Posts Tagged ‘circumference’

PostHeaderIcon The Earth is Round

…and it has been for a LONG time. At least, since the late 1000BCE. There’s been a weird misconception that in the time around 5th to 15th century, we all thought our Earth was flat. Then Columbus struck out on his boat and upon returning changed it all.

Truth is, many different scholarly Greeks had discovered, proved, calculated, however you want to call it, that our Earth was indeed a big blue ball. In fact, once this development sprouted out of Ancient Greece in the centuries before the Roman Empire even got off the ground, the ideals of a spherical Earth pervaded through Europe clear into modern day. The idea of a flat Earth between educated peoples in the days of Columbus was next to none.

But how on Earth did we figure out the Earth was round way back before satellites and computers? Well, one man named Ἐρατοσθένης (Eratosthenes) was able to get the answer using simple math that another Greek, Πυθαγόρας (Pythagoras), developed. If you remember your right-angle triangles you might already know where this is headed.

Sunlight for Eratosthenes

Sunlight for Eratosthenes

In his publication of “Περὶ τῆς ἀναμετρήσεως τῆς γῆς” (On the Measurement of the Earth) he explained the details of his method. Eratosthenes read that on the summer solstice at noon in the city of Syene, rays from the Sun would reach the bottom of the deepest well. In other words, the Sun would be directly overhead. He knew that on the same day in Alexandria, the sun was not directly overhead. Since he assumed that Alexandria was basically due north of Syene, he figured that the arc distance between the two locations was roughly 1/50 of a full circle (7°12′) north of the zenith at the same time.

How Eratosthenes figured out the distance from Alexandria to Syene is a somewhat unsettled. Some say he hired someone to measure the distance, others says that he estimated the distance from the average time required for a caravan of camels to travel the distance, and another that he walked the distance himself. However it was measured, the distance was determined to be about 5,000 stadia.

With all this, he foudn his final value of 700 stadia per degree, which would multiply out to a circumference of 252,000 stadia. There were at least two different units in common use at the time, equivalent to 157.5 m and about 185 m. That put Eratosthenes’s value between 39,690 km and 46,620 km. The circumference of the Earth around the poles is now measured to be around 40,008 km. If you average ou, this puts Eratosthene’s answer within roughly 7.8%! All with shadows and simple math.

This method, while hindered by low precision data, was very accurate and was accepted for hundreds of years afterwards. Even other astronomers/geographers used his method and other methods in its likeness to further maintain the accuracy of the Earth’s circumference.

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