Saturn from Cassini Astronomy 161:
An Introduction to Solar System Astronomy
Prof. Richard Pogge, MTWThF 2:30

Lecture 4: Measuring the Earth

Key Ideas:

Ancient ideas about the Earth.

The Spherical Earth

Measuring the Earth's Circumference:

The Four Corners of the Earth

The most common ancient theme is that of a Flat Earth surmounted by a hemispherical sky. In some cultures, the canopy of the sky was held up by immense trees or gigantic mountains.

Myth & Metaphor

These fanciful views are Representations rather than Portrayals of reality.

Classical Greece

The Ancient Greeks were intoxicated by geometry, form, and symmetry.

A sphere is the most perfect geometric solid

500 BC:
Pythagoras proposed a spherical earth purely on aesthetic grounds
400 BC:
Plato espoused a spherical earth in his 4th and final dialogue Phaedo, giving it wider circulation (the Pythagoreans were somewhat disreputable in Athenian circles)

Aristotle gets Physical...

Aristotle (384-322 BC) also proposed a spherical earth on geometric grounds, but backed up his assertion with physical evidence (described in his On the Heavens of 350BC[4.1])

Aristotle's demonstration was so compelling that a spherical Earth was the central assumption of all subsequent philosophers of the Classical era (up to ~300 AD).

He also used the curved phases of the moon to argue that the Moon must also be a sphere like the Earth.

How Big is the Earth?

Having established its shape, what is the size of the Earth?

Challenge: How do you measure something really big?

Solution: Apply the methods of Geometry.

Eratosthenes of Cyrene

Born in Cyrene (now Shahhat Libya) in 276 BC. He was the 2nd Librarian of Alexandria until his death around 195 BC.

It was known that on the day of the Summer Solstice in Syene Egypt (modern Aswan), the Sun was straight overhead at noon and did not cast shadows. Syene is on the lower Nile in southern Egypt.

On that same day, the noon Sun cast shadows at Alexandria, located north of Syene on the Nile delta.

Shadowless in Syene

Eratosthenes knew that no shadows on the Summer Solstice meant that Syene was on the boundary of the northern tropic zone (the Tropic of Cancer).

By measuring the length of the shadow in Alexandria at noon on the Summer Solstice when there was no shadow in Syene, he could measure the circumference of the Earth!

High Noon on the Summer Solstice

[Click on the image to view full size (34k)]

At Syene:
The Sun is directly overhead, no shadows are cast at that moment.

At Alexandria:
The Sun is 712/60 degrees south of overhead, casting shadows.

Since a full circle is 360 degrees, the arc from Alexandria to Syene is thus approximately 1/50th of a full circle (the sun angle above divided by 360).

Therefore, the circumference of the Earth is 50 times the distance from Alexandria to Syene.

Question 1: How far is Alexandria from Syene?
5000 stadia

Question 2: How big is 1 stadion?
600 Greek Feet (length of a foot race in a Greek "stadium")

The best modern guess is that 1 stadion = 185 meters, based on the "Attic Stadion" measured from the Stadium at Athens.[4.2]

Putting Eratosthenes result into modern units, his estimate of the circumference of the Earth is as follows:

Circumference = 50 x 5000 stadia = 250,000 stadia
250,000 stadia x 185 meters/stadion = 46,250 kilometers

The modern measurement is 40,070 kilometers.

Eratosthenes' estimate is only about 15% too large!

Claudius Ptolemy (c. 140 AD)

Claudius Ptolemais (Ptolemy for short) was a Geometer and Astronomer of the late Classical Age in Alexandria. His work was immensely influential in later centuries, as we'll see in later lectures.

Ptolemy made a similar geometric estimate based on stellar (rather than solar) measurements made earlier by Marinus of Tyre (by way of Posidonius). This estimate yields a circumference of 28,800 kilometers, which is ~28% smaller than the correct circumference (40,070 km).

[Note: By Ptolemy's time, we are actually on better grounds for converting Classical Roman units to modern units, largely because many Roman roads and measuring techniques have survived from antiquity.]

Return of the Flat Earth

By about 300AD, the idea of a Flat Earth was revived:

By 1300, the works of Ptolemy and others arrived in Europe by way of Islamic Spain, and fully restored the Spherical Earth to respectability.

Contrary to popular myth, very few educated people after about 300 BC doubted that the Earth was a sphere. While a few early Christian thinkers did try to reject the idea, there is nothing in Christian beliefs that dictates a Flat Earth, in fact it says virtually nothing at all on the matter.

They all laughed...

Eratosthenes' work was lost, except for a description of his method in an obscure source.[4.3]

Ptolemy's estimate survived in his influential writings on geography. An interesting consequence of this transmission was:

Unlike many others of his time, however, Columbus not only argued for a smaller Earth, he also convinced the Spanish government to provide him the means to put his claims to the test.

The rest, as they say, is history...

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Updated: 2007 September 17
Copyright Richard W. Pogge, All Rights Reserved.