### 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).

### 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:
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.
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:
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:
Then from command line, type earth_venus_3_b & earth_venus_3_d

### Data Tables (ref.2)

Planets Perihelion Mean Orbit Aphelion Eccentricity Inclination Tropical Year Equatorial Diameter Mass

106 km 106 km 106 km
degrees days km 1024 kg
Mercury 46.00 57.91 69.82 0.205631 7.0049 87.968 4879.4 0.3302
Venus 107.48 108.21 108.94 0.006733 3.3947 224.695 12103.6 4.8685
Earth 147.09 149.60 152.10 0.016710 0. 365.242 12756.2 5.9736
Mars 206.62 227.92 249.23 0.093412 1.8506 686.973 6794. 0.64185
Jupiter 740.52 778.57 816.62 0.048393 1.3053 4330.6 142984. 1898.6
Saturn 1352.2 1433.5 1514.5 0.054151 2.4845 10746.9 120536. 568.46
Uranus 2741.3 2872.46 3003.6 0.047168 0.76986 30589. 51118. 86.832
Neptune 4444.4 4495.1 4545.7 0.0085859 1.7692 59800. 49528. 102.43

### Other planets

To create this drawing and animation:
Then from command line, type planets_b

Prompts & Inputs
radius of reference planet(def=149.60) default value
How many days in one rotation of reference planet(def=365.242) default value
How many days in one rotation of comparison planet(def=224.695) 87.968
one step in earth's days(def=3 ) 1
How many steps(def = 973) 365
delay speed between position change(def= 50 ms) 20
-------------animation for Earth_Mercury
*************** earth_mercury.dwg ***************

To create this drawing and animation:
Then from command line, type planets_b

Prompts & Inputs
How many days in one rotation of reference planet(def=365.242) default
How many days in one rotation of comparison planet(def=224.695) 686.973
one step in earth's days(def=3 ) 5
How many steps(def = 973) 1168
delay speed between position change(def= 50 ms) 20
-------------animation for Earth_Mars
*************** earth_mars_16yrs.dwg ***************

To create this drawing and animation:
Then from command line, type planets_b

Prompts & Inputs
How many days in one rotation of reference planet(def=365.242) default
How many days in one rotation of comparison planet(def=224.695) 4330.6
one step in earth's days(def=3 ) 10
How many steps(def = 973) 450
delay speed between position change(def= 50 ms) 20
-------------animation for Earth_Jupiter
****************** earth_jupiter.dwg ******************

To create this drawing and animation:
Then from command line, type planets_b

Prompts & Inputs
How many days in one rotation of reference planet(def=365.242) default
How many days in one rotation of comparison planet(def=224.695) 10746.9
one step in earth's days(def=3 ) 30
How many steps(def = 973) 365
delay speed between position change(def= 50 ms) 20
-------------animation for Earth_Saturn
*************** earth_saturn.dwg ******************

To create this drawing and animation:
Then from command line, type planets_b

Prompts & Inputs
How many days in one rotation of reference planet(def=365.242) default
How many days in one rotation of comparison planet(def=224.695) 30589
one step in earth's days(def=3 ) 30
How many steps(def = 973) 1025
delay speed between position change(def= 50 ms) 20
-------------animation for Earth_Uranus
*************** earth_uranus.dwg ***************

To create this drawing and animation:
Then from command line, type planets_b

Prompts & Inputs
How many days in one rotation of reference planet(def=365.242) 4330.6
How many days in one rotation of comparison planet(def=224.695) 10746.9
one step in earth's days(def=3 ) 100
How many steps(def = 973) 250
delay speed between position change(def= 50 ms) 20

*************** jupiter_saturn.dwg ***************

To create this drawing and animation:
Then from command line, type planets_b

Prompts & Inputs
How many days in one rotation of reference planet(def=365.242) 30589
How many days in one rotation of comparison planet(def=224.695) 59800.
one step in earth's days(def=3 ) 1000
How many steps(def = 973) 200
delay speed between position change(def= 50 ms) 20

*************** uranus_neptune.dwg **************

#### References

Go to   Fun_Math Content Table   Earth Moon & Sun

All comments should be sent to Takaya Iwamoto

Last Updated Nov 21-st, 2006