## 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 |

Hypotenuse / (Earth Radius + Moon Radius) | 1.618 (Φ) | A²+B²=C² |

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.

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 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.)

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

November 22, 2012 at 9:57 pmThis is just WOW!

Andrea says

January 18, 2013 at 2:41 amDo you know golden point on earth!!

It is Holy Kaaba in Mecca ……watch it on youtube…!

Gary Meisner says

January 20, 2013 at 12:19 amAnd see the article and discussion on it on this site at “The Golden Ratio Point of the Earth.”

EKIM says

September 25, 2018 at 1:53 pmWell 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

October 10, 2018 at 9:52 amYou 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

October 12, 2018 at 3:35 amThe 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

April 9, 2013 at 4:53 pmWHOA!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1111

Daviid says

September 4, 2013 at 8:43 pmhttp://tallbloke.wordpress.com/2013/02/20/a-remarkable-discovery-all-solar-system-periods-fit-the-fibonacci-series-and-the-golden-ratio/

behnam falamarzi says

January 2, 2015 at 7:09 amI believe God created everything in order

Granger says

August 28, 2015 at 11:10 pmVery interesting. This challenges many materialistic views of science that claim the universe is an accidental happening

Harmen Mulder says

November 12, 2015 at 6:31 amThis is genius

Paykasa Bozdurma says

April 8, 2016 at 5:15 amDo you know golden point on earth!!

Gary B Meisner says

April 9, 2016 at 8:55 amYes, I’ve investigated this topic. There are actually many golden ratio points depending on where you start. See https://www.goldennumber.net/golden-ratio-of-earth/.

Rasheed Usman says

March 14, 2018 at 6:42 amMakkah

Sabrina lock says

June 17, 2016 at 5:37 ami agree good tune

Skeptic says

July 5, 2016 at 10:57 pmYour 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

July 9, 2016 at 4:24 pmHello, 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

August 7, 2016 at 5:00 pmYou 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+Φ-φ years

Eclipse year ≈ (18+φ)² days. ( 18+φ days short of a solar year).

12 full Moons ≈ (18+φ) (18+Φ-φ) 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

August 7, 2016 at 8:20 pmThose are some very interesting relationships, Vonnwolf. Keep them coming.

Vonnwolf says

August 7, 2016 at 9:19 pmHere’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 twenty-four 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

August 14, 2016 at 4:03 amThanks. I cover this one at the Fibonacci 24 Repeating Pattern page.

Vonnwolf says

August 12, 2016 at 9:06 pmHere’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

August 14, 2016 at 4:41 amInteresting, 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?

Paykasa Bozdurma says

October 16, 2016 at 6:48 pmVery interesting. This challenges many materialistic views of science that claim the universe is an accidental happening..

Rasheed Usman says

March 14, 2018 at 6:41 amOf Course.

karl says

January 11, 2018 at 10:20 amrevelatory

Abhijit Chaterji says

January 20, 2018 at 7:03 amCan 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

January 20, 2018 at 10:03 amI’ve answered this question on Quora in several different ways. See the posts here:

https://www.quora.com/What-are-some-applications-of-the-golden-ratio/answer/Gary-Meisner

https://www.quora.com/What-is-the-golden-ratio-and-where-is-it-used-in-our-day-to-day-life/answer/Gary-Meisner

https://www.quora.com/How-can-the-golden-ratio-help-me-in-my-daily-life/answer/Gary-Meisner

https://www.quora.com/How-do-I-use-the-Golden-Ratio-to-design-logos/answer/Gary-Meisner

https://www.quora.com/How-can-the-golden-ratio-or-the-Fibonacci-series-be-used-in-engineering-design-and-not-just-for-aesthetics/answer/Gary-Meisner

Rasheed Usman says

March 14, 2018 at 6:44 amIs there any golden ratio with regard to the position of Earth in Solar System ?

Gary B Meisner says

March 19, 2018 at 8:48 amYes. See https://www.goldennumber.net/solar-system/ for more.

adri says

March 29, 2018 at 2:39 pmThe 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

June 9, 2018 at 9:36 pmUsing 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

June 11, 2018 at 2:19 amread the books by Richard Heath and his brother Robin Heath and you will see this in far greater details explained.

Lee Pretorius says

August 4, 2018 at 1:34 amWhat 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