DANCES OF PLANETS

Penned by: Priyam Joshi


The heavens are filled with something fantastic. The night sky is relaxing to us no matter where we are in the world. According to Tumblr user Howard Arrington, the sky has more appealing things to give us: the planets’ Planetary Dance!

[1] Dance of Earth and Venus

He discovers that the planets in the heavens dance to the magnificent melody of the cosmos as they move in perfect orbital patterns. Arrington’s conclusions are supported by geometry and mathematics. More mathematical and geometric harmony exists than we are aware, he claims. The inspiration for this piece came from a book that Larry Pesavento gave him. The author John Martineau’s book “A Little Book of Coincidence” provides an illustration of the orbital.

He began by drawing a line every few days between any two planets’ positions using their orbits as a starting point. He discovered that intriguing patterns develop and that each planetary couple has its own distinctive dance beat because the inner planet orbits more quickly than the outer planet.

[2]

He uses the example of the Earth-Venus dance, which, after eight Earth years, returns to its original starting position. Thirteen Venus years are equal to eight Earth years.
Keep in mind that the Fibonacci number series includes the numbers 8
and 13.
Earth: 8 x 365.256 days a year = 2,922.05 days.

Venus: 224.701 x 13 years times =2,921.11 days each year (i.e. 99.9 percent )

8 years of Earth = 13 years of Venus


This lovely five-petal flower(Image [1]) with the Sun in its center is the result of eight years of observing the Earth-Venus dance. Another Fibonacci number is five. Another noteworthy fact that Arrington discovered was that the ratio of the inner orbit of Venus to the outer orbit of the Earth is determined by a square.

3:11 is the ratio of the Moon’s radius to that of the Earth.
Moon’s radius is 1,080 miles, or 3 x 360.
Radius of the Earth = 3,960 miles = 11×360 = 33 x 1 x 2 x 3 x 4 x 5
5,040 miles is equal to the sum of the earth’s and the moon’s radii.
Hence 1 x 2 x 3 x 4 x 5 x 6 x 7 = 7 x 8 x 9 x 10

The Moon takes 27.3 days to complete one orbit, giving a ratio of 3:11 or 27.3 percent. The average rotation time of a sunspot is 27.3 days. Incredibly, Venus and Mars’s closest-to-farthest distance ratio during the Mars-Venus dance is 3:11. Between them, the Earth revolves. According to this scaled depiction, the diameters of the Moon and Earth “Square the Circle.”

The dotted square and circle both have equal-length perimeters. The dotted red square’s perimeter is 4 times the size of the Earth, or 4 x 7,920 miles, or 31,680 miles. The radius of the dotted blue circle is 2 pi, and its circumference is 2 pi x 5040 miles, or 31,667 miles. (99.9%, for example)

[3]

The idea is really quite simple by treating each planet’s orbit as a concentric circle whose radius is proportional to the planet’s distance from the sun. The planets orbit the sun at different rates. For each incremental movement of the outer planet around the circumference, such as at a 5 degree interval, a straight line is then drawn to connect the 2 planets. On the first drawing of the Earth-Venus pair, the outer planet made 8 orbits around the sun. You can see there are 8 vector lines into each of the incremental draw points around the circumference of the circle. With each orbit of the outer planet, a different color was used for the lines drawn. The pattern that emerges is unique and
beautiful, a function of the harmonic of the orbital speed differences of the two planets.

To dive deeper into the sea of the cosmic dances, do check out the following references!

References:

  1. https://themcdonalds.net/dance-of-the-planets-tracking-the-wanderers/
  2. https://www.marksmath.org/visualization/earth_venus_dance/
  3. https://arcscience.com/dance-of-the-planets/

Image References:

  1. https://www.math.wustl.edu/News2015/News2015_Mar_Dances.html
  2. https://in.pinterest.com/pin/dances-of-the-planets-8-pictures–370561875570587779/
  3. https://tex.stackexchange.com/questions/576423/a-more-precise-dance-of-planets-with-metapost-and-tikz