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The story of Eratosthenes and Earth’s circumference, as told by Carl Sagan

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Eratosthenes was a Greek mathematician, geographer, and astronomer who lived in the 3rd century BCE. He was the chief librarian at the Library of Alexandria and made important contributions to mathematics, geography, and astronomy.

But perhaps Eratosthenes is best known for his calculation of the Earth’s circumference. American astronomer, planetary scientist, astrophysicist, and author Carl Sagan tells the tale of Eratosthenes and the Earth’s circumference in this clip from the 1980 science mini-series Cosmos.

carl sagan and the 7 degree difference between cities
After hearing that the shadows disappeared at noon in the town of Syene (now known as Aswan), Eratosthenes achieved his understanding of our planet’s size by comparing the angle of the sun’s rays in the port city of Alexandria-at the same time. Then he measured the distance between the cities.

With a 7° difference in the shadows and a distance of around 800 kilometers, a calculation could be made: “Angle of shadow in Alexandria / 360 degrees = Distance between Alexandria and Syene / Circumference of Earth” or 7/360 = 800/x. From Scientific American:

“In 200 B.C. Eratosthenes estimated Earth’s circumference at about 46,250 kilometers (28,735 miles). Today we know our planet’s circumference is roughly 40,000 kilometers (24,850 miles). Not bad for a more than 2,000-year-old estimate made with no modern technology!”

the well at noon

• Measure Earth’s Circumference with a Shadow from Science Buddies.

Watch these related videos next on TKSST:
• Three proofs that Earth is round with NASA’s Michelle Thaller
• The science of solar eclipses: How do solar & lunar eclipses work?
• How do we study the stars & measure extreme distances in space?
• Carl Sagan’s Cosmic Calendar

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