ESPL: Dances of the Planets

The planets in the heavens move in exquisite orbital patterns, dancing to the Music of the Cosmos. There is more mathematical and geometric harmony than we realize. 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. .

Take the orbits of any two planets and draw a line between the two planet positions every few days. Because the inner planet orbits faster than the outer planet, interesting patterns evolve. Each planetary pairing has its own unique dance rhythm. For example, the 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.)

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.

Let me share with you other facts about cosmic harmony. 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%)

Article by Howard Arrington

The dance patterns were drawn by the following ESPL program using a chart window for the canvas. The chart bars and grid were hidden so the canvas was blank. Edit the Planet1 and Planet2 variable values to select the planet pairing, with the planets numbered beginning with Mercury = 1.

var {global variables} i,c,Planet1,Planet2: integer; Planet1Year,Planet2Year: real; Planet1Radius,Planet2Radius: real; Interval,Orbits: real; yBottom,yCenter,xCenter: real; a1,a2,a1Interval,a2Interval: real; r,r1,r2,rStop: real; x1,y1,x2,y2: real; function Year(i: integer): real; {orbital period in days} begin if i=1 then Result:=87.969 else if i=2 then Result:=224.701 else if i=3 then Result:=365.256 else if i=4 then Result:=686.980 else if i=5 then Result:=4332.6 else if i=6 then Result:=10759.2 else if i=7 then Result:=30685 else if i=8 then Result:=60190 else if i=9 then Result:=90465; end; function Orbit(i: integer): real; {mean orbit distance in 10^6 km} begin if i=1 then Result:=57.91 else if i=2 then Result:=108.21 else if i=3 then Result:=149.60 else if i=4 then Result:=227.92 else if i=5 then Result:=778.57 else if i=6 then Result:=1433.5 else if i=7 then Result:=2872.46 else if i=8 then Result:=4495.1 else if i=9 then Result:=5869.7; end; function Name(i: integer): string; begin if i=1 then Result:='Mercury' else if i=2 then Result:='Venus' else if i=3 then Result:='Earth' else if i=4 then Result:='Mars' else if i=5 then Result:='Jupiter' else if i=6 then Result:='Saturn' else if i=7 then Result:='Uranus' else if i=8 then Result:='Neptune' else if i=9 then Result:='Pluto'; end; begin {main program} Planet1:= 3; {select outer planet} Planet2:= 2; {select inner planet} Orbits := 8; {number of outer rotations} Planet1Year := Year(Planet1); Planet2Year := Year(Planet2); Planet1Radius := Orbit(Planet1); Planet2Radius := Orbit(Planet2); Interval := Planet1Year/75; {days} FindWindow(eChart); yBottom:=PriceToY(GetVariable(eScaleLow)); yCenter:=2+yBottom/2; xCenter:=100+yCenter; r1:=yCenter; {outer radius} r2:=r1*Planet2Radius/Planet1Radius; {inner radius} r:=0; rStop:=Planet1Year * Orbits; a1:=0; a1Interval:=2*pi*Interval/Planet1Year; a2:=0; a2Interval:=2*pi*Interval/Planet2Year; SetPen(clBlue); {print labels} TextOut(120,10,Name(Planet1)); TextOut(120,30,Name(Planet2)); TextOut(120,yBottom-30,inttostr(Orbits)+' orbits'); while r<rStop do begin i:=trunc(r/interval/75); {use different color each orbit} if i=0 then c:=clBlack else if i=1 then c:=clBlue else if i=2 then c:=clRed else if i=3 then c:=clGreen else if i=4 then c:=clPurple else if i=5 then c:=clMaroon else if i=6 then c:=clNavy else if i=7 then c:=clDkRed else c:=clOrange; SetPen(c,1,eSolid,pmCopy); a1:=a1-a1Interval; {angle1} a2:=a2-a2Interval; {angle2} x1:=r1*Cos(a1); y1:=r1*Sin(a1); {convert polar to rectangular coordinates} x2:=r2*Cos(a2); y2:=r2*Sin(a2); MoveToLineTo(x1+xCenter,y1+yCenter,x2+xCenter,y2+yCenter); {draw line} r:=r+Interval; {move around outer circumference} end; end;