You can measure the circumference of the Earth too! Simple experiments-I

I have an unhealthy man-crush on Eratosthenes, even though he has been dead for close to two thousand and two hundred years ( I know it sounds odd and to some people sick, but listen to what I have to say for him and therefore in my defence). He had the nickname of beta as he proved to his friends that he was the second best in any field- he was a true polymath excelling in mathematics, astronomy, cartography; he was also a poet and an athlete! He was a man to be admired. I will outline his experiment where he calculates the circumference of the earth. The best thing about this is that anyone can do it for themselves! I mean this experiment is well over two thousand years old! I'll give a slightly revised edition as Eratosthenes did not know about meridians and latitudes

Let us assume that the earth is a sphere ( It is not exactly a sphere, but let us assume it!) We know that the rays of the sun are parallel to the earth. Let us take two places on the same meridian (or longitude or actual timezones :P), during the equinox. We take two sticks of equal length and take them to two places apart on the same longitude. The shadows cast by these sticks are then measured and their angle to the vertical is determined- this is akin to finding out the latitude. This has to be done at noon, when the sun is at it's zenith and the first stick will cast no shadow- while the second stick, some distance on the meridian will do so. This is a measure of the difference in latitude (Difference in angles to the vertical the shadows make). Now find the angles made by these shadows to the vertical and find their difference! Then finding the circumference of the earth is a piece of cake! Let a hairy Eratosthenes show you (Being hairy was manly then!)





You know the distance between the sticks, X- you know the difference between the angles, which is A. All you do is plug in the arc length formula and "Voila!" Solve for the circumference, S!

Eratosthenes was a bit lucky though- he got lucky with his guess for the distance between his sticks (one was in Alexandria and the other was in Ancient Syene and the ancients had a measurement system which was as reliable as a mule is easygoing and timid). Secondly the two cities were not on the same longitude, but were close enough to each other so that the result was not distorted beyond recognition. But still it was a very good estimate and he successfully calculated the circumference of the earth!

I know that we can't travel a good 800 kms just to measure sticks' shadow lengths! Use an atlas is all I can say! Unlike Eratosthenes, we are not paid to measure lengths of a stick (or two!). But it is still fun and some nice trivia and I was in a thoroughly nerdy mood, considering I am jobless and watching a whole lot of youtube!