Astronomy 171
Solar System Astronomy
Prof. Paul Martini

Lecture 4: Measuring the Earth

Key Ideas

Ancient Ideas of the Earth

Most ancient peoples thought the Earth was Flat.
Homeric:: A flat disk surrounded by a world ocean.
Brahmin (India):: World mountain resting on the back of elephants, themselves on the back of a giant turtle swimming in an infinite sea.
Also World Tree (Hindu, Norse), Tent Canopy (Egyptian)

Classical Greece

Aristotle

Aristotle (384-322 BC) used physical arguments to determine the Earth was spherical:: Hulls of ships vanish first when they disappear over the horizon; Travelers going south see the southern constellations cross the meridian at higher elevation.; The Earth's shadow during a Lunar Eclipse is round.

No Flat Earth (or Moon)

Aristotle's demonstration was so compelling that a spherical Earth was the central assumption of all subsequent philosphers of the Classical Era.
He also used the curved phases of the Moon to argue that the Moon must also be a sphere.
How can we measure the size of the Earth? With geometry

Eratosthenes of Cyrene

Born in Cyrene (now Shahhat, Libya) in 276 BC, lived until about 195 BC.: Librarian of Alexandria
Travelers reported that at noon on the Summer Solstice in Syene, Egypt (modern Aswan), the Sun was straight overhead and cast no shadows.
On the same day, shadows were cast at noon in Alexandra.

Shadowless in Syene

No shadows on the Summar Solstice means that Syene is on the Tropic of Cancer
Alexandria is almost directly due north of Syene (lies on approximately the same Meridian or at the same Longitude) and shadows are cast
Measuring the angle of the Sun in Alexandria at noon on the Summer Solstice lets you measure the circumference of the Earth!

Noon on the Summer Solstice

At Syene:: Sun directly overhead, no shadows cast
At Alexandria:: Sun 7 14/60 degrees south of overhead, casting a shadow
Since a full circle is 360 degrees, the arc from Alexandria to Syene is (7 14/60)/360 = 7.233/360 ~ 1/50th

The Road to Syene

The circumference of the Earth is 50 times the distance from Alexandria to Syene 50 times the distance from Alexandria to Syene.
How far is Alexandria from Syene?: 5000 Stades
How big is 1 Stade?: 600 Greek feet; Best guess is that 1 stade = 157 meters

The Circumference of the Earth

Eratosthenes computed the circumference as: 50 x 5000 stades = 250,000 stades; 250,000 stades x 157 meters/stade = 39,250 km
The modern value is:: 40,070 km.
The difference is only 2%!!
There were actually numerous measurement errors in this estimate, so he was lucky to get so close to the correct value.

Ptolemy: The Geographer

Greek astronomer and geographer
Lived c. 100-150 AD in Alexandria, Egypt
Based his estimate on stellar measurements.: Observations by Marinus of Tyre; Gave a circumference of 28,800 km; (This is only 72% of the correct size)

Return of the Flat Earth

By ~300 AD, the Flat Earth was revived.: Early Christians rejected the "pagan absurdity" of a spherical Earth; This view was held sporadically until about 1300 AD.
By 1300, the ancient works of Ptolemy and others arrived by way of Islamic Spain.

Earth during the Renaissance

Acceptance of a spherical Earth in Europe
Educated people DID NOT think the Earth was flat
Eratosthenes' work was lost, except for mention of his estimate in an obscure source
Ptolemy's smaller estimate survived in his influential writings on geography.
Among those influenced by his work was a certain Genoese sailor...

Ptolemy and Columbus

The fall of Constantinople in 1453 AD cut off easy trade between Europe and Asia
Both the overland route and sea route around Africa were dangerous
Ptolemy's underestimate of the size of the Earth and overestimates of the size of China led Columbus to conclude he could reach Asia by sailing West...
If he had had Erastosthenes value, he would have known he could not carry sufficient supplies to reach China.

See A Note about Graphics to learn why some of the graphics shown in the lectures are not reproduced with these notes.