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Astronomy 161:
An Introduction to Solar System Astronomy
Prof. Richard Pogge, MTWThF 9:30
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Lecture 4: Measuring the Earth
Key Ideas:
Ancient ideas about the Earth.
- Flat Earth, World Tree or World Mountain
The Spherical Earth
- Appeal to perfect symmetry
- Demonstration by Aristotle
Measuring the Earth's Circumference:
- Eratosthenes of Cyrene
- Claudius Ptolemy
The Four Corners of the Earth
The most common ancient theme is that of a Flat Earth.
- Homeric: A flat disk surrounded by a world ocean.
- Inca: Called their land Tehuantinsuyu: "The Four
Corners of the Earth"
- Ancient Egyptian: The sky was a tent canopy stretched
between mountains at the four corners of the Earth.
World Trees and Mountains also figure in early mythology:
- Hindu Vedas: Tree of Knowledge holding up the Universe.
- Norse Eddas: Yggdrasil, the World Ash Tree
- Brahmin World Mountain, resting on the back of elephants,
themselves on the back of a giant turtle swimming in an
infinite sea.
Myth & Metaphor
These fanciful views are Representations rather than Portrayals
of reality.
- The great myths and metaphors make the world seem
intelligible and beautiful to the people who invented
them.
- They serve cultural purposes motivated by an aesthetic we
can only guess at.
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 the Phaedra,
giving it wider circulation (the Pythagoreans where
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])
- Persons living in southern lands see southern constellations higher
above the horizon than those living in northern lands.
- The shadow of the Earth on the Moon during a lunar eclipse is round.
- The fact that objects fall to Earth towards its center means that if
it were constructed of small bits of matter originally, these parts
would naturally settle into a spherical shape.
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?
Have established the shape, what is the size?
Question: How do you measure something really
big?
- Mountains too high to climb...
- The Earth too large to trail a string behind you...
Answer: Use 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 Stades
- Question 2: How big is 1 Stade?
- 600 Greek Feet (length of a foot race in a Greek
"stadium")
The best modern guess is that 1 stade = 185 meters, based on the
"Attic Stade" 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 stades = 250,000 stades
250,000 stades x 185 meters/stade = 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 value gave a circumference of 28,800 kilometers. This
is about 72% 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:
- Early Christian rejection of the "pagan absurdity" of a
spherical earth.
- This view was held sporadically until about 1300 AD.
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:
- It makes the eastern tip of Asia closer to the western
tip of Europe than it would be otherwise.
- This fact (along with some other finagling) convinced
Columbus that he might be able to reach Japan by sailing
West from the Canaries.
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: 2006 September 19
Copyright ©
Richard W. Pogge, All Rights Reserved.