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Erastosthenes: Measuring the Size of the Earth

Erastosthenes: Measuring the Size of the Earth. Scott Morrison 8.282J / 12.402J 5 Feb 2009. Erastosthenes of Cyrene (275 - 194 B.C.). Chief librarian of Alexandria from 240 B.C. until his death His goal: to “reform the map of the world” in a systematic way

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Erastosthenes: Measuring the Size of the Earth

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  1. Erastosthenes: Measuring the Size of the Earth Scott Morrison 8.282J / 12.402J 5 Feb 2009

  2. Erastosthenes of Cyrene(275 - 194 B.C.) • Chief librarian of Alexandria from 240 B.C. until his death • His goal: to “reform the map of the world” in a systematic way • Most famous for giving a good estimate for the Earth's size

  3. Erastosthenes of Cyrene(275 - 194 B.C.) The world as described by Herodotus, ca. 450 B.C.

  4. Erastosthenes of Cyrene(275 - 194 B.C.) Erastosthenes' improvements to the world map, 194 B.C.

  5. Erastosthenes of Cyrene(275 - 194 B.C.) • The Greeks had known several earth models by 500 B.C. • Homer: disk-shaped earth, heavenly dome • Pythagoras: ball-shaped earth, celestial sphere • Again, our observations of the stars make it evident, not only that the earth is circular, but that it is a circle of no great size. For quite a small change of position to south or north causes a manifest alteration of the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward” • Aristotle, “On the Heavens”, Book II, Chapter 14

  6. Erastosthenes of Cyrene(275 - 194 B.C.) • Obvious question: how big? • Observations: • At Syene, no shadows • At Alexandria, 1/50 of circle • Distance is 5000 stades • Assumptions: • Earth is a perfect sphere • Sun's rays parallel • Syene is due south of Alex. 250,000 stades = 39,700 to 45,000 km Actual: 40,075 km

  7. Erastosthenes of Cyrene(275 - 194 B.C.) • How good are these measurements? • Syene is actually 30' north of Tropic or Cancer • Actual angle between cities is 7' less than stated • True distance is 5,300 stades by road—4,530 stades directly • Assumptions? • Oblate spheroid: error is 1 part in 300 • Rays are parallel to 1 part in 100,000 • 2° longitude between the two—so effective distance is 5% less • Whichever definition of a stade you use, error is about 10%.

  8. Erastosthenes of Cyrene(275 - 194 B.C.) • An amusing story about Columbus and his trip to Japan America: • Marinus of Tyre (ca. 70 - 130 A.D.) got a circumference 20% smaller. He wrote that the “terrestrial landmass” (i.e. Eurasia) subtended five-eighths of Earth, leaving only 135° of ocean. • Al-Farghani: 1 degree = Arabic miles (1830 m). Columbus used Italian miles (1238 m) instead. • Result: he thought the distance to the Orient was 3,700 km, not 19,600 km.

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