Measuring the Earth With a Stick

HAVE you ever heard of the Greek mathematician and astronomer Eratosthenes? His name is probably best known among astronomers. Why do they think so highly of him?

Eratosthenes was born about 276 B.C.E. and received some of his education in Athens, Greece. He spent a good part of his life, however, in Alexandria, Egypt, which at that time was under Greek rule. In about 200 B.C.E., Eratosthenes set out to determine the dimensions of the earth by using a simple stick. ‘Impossible!’ you may say. How did he do it?

In the city of Syene (now called Aswân), Eratosthenes observed that at noon on the first day of summer, the sun was directly overhead. He knew this because there was no shadow cast when the sunlight reached the bottom of deep wells. However, at noon on the same day in the city of Alexandria, which was located 5,000 stadia * to the north of Syene, a shadow could be observed. That gave Eratosthenes an idea.

Eratosthenes set up a gnomon, a simple upright stick. When the sun was overhead at noon, he measured the angle of the shadow that the stick cast in Alexandria. He determined the angle to be 7.2 degrees from vertical.

Now, Eratosthenes believed the earth to be spherical, and he knew that there are 360 degrees in a circle. So he divided 360 by the angle he had measured, 7.2. The result? His angle was one fiftieth of a full circle. He then deduced that the distance from Syene to Alexandria, or 5,000 stadia, must be equal to one fiftieth of the circumference of the earth. By multiplying 50 by 5,000, Eratosthenes came up with the figure of 250,000 stadia as the circumference of the earth.

How close did his figure come to present-day calculations? The figure of 250,000 stadia is equal to between 25,000 and 29,000 miles [40,000 and 46,000 km] in current measurements. Using orbiting spacecraft, astronomers measured the earth’s polar circumference and submitted the figure of 24,860 miles [40,008 km]. Thus, over 2,000 years ago, Eratosthenes came astoundingly close to the modern-day figure. His accuracy is all the more remarkable when you consider that the man used only a stick and geometric reasoning! Astronomers today use this geometric method as a basis for measuring distances outside our solar system.

Some might find it especially remarkable that Eratosthenes knew that the earth is round. After all, up until just a few hundred years ago, even some wise men involved in science believed that the earth was flat. The ancient Greeks had deduced the earth’s shape from their scientific observations. However, about 500 years before Eratosthenes, a Hebrew prophet was inspired to write: “There is One [God] who is dwelling above the circle of the earth.” (Isaiah 40:22) Isaiah was no scientist. How did he know that the earth was round? It was divine inspiration that revealed this truth.

[Footnote]

^ par. 4 Stadia were Greek units of length. Though the exact value varied locally, one stadium is believed to have been about 530 to 600 feet [160 m to 185 m].

[Diagram on page 13]

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Sunray

Syene

7.2°

Alexandria

7.2°