How do you measure the circumference of the Earth? It’s not like you can take out a meter stick and lay it end to end hundreds of thousands of times. Today with satellite technology and GPS we can easily complete this task and get an extremely precise answer: 40,075.017 kilometers. But how might a Greek scientist living in 3rd century BC Egypt accomplish such an undertaking?
The answer is ingenious. It always amazes me how brightest of minds comes up with the most remarkably clever solutions to seemingly impossible questions. Who wakes up in the morning and declares, “I want to measure the circumference of the Earth?” or any other crazy question of that type? Talk about taking on the some of the greatest challenges head on.
But I digress, how did a man named Eratosthenes find an answer to a presumably unattainable question? He did so by harnessing the power of the Sun and his knowledge of basic geometry. Eratosthenes lived in the Egyptian city of Alexandria, but had a correspondent in Swenet (now modern day Aswan). Eratosthenes’ friend in Swenet told him about a well in town that one could see all the way down to the water on the day of the Summer Solstice at Noon. This may not sound all that exciting but what that really means is that there is no shadow on this special day of the year. Even the lack of a shadow may not seem all that earth-shattering, but the lack of a shadow means that the Sun is directly overhead, at the zenith.
Eratosthenes pocketed this information and then observed the Sun in his home of Alexandria on the Summer Solstice at Noon. What he found was that shadows were cast in Alexandria and thus the Sun was not directly overhead. So, being a curious man, Eratosthenes pulled out his trusty gnomon (an ancient tool for measuring angles), and measured the angle of sunlight at Alexandria. What he found was that the Sun was about 1/50th of a circle from the zenith at Noon on the solstice. This comes out to roughly 7.5 degrees. Next, using basic theorems of geometry, he equated the angle of sunlight to the angular distance between the two cities as measured from the center of the Earth. Now knowing the angle is only half the battle in determining a measurement for the Earth’s circumference. Eratosthenes needed a measurement of the metric distance between the two cities. The story says that, as any right-minded man would do, he hired an army to march from Swenet to Alexandria and keep count of the number of steps they took during their journey. The marching soldiers related their steps to the Egyptian unit called the stadia, which translates to 157.5 meters, and came up with 5000 stadia between the cities. When a little algebra is applied, this comes out to about 700 stadia per degree of Earth. Now multiplying by 360 degrees and changing units from stadia to meters, you get 39,690 kilometers as the circumference of the Earth, which is a 1.6% difference from our current accepted value! 1.6% off! There are modern day experimental labs which strive for anything less than 5% error, never mind less than 2%!
It astonishes me how the grandest questions often have the cleverest, yet simplest solutions. More often than not in astronomy, scientists must come up with clever, indirect methods of measurement, since the objects that astronomy deals with are too big and/or too far away to measure directly. But the thrill of exploration and the innate human desire to learn has driven the brightest minds of every generation to come up with new and ingenious ways to come up with answers to the biggest of questions, using nothing but wit and basic mathematical principles.
