Carl Sagan Globular Earth Deduced By Eratosthenes


Carl Sagan Globular Earth Deduced By Eratosthenes

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[Carl Sagan Globular Earth Deduced By Eratosthenes]

[Carl Edward Sagan (Born: November 9, 1934):] Source:
There was once a time when our little planet seemed immense. When it was the only world we could explore. Its true size was first worked out in a simple and ingenious way by a man who lived here in Egypt, in the third century B.C.

This tower may have been a communications tower. Part of a network running along the North African coast by which signal bonfires were used to communicate messages of state. It also may have been used as a lighthouse a navigational beacon for sailing ships out there in the Mediterranean Sea. It is about 50 kilometers west of what was once one of the great cities of the world, Alexandria.

In Alexandria, at that time there lived a man named Eratosthenes. One of his envious contemporary called him beta, the second letter of the Greek alphabet because, he said, Eratosthenes was second best in the world in everything. But it seems clear that, in many fields, Eratosthenes was alpha. He was an astronomer, historian, geographer, philosopher, poet, theater critic and mathematician. He was also the chief librarian of the Great Library of Alexandria. And one day while reading a papyrus book in the library, he came upon a curious account.

Far to the south, he read at the frontier outpost of Syene something notable could be seen on the longest day of the year.

On June 21st, the shadows of a temple column, or a vertical stick would grow shorter as noon approached. And as the hours crept towards midday the Sun’s rays would slither down the sides of a deep well, which on other days would remain in shadow. And then, precisely at noon columns would cast no shadows. And the Sun would shine directly down into the water of the well. At that moment, the Sun was exactly overhead.

It was an observation that someone else might easily have ignored. Sticks, shadows, reflections in wells, the position of the Sun simple, everyday matters of what possible importance might they be?

But Eratosthenes was a scientist and his contemplation of these whole new matters changed the world in a way, made the world. Because Eratosthenes had the presence of mind to experiment, to actually ask whether back here, near Alexandria a stick cast a shadow near noon on June the 21st. And it turns out, sticks do.

An overly skeptical person might have said that the report from Syene was an error. But it’s an absolutely straightforward observation. Why would anyone lie on such a trivial matter?

Eratosthenes asked himself how it could be that at the same moment a stick in Syene would cast no shadow and a stick in Alexandria, 800 kilometers to the north would cast a very definite shadow.

[Carl Edward Sagan:] Source:
Here is a map of ancient Egypt. I’ve inserted two sticks, or obelisks. One up here in Alexandria and one down here in Syene. Now, if at a certain moment each stick casts no shadow, no shadow at all. That’s perfectly easy to understand, provided the Earth is flat. If the shadow at Syene is at a certain length and the shadow at Alexandria is the same length that also makes sense on a flat Earth. But how could it be, Eratosthenes asked that at the same instant there was no shadow at Syene and a very substantial shadow at Alexandria?

The only answer was that the surface of the Earth is curved. Not only that, but the greater the curvature, the bigger the difference in the lengths of the shadows.

The Sun is so far away that its rays are parallel when they reach the Earth. Sticks at different angles to the Sun rays will cast shadows at different lengths.

So the observed difference in the shadow lengths, the distance between Alexandria and Syene had to be about seven degrees along the surface of the Earth.

By that, I mean, if you would imagine these sticks extending all the way down to the center of the Earth they would there intersect at an angle of the bottom seven degrees. Well, seven degrees is something like a 50th of the full circumference of the Earth, 360 degrees.

Eratosthenes knew the distance between Alexandria and Syene. He knew it was 800 kilometers. Why? Because he hired a man to pace out the entire distance so that he could perform the calculation I’m talking about.

Now, 800 kilometers times 50 is 40,000 kilometers. So that must be the circumference of the Earth. That’s how far it is to go once around the Earth. That’s the right answer.

[Carl Sagan:] Source: L Y B I O . N E T
Eratosthenes’ only tools were sticks, eyes, feet and brains. Plus a zest for experiment. With those tools, he correctly deduced the circumference of the Earth to high precision with an error of only a few percent. That’s pretty good figuring for 2200 years ago.

Carl Sagan-globular Earth Deduced By Eratosthenes

Carl Sagan-globular Earth Deduced By Eratosthenes

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