The distances of each planet from the Sun can be described by a unique geometric representation, or Solar Geometry, for each pair of planets, as shown below. Alan Bennett’s original Solar Geometries show more intricate interrelationships between the planets. The geometries below are simplified to illustrate the basic concepts within them.
Click on any diagram below for a more detailed explanation.
Mercury and its Aphelion / Perihelion: A circle divided by 4
Mercury = 1
Perihelion = 2- ½ (√2+1) = 0.792893
Aphelion = ½ (√2+1) = 1.207107
Mercury = 1
Click on above image for details
Start with a circle for Mercury’s mean orbital distance, and divide the circle into four equal sections. Construct a square with sides of the same length. The midpoint between the radius of the circle and the diagonal of the square is Mercury’s aphelion (A), the outside point of its orbit. The same distance towards the Sun is Mercury’s perihelion (P), the inside point of its orbit.
Mercury – Venus: A circle divided by 6
Venus = Mercury * (½ ( √3 + 1 )) ² = 1.866025
Venus = 1.000000 *1.866025 = 1.866025
Mercury * (½ ( √3 + 1 )) ² = Venus
Click on above image for details
Start with a circle for Mercury’s mean orbital distance, divide the circle into six equal sections. Draw a line to form the equilateral triangle of one section and then draw a square using lines of the same length to get the orbital distance of Venus.
Venus – Earth: The Golden Ratio
Earth = Venus ¾ * ½ ( √5 + 1 ) = 2.583306
Earth = 1.596571 * 1.618034 = 2.583306
Venus ¾ * (½ ( √5 + 1 )) = Earth
Click on above image for details
Start with the ¾ power of the orbital distance of Venus, and then construct the well known “golden section” or “Divine Proportion” to get to the mean orbital distance of Earth.
Earth – Mars: A circle divided by 12
Mars = Earth ¾ * ½ ( √6 + √2 ) = 3.936458
Mars = 2.037661 * 1.931852 = 3.936458
Note: ½ ( √6 + √2 ) = 2 * Cosine 15º = 1.931852
Also: √ (2 * Venus) = √ (Diameter of Venus) =1.931852
Earth ¾ * (½ ( √6 + √2 )) = Mars
Click on above image for details
Start with a circle using the ¾ power of the orbital distance of Earth as its radius. Divide the circle into twelve equal sections. Draw a line to form the isosceles triangle of the section and then draw another isosceles triangle on the other side using lines of the same length, forming a diamond, to get the orbital distance of Mars.
Mars – Jupiter: A square expanded
Jupiter = Mars * ( √2 + 2 ) = 13.439908
Jupiter = 3.936458 * 3.414214 = 13.439908
Mars * ( √2 + 2 ) = Jupiter
Click on above image for details
Start with the orbital distance of Mars, add a square made with the orbital distance of Mars turned on a diagonal and then add the orbital distance of Mars again to get the orbital distance of Jupiter.
Simple, elegant geometries
The geometries that result are beautiful and elegant, yet simple. Did these intriguing patterns happen by coincidence . . . or by design? Before you decide, take a look at the intriguing mathematical relationships that relate the distances of the planets to each other.
Brace yourself like a man; I will question you, and you shall answer me. “Where were you when I laid the earth’s foundation? Tell me, if you understand. Who marked off its dimensions? Surely you know! Who stretched a measuring line across it? On what were its footings set, or who laid its cornerstone–while the morning stars sang together and all the angels shouted for joy? (Job 38:3-7)