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How the earth was measured - the Classical Era
The Spherical Earth
The notion that the earth is a sphere goes way back in our history. Pythagoras, back in 500 BC proposed a spherical earth, though he offered no evidence, his proposed spherical earth was based purely on aesthetic grounds. It wasn't until Aristotle (384-322 BC) proposed a spherical earth in his book "on the heavens" in 350 BC, now we see physical evidence being espoused.
People living in the southern lands see southern constellations higher above the horizon than those living in northern lands. If you were to move in a southerly direction you would literally be moving along the curve of the earth ( any direction actually, I just used south as an example) thats why the southern constellations would get higher above your horizon as you moved further southward.
The shadow of the earth on the moon during a lunar eclipse is round. The next lunar eclipse try and get out and take a good look, it's really awesome to watch and you can clearly see the round shadow of the earth on the moon. The round shadow is only possible if the earth was a sphere.
Aristotle also noted in his book, the fact that objects fall to Earth towards its center means that if it were constructed of matter originally, these parts would naturally settle into a spherical shape. We know today that is exactly how planetary bodies form in our universe. The evidence was so compelling for a spherical earth it became widely believed amongst the philosophers and others in the Classical era.
Having determined it's shape, the questions arise, what is the earths size? How do you measure something that is a whole lot bigger than you ?
Eratosthenes (276 - 195 BC) was the Librarian of Alexandria, Egypt. The Library was a repository of knowledge and learning. The many books that the library housed drew scholars from all over the Mediterranean, in it's day it was the intellectual center for research and learning.
The motion of the heavenly bodies in the sky were well known back in the Classical Greek Era. They knew, that on the day of the summer solstice, in Syene, Egypt (modern Aswan) the sun was straight overhead at noon and did not cast shadows. Syene is on the lower Nile in southern Egypt. Also on the same day, at noon, the sun would cast shadows at Alexandria, located north of Syene on the Nile delta.
The shadow cast in Alexandria allows the circumference of the earth to be measured
Eratosthenes knew that on the summer solstice in Syene that the sun was directly overhead and a stick in the ground would cast no shadow. He also knew in a stick would cast a shadow in his home of Alexandria and with that knowledge he figured out a way to measure the circumference of the earth.
By measuring the angle from the shadow cast in Alexandria Eratosthenes was able to figure out the sun was about 7 and 12/60th degrees south of overhead. Since a full circle is 360 degrees, divide the sun angle by 360 and we get 1/50th of a full circle. We now know the distance from Alexandria to Syene is 1/50th the circumference of the earth. Figure out the distance between the two cities and multiply by 50 and you have the size of the earth.
First we need to know the distance between the two cities. At the time of Eratosthenes Alexandria to Syene was a major trade route and the estimated distance was 5000 stadia. So doing the math we end up with, circumference = 50 x 5000 stadia = 250,000 stadia. Thats all well and good, but we want our distance expressed in kilometers. So. How big is a stadia? No problem, 600 Greek feet. How big is a Greek foot ? You can see the ambiguity of the measurements becomes a problem. The best modern guess is 1 stadia equals anywhere between 150 - 185 meters in length. A stadia is a measurement of a foot race that was held in a Greek Stadium. Archaeologist have measured the Stadium at Athens and come up with what they call the "Attic Stadion" 185 meters; some scholars think this is the stadia Eratosthenes would be using. If we take 250,000 stadia X 185 meters we get 46,250 kilometers, not bad, the actual circumference of the earth is 40,070 km. Eratosthenes estimate is only 15% to large. Now when you consider the possible difference in the exact number of meters in a stadia, who knows Eratosthenes may have gotten the measured circumference exact.
Fast forward three hundred years and we meet Claudius Ptolemy (87 - 150 AD). He was a Geometer and Astronomer of the late Classical Age in Alexandria. His work was immensely influential in later centuries.
One of Ptolemy’s main works is his Geography, a list of geographical coordinates of the world that was known in his day. He relied on work from Marinos of Tyre, and on the astronomical observations made by others from the ancient Roman and Persian Empire. Ptolemy made a geometric estimate based on stellar measurements, unlike Eratosthenes solar measurements. Ptolemy's estimate yields a circumference of 28,800 kilometers, which is 28% smaller than the correct value (40,070 km). We can easily convert Classical Roman units to modern units, largely because many Roman roads and measuring techniques have survived from antiquity. This value of 28,800 km will be a major factor in influencing a trip that would change the world.
Unfortunately the works of Eratosthenes was lost and we only know of him and his work through second hand accounts of other writers. On the other hand, Ptolemy's major works have survived, the most important being the Almagest, which was a term derived from the original Greek name for The mathematical Compilation. Ptolemy's Almagest, along with Euclid's Elements, shares the glory of being the scientific text longest in use.
Ptolemy’s work enjoyed high status, it was often referred to as the greatest, and some scholars felt Eratosthenes values for the size of the earth were way to large. As far as they knew, there was only the connected continents of Europe, Asia, and the Orient. As a result, over the years, any maps being produced were an under-estimation of the actual size.
This led the seafaring gentlemen Christopher Columbus to devised a plan to sail west to reach the east. Having high confidence in his plan he was able to convince King Ferdinand of Spain to sponsor the expedition. Little did Columbus know the world was about to get a whole lot larger.
How a measurement of the earth inspired a new Journey
In August of 1492, Christopher Columbus sets sail with the command of three ships from the Spanish port of Palos. The beginning of a new Journey sailing west to the east, too sail around the earth. The rest, as they say, is history.