ERATOSTHENES VISITS PUEBLO WEST
Eratostenes (276 to 194 B.C.) st
Just for fun to celebrate the recent Solstice (June 21 ), I decided to emulate the
great Greek geometer Eratosthenes and try to measure the circumference of the
Earth from my backyard in Pueblo West!
As the story goes, Eratosthenes asked himself why should a stick in Syene (Egypt)
cast no shadow when far to the north in Alexandria there would be a distinct
shadow? Eratosthenes correctly surmised that the only way this could happen is if
the Earth were curved – otherwise, if the Sun were directly over a flat Earth, there
would be no shadows anywhere!
His reasoning was similar to Figure 1. He placed a vertical stake in the ground in Alexandria and measured the
length of its shadow at a precise time, and calculated its angle (Figure 1) by simple trigonometry. The “shadow
angle” is the same angle as that
subtended by the curvature of the
Earth (alternate interior angles
are equal – remember 10th grade
geometry class?).
So I drove a stake in the ground
(see Figure 2) and measured the
length of its shadow (Figure 3) at
solar noon (actually the shortest
shadow occurred just before 1:00
MDT). From the height of the
stake I was able calculate the
subtended angle (14.90
degrees). I divided that into 360
degrees and got a factor of
24.16; in other words, I am about
1/24 around the world from where
the Sun is directly overhead. Now
if I multiply 24.16 times
the distance between Pueblo
West due south to the Tropic of
Figure 1 Cancer (where the Sun is
overhead at Solstice so the angle
subtended by the Sun is zero degrees), I would calculate the circumference of the Earth!
Figure 2: My experimental setup to capture
the Sun’s shadow. The concrete block is
prevent movement due to the famous Pueblo
West winds. Figure 3: My high-tech method of
measuring the shadow. At this point Eratosthenes hired someone to pace off the distance between Syene and Alexandria, but I don't
have that level of commitment. I merely consulted my globe and noted that Durango, Mexico, lies near the
Tropic of Cancer and is almost due south of my backyard. From my road atlas I determined the distance
between Pueblo West and Durango at 1,023.5 miles.
Multiplying 1,023.5 miles by 24.16 gave me about 24,730 miles. The actual circumference (through the poles)
is 24,860 miles, an uncanny error of only 0.5% on my first try - no fudging at all, honest!
This is how science nerds have fun!
(By the way, Eratosthenes calculated the circumference of the Earth to be 40,000 kilometers or 24,850 miles.
He obviously took better measurements than I did!