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

Most famous for giving a good estimate for the Earth's size

Erastosthenes of Cyrene(275 - 194 B.C.)

The world as described by Herodotus, ca. 450 B.C.

Erastosthenes of Cyrene(275 - 194 B.C.)

Erastosthenes' improvements to the world map, 194 B.C.

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

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

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%.

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.