurma says
Very interesting. This challenges many materialistic views of science that claim the universe is an accidental happening..
Rasheed Usman says
Of Course.
karl says
revelatory
Abhijit Chaterji says
Can we practically use Phi the Golden Ratio to gain in our daily life? What are the daily things one can do to gain from this powerful revelation of Phi. So far we have been able to deduce mathematically but how can I use this in daily life?
Gary B Meisner says
I’ve answered this question on Quora in several different ways. See the posts here:
https://www.quora.com/Whataresomeapplicationsofthegoldenratio/answer/GaryMeisner
https://www.quora.com/Whatisthegoldenratioandwhereisitusedinourdaytodaylife/answer/GaryMeisner
https://www.quora.com/Howcanthegoldenratiohelpmeinmydailylife/answer/GaryMeisner
https://www.quora.com/HowdoIusetheGoldenRatiotodesignlogos/answer/GaryMeisner
https://www.quora.com/HowcanthegoldenratioortheFibonacciseriesbeusedinengineeringdesignandnotjustforaesthetics/answer/GaryMeisner
Rasheed Usman says
Is there any golden ratio with regard to the position of Earth in Solar System ?
Gary B Meisner says
Yes. See https://www.goldennumber.net/solarsystem/ for more.
adri says
The following books will be eye openers to anyone reading them:
Adri de Groot, The Secret World of Numbers. Available on http://www.Lulu.com.
Richard Heath, The Matrix of Creation. St. Dogmaels: Bluestone Press, 2002.
Robin Heath, Sun, Moon, & Earth. New York: Walker & Company/Wooden Books, 1999.
John Martineau, A Little Book of Coincidence. New York: Walker & Company/Wooden Books, 2001.
Peter Plichta, God’s Secret Formula: Deciphering the Riddle of the Universe and the Prime Number Code. Rockport, MA: Element Books, 1997.
Regianno says
Using the Fibonacci scale versus distance of each planet from the Sun, one must consider the weight of the matter of each in the formula. Does anyone already have this calculation?
dr. adrian de groot says
read the books by Richard Heath and his brother Robin Heath and you will see this in far greater details explained.
Lee Pretorius says
What about the golden spiral formed by tracking the moon in a lunar eclipse. I have an image I can mail you to indicate what I mean
BigJBigL says
So much to say here but I have so much to do.
Egyptian hieroglyphs of the “light bulbs” pointed towards one another…
Plasma bulbs emitting waves of Golden Proportions towards a center point.
The only proportion which matter can manifest from.
The pathway back to homeostasis as well as where we came from.
Are you ready for your mind to explode? Dont go down this rabbit hole unless you can step away from reality for a month.
Here you go….. Google “Dan Winter Golden Ratio Everything” 😀
guideadda says
read the books by Richard Heath and his brother Robin Heath and you will see this in far greater details explained.
https://www.amazon.com/SunMoonEarthWoodenBooks/dp/0802713815
guideadda says
You guys have no idea just how extensive the Φ ratio permeates the natural physical world! You’ve only scratched the surface with the mainstream information on that ratio. https://www.guideadda.com/havellsmaxrouvwaterpurifier/
A. Skeptic says
Do you even know Pythagoras’ theorem ?
Hypotenuse squared equals Opposite squared plus Adjacent squared.
So if the vertical is root phi and the horizontal is one the hypotenuse is root (phi + 1 )
Gary B Meisner says
Yes, the Pythagorean Theorem was used to derive and test the very close golden ratio relationship in the dimensions of the Earth and Moon. Based on your comment though, I see that it could have been presently more clearly and have made some improvements. Thank you for your feedback. Skeptic or not, the math does work to within 0.009% accuracy.