The Earth And The Moon [1]
Here is a simple and elegant way of
establishing the relative sizes of the earth and the moon. Start with a 3:4:5
triangle (shown in yellow in the diagram to the right), project a 3x3 square from
the shorter side and then draw another 3:4:5 triangle off the other side of the
square. From the bottom line of the resultant figure, project another square,
this time 11x11. Draw a circle in each of these squares.
From the 3:4:5 triangle we can calculate the following figures:
3 + 4 +5 = 12
3 x 4 x 5 = 60
12 + 60 = 72
12 x 60 = 720
You will recognize 12 and 60 as being the basis of how we measure
time. The figure of 72 relates to an astronomical phenomenon called
precession (because of the slow wobble of the earth's axis, the night sky
appears to revolve in a complete circle but not that you would notice. It takes
72 years to move through 1° of that circle) The next figure, 720 is the
one which relates to our two circles in the above diagram. Multiplying this
figure by the diameters we see:
720 x 3 = 2160
720 x 11 = 7920
The moon has a diameter of 2160 miles and the earth has a diameter of 7920 miles.
I found the information above at a very interesting site in England, called Inch Perfect, created by a gentleman named John Douglas. Unfortunately his email address is no longer valid, and so I was unable to contact him regarding the use of the above information. Hopefully he will not mind my copying of his data. And should he chance to see this page, I hope he will find my method and results as interesting as I found his.
Here are his calculated values compared to the actual earth and moon diameters:
The moon has an
actual equatorial diameter of 2160.01 miles (3476.2 km
[2]).
Difference between 2160
and 2160.01 is 0.00046%.
The earth has an
actual equatorial diameter of 7926.38 miles (12756.274 km
[3]).
Difference
between 7920 and 7926.38 is 0.081%.
Incredibly close!
At first I was intrigued that one could extract the diameters of the earth and moon, in miles, from such a simple geometric design. Then, I began to wonder if more earth-moon information could be found within the figure . . .
Look at the diagram to the right.
It's constructed the same as the one above, but I have replaced the circles with
spheres. The volumes of the two spheres are as follows:
V = volume d = diameter
Vblue = 14.1371669412 (volume of blue sphere)
Vred = 696.909970321 (volume of red sphere)
Amazingly, raising the ratio of Vred / Vblue to the 3rd or 5th power, provides both the earth-moon and earth-sun distances in miles -- as follows:
Here are my calculated values compared to the actual earth-moon and earth-sun distances:
The actual mean earth-moon distance is
238,855.08 miles (384399.9 km [2]).
Difference between my value of 239,592 and 238,855.08 is 0.31%.
The actual mean earth-sun distance is
92,955,817.7 miles (149597887.5 km [3]).
Difference
between my value of 92,666,249 and 92,955,817.7 is 0.31%.
Again, very close!
It seems that the simple geometric figure, constructed at the top of this page, can provide four important pieces of earth-moon data:
2160 Diameter of moon in miles
7920 Diameter of earth in miles
239592 Distance between earth and moon in miles
92666249 Distance between earth and sun in miles
March 10, 2003
References:
1. Inch Perfect.
Accessed 8 March 2003
<http://www.users.zetnet.co.uk/estatopia/inch5.htm#spheres>
2. Moon - Wikipedia, the free encyclopedia.
Accessed 15 July 2006
<http://en.wikipedia.org/wiki/Moon>
3. Earth - Wikipedia, the free encyclopedia.
Accessed 15 July 2006
<http://en.wikipedia.org/wiki/Earth>
