Daily Archives: May 2, 2019

How he did it

Just to recap from the last couple of posts: First, Eratosthenes guessed the Earth was round like a ball. Second, he knew that at noon on the Summer solstice, the Sun shone directly overhead in the town of Syene, which was 5,000 stadia south of Eratosthenes.

Third, Eratosthenes guessed the Sun was really big—huge, even. He noticed that shadows cast by the Sun are all parallel, so all the Sun’s rays must be parallel, too. Parallel means 2 or more lines that never touch—they stay the same distance from each other. Think train tracks.

SO, Eratosthenes—in Alexandria, 5,000 stadia north of Syene—put a stick (like the gnomon of a sundial) in the ground and made sure it was plumb. That stick was pointing down to the center of the Earth. If Earth is round, the well in Syene and Eratosthenes’ stick won’t be parallel, right? They’ll be at an angle to each other. Eratosthenes didn’t know exactly how many degrees that angle was, but in Alexandria at noon on June 21st, his stick cast a shadow.

There weren’t any shadows in Syene, because the Sun was directly overhead. He measured the stick, he measured the shadow, and used those measurements to draw an angle. The angle turned out to be a little over 7 degrees, or 1/50 of a circle.

Eratosthenes knew the distance from Alexandria to Syene was 5,000 stadia. He multiplied 5,000 by 50 to get the circumference of the Earth—250,000 stadia. In modern measurements that works out to be 28,738.418 miles or 46,250 kilometers.

The actual polar circumference of Earth is about 24,860 miles or just a bit over 40 thousand kilometers. The stadion Eratosthenes used may have been a little different from the standard unit. But even today, right now, if you search the internet for the circumference of the Earth, you won’t get just one answer.

Eratosthenes was a genius who used what he knew and observed, along with what he guessed at, to calculate something that no one knew—and he did it pretty accurately.

Back to the beginning of The Western Civ User’s Guide to Time & Space