Mathematical and geometrical dance of the planets

There is something cosmic in the skies. Even if we look at the night sky from where we are, it has a calming effect on us. A Tumblr user, Howard Arrington has found that the sky has something more beautiful to offer us. The Dance of the planets!

He finds that the planets in the heavens move in exquisite orbital patterns, dancing to the great music of the cosmos. Arrington has based his findings on mathematics and geometry. “There is more mathematical and geometric harmony than we realize,” he says. The idea for this article is from a book Larry Pesavento shared with me.  The book, ‘A Little Book of Coincidence’ by John Martineau, illustrates the orbital patterns and several of their geometrical relationships,” he adds.

He started of by taking the orbits of any two planets and drawing a line between the two planet positions every few days.  Because the inner planet orbits faster than the outer planet, he found out that interesting patterns evolve and each planetary pairing has its own unique dance rhythm.

He cites the example of Earth-Venus dance returns to the original starting position after eight Earth years.  Eight Earth years equals thirteen Venus years.

Note that 8 and 13 are members of the Fibonacci number series.

Earth:     8 years * 365.256 days/year  =  2,922.05 days                   

Venus:  13 years * 224.701 days/year  =  2,921.11 days (ie. 99.9%)

Watching the Earth-Venus dance for eight years creates this beautiful five-petal flower with the Sun at the center.  (5 is another Fibonacci number.)


Arrington noticed another intriguing fact is the ratio between the Earth’s outer orbit and Venus’s inner orbit is given by a square.


In the following dance patterns, the planet pairing is given and the number of orbits of the outer planet.  Enjoy these beautiful patterns.







The radius of the Moon compared to the Earth is three to eleven, ie. 3:11.

Radius of Moon = 1,080 miles =  3 x 360

Radius of Earth  = 3,960 miles = 11 x 360 = 33 x 1 x 2 x 3 x 4 x 5

Radius of Earth plus Radius of Moon = 5,040 miles = 1 x 2 x 3 x 4 x 5 x 6 x 7 = 7 x 8 x 9 x 10

The ratio 3:11 is 27.3 percent, and the orbit of the Moon takes 27.3 days.  27.3 days is also the average rotation period of a sunspot.  The closest : farthest distance ratio that Venus and Mars each experiences in the Mars-Venus dance is incredibly 3:11.  The Earth orbits between them.

The sizes of the Moon and the Earth ‘Square the Circle’ as shown in this illustration, which is drawn to scale.  The perimeters of the dotted square and the dotted circle are the same length.


The perimeter of the dotted red square is 4 x Earth’s diameter = 4 x 7,920 miles = 31,680 miles.

The circumference of the dotted blue circle is 2 pi x radius = 2 x 3.142 x 5040 miles = 31,667 miles.  (ie. 99.9%)


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