Harmony in the Solar System

Source of contents for this section

Most of the contents and astronomical data for this section come from a small, but beautiful book by John Martineau (Ref.2).

List of animations posted on this page.(Click the text to watch animation.)
animation for earth_venus_1
animation for earth_venus_1_color.
animation for earth_venus_2
animation for earth_venus_2_color.
animation for earth_venus_3_b
animation for earth_venus_3_d.
animation for Earth_Mercury
animation for Earth_Mars
animation for Earth_Jupiter
animation for Earth_Saturn
animation for Earth_Uranus

Beautiful relationship between the Venus and the Earth

The Sun at the center

The orbits of all the planets around the Sun are the ellipses with very small eccentricities. So the paths of the Venus and the Earth are very close to the circles with their mean orbit,which are the average of Perihelion(semi major axis) and Aphelion(semi minor axis). When the center of Venus and the Earth is connected by a line segment, then the result after 8 years will look like the following pictures. What an amazing show !! Note that the red sphere in the center is the Sun, yellow ball , the Venus and green ball, the Earth.

------------------animation for earth_venus_1-------------------animation for earth_venus_1_color.---------
******************** earth_venus_1.dwg ******************** **************** earth_venus_1_color.dwg ****************

To create this drawing and animation:
Load planets_motion.lsp (load "planets_motion")
Then from command line, type earth_venus_1 & earth_venus_1_color
Note* : This program requires green_ball.dwg, red_ball.dwg & yellow_ball.dwg .

Inut data for the Venus and the Earth are given in the Data Table in this topic.
Radii are 108.21 & 149.60.
Tropical years are 224.695 & 365.242.
The angular motion step per day is (360/365.242) degrees for the Earth , and (360/224.695) degrees for the Venus.
So when the Earth goes around the Sun 8 times(= 365.242 x 8 = 2921.936 days), the Venus makes about 2921.936/224.695 = 13.0040 turns around the Sun.
The pictures are created by incrementing angles by 3 days. So the total steps is set to 2921.936/3 = 974 .

Viewers on the Earth (1)

For the observer's eyes on the Earth, the Sun moves around the Earth and the Venus going around the Sun.
So the path of Venus for 8 years looks like the pictures below.

-------------animation for earth_venus_2-------------------animation for earth_venus_2_color.---------
******************** earth_venus_2.dwg ******************** **************** earth_venus_2_color.dwg ****************

To create this drawing and animation:
Load planets_motion.lsp (load "planets_motion")
Then from command line, type earth_venus_2 & earth_venus_2_color

Viewers on the Earth (2)

If the Sun and the Venus is connected with a line, during the 8 years, the lines create a beautifull pattern.
5 different colors are assigned to 5 cycles during the Earth's 8 turns and Venus' 13 turns around the Sun.
The sequence is starting with red, yellow,green, cyan and then ends up with blue.
The second picture is for illustrating the so-called "retrogress" motion as seen from the Earth when
the path of Venus makes a loop .

-------------animation for earth_venus_3_b-------------------animation for earth_venus_3_d.---------
****************** earth_venus_3_b.dwg ****************** ****************** earth_venus_3_d.dwg ******************

To create this drawing and animation:
Load planets_motion.lsp (load "planets_motion")
Then from command line, type earth_venus_3_b & earth_venus_3_d