SHAPE & SIZE OF THE EARTH

Key Concepts

Aristotle (4th century BC) showed that the Earth is spherical.
Eratosthenes (ca. 200 BC) determined the size of the Earth.
No one laughed at Christopher Columbus when he said the world was round.

(1) Aristotle (4th century BC) showed that the Earth is spherical.

The first person recorded as saying the Earth is spherical was the Greek philosopher Pythagoras, who lived in the 6th century BC. Pythagoras, although he realized the importance of mathematics in describing the universe (the famous Pythagorean Theorem is attributed to him), was not a rigorous scientist. He supported his statement that the Earth is spherical with the mystical-philosophical reason that the sphere is the `perfect shape', and that the Earth must therefore be spherical.

The philosopher-scientist Aristotle, who lived in the 4th century BC, was the first to give REASONS why the Earth is spherical. He supported his statement that the Earth is spherical with three pieces of directly observed evidence.

(1) Matter is drawn to the center of the Earth by gravity. This tends to compress the Earth into a spherical shape. (This is the weakest of Aristotle's arguments; rock is stiff, and is able to resist the tendency to be compressed into a sphere.)

(2) As you move from north to south, new constellations are seen rising above the southern horizon.

(This is a stronger argument, but still only proves that the Earth is curved in the north - south direction, not in the east - west.)

(3) During a lunar eclipse, the Earth's shadow on the Moon is always round. The only object whose shadow is always circular, no matter what its orientation, is a sphere. (This is the strongest of Aristotle's arguments.)

During the Middle Ages, Aristotle was the standard scientific authority in the Christian and Muslim worlds. Literate individuals (who were, of course, a minority at the time) believed Aristotle's statement that the world is spherical. The Divine Comedy, for instance, written by Dante in 1300 AD, makes the basic assumption that the Earth is a sphere - an assumption that Dante shared with all his readers.

(2) Eratosthenes (ca. 200 BC) determined the size of the Earth.

Not only did ancient and medieval astronomers know the shape of the Earth (starting with Aristotle around 350 BC), they also knew the approximate size of the Earth (starting with Eratosthenes around 200 BC). Eratosthenes was the head librarian at the famous Library of Alexandria. He was able to determine the size of the Earth without ever having to leave the city of Alexandria (in northern Egypt).

Eratosthenes read, in one of the many scrolls contained in the Library of Alexandria, that at noon on June 21 (the time of the Summer solstice), in the town of Syene, the Sun is at the zenith, directly overhead. (Syene is the modern city of Aswan, located south of Alexandria, on the banks of the Nile.) The next time June 21 rolled around, Eratosthenes stepped outside, and determined that the Sun was NOT directly overhead as seen from Alexandria, but was 7.2 degrees south of the zenith (the point directly overhead). Eratosthenes was able to use these observations to determine the size of the Earth, but only if he made a few assumptions first.

THE ASSUMPTIONS OF ERATOSTHENES:

The Earth is spherical - this had been known since Aristotle had figured it out a century and a half earlier.
The Sun is very far away, compared to the size of the Earth - this implies that a ray of sunlight striking Alexandria and a ray of sunlight striking Syene are essentially parallel.
Alexandria is due north of Syene - this isn't exactly true, but it only introduces a minor error into the result.

Using his observations and assumptions, Eratosthenes was able to make the diagram below:

A ray of sunlight strikes Syene perpendicular to the ground. A parallel ray of sunlight strikes Alexandria at an angle of 7.2 degrees from the perpendicular. The laws of geometry (as compiled by Euclid, a century before the time of Eratosthenes) tell us that the angle from Alexandria to the center of Earth to Syene must also be 7.2 degrees.

Eratosthenes said, at this point, `Seen from the center of the Earth, Alexandria and Syene are 7.2 degrees apart; that's 1/50 of a complete circle. The distance between Alexandria and Syene, as measured on the surface of the Earth, must then be 1/50 of the complete distance around the Earth.' To find the circumference of the Earth, Eratosthenes simply had to find the distance between Alexandria and Syene, and multiply it by 50. The road from Alexandria to Syene was a well-traveled trade route, and the Alexandria - Syene distance was well known.

Distance from Alexandria to Syene = 5000 stades.
Circumference of the Earth = 50 x 5000 = 250,000 stades.

The `stade' was a common unit of length in the ancient world. Unfortunately, the length of the stade varied from place to place. The most commonly used value was the Olympic stade of 0.185 kilometers (corresponding to the length of the foot races run at the ancient Olympic games). If Eratosthenes used the Olympic stade, he found a value for the circumference of 46,250 kilometers (15% longer than the true value of 40,000 kilometers). However, since he was in Egypt, he might have been using the Egyptian stade of 0.157 kilometers. This would have given a value for the circumference of 39,300 kilometers, only 2% smaller than the true value.

No matter which `stade' Eratosthenes was using, he came remarkably close to the truth. He was well aware that the Earth, with a circumference of roughly 40,000 kilometers, was much larger than the Mediterranean world with which he was familiar. (The Mediterranean Sea is about 4000 kilometers long from east to west.)

(3) No one laughed at Christopher Columbus when he said the world was round.

He was correct when he said the Earth is spherical, but every educated individual knew that already. The interesting part about the Columbus saga is not that Columbus was right about the shape of the Earth, but that he was wrong about its SIZE. Eratosthenes was lucky to get the size of the Earth so accurately - the errors in his measurements just happened to cancel each other out. Other astronomers, after Eratosthenes, made similar calculations with similar data and got values as small as 30,000 kilometers or so and as large as 50,000 kilometers. Columbus wanted to sell people on the idea that the journey westward from Europe to Asia was a short one. Thus, from all the values published for the circumference of the Earth, he picked the smallest one: 30,000 kilometers. A small Earth means a short journey. From all the values published for the distance eastward from Europe to Asia, he picked the largest one. A long journey eastward means a short journey westward. Columbus was basically picking and choosing from the available numbers to support his preconceived notions. The end result: Columbus computed the distance westward from the Canary Islands (his jumping-off point) to Japan as being only 4000 kilometers. The actual value is 20,000 kilometers. What saved Columbus from becoming fish food is that the Bahamas are about 4000 kilometers west of the Canaries.

Columbus had convinced himself that Asia was only 4000 kilometers west of the Canaries - thus, when he discovered land in that position, he stubbornly clung to his belief that he had landed on islands lying just off the coast of Asia, even during his three subsequent journeys to the New World.

updated: