measuring the solar system eratosthenes, aristarchus the century after euclid
TRANSCRIPT
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MEASURING THE SOLAR SYSTEM
Eratosthenes, Aristarchus
The century after Euclid
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SHADOWS
SIZE OF EARTH
ERATOSTHENES - 225 BC
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ERATOSTHENESBELIEVED EARTH TO BE SPHERICAL
SUN’S RAYS NEARLY PARALLEL
THEREFORE SUN’S RAYS ARRIVE AT DIFFERENT ANGLES
AT DIFFERENT LOCATIONS
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SIZE OF EARTH
• ON JUNE 21, AT NOON, THE SUN IS DIRECTLY OVERHEAD AT SYENE, EGYPT.
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SIZE OF EARTH• ERATOSTHENES MEASURED THE
ANGLE OF THE SUN AT ALEXANDRIA, 5000 STADES NORTH, ON THE SAME DATE, FINDING IT WAS 1/50 OF A FULL CIRCLE FROM OVERHEAD.
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THE PROBLEM HAS BEEN REDUCED TO GEOMETRY
SYENE
ALEXANDRIA
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ALEXANDRIA
SYENE
ALEXANDRIA MUST BE 1/50 OF THE EARTH’S CIRCUMFERENCE NORTH
OF SYENE, SO THE CIRCUMFERENCE MUST BE 250,000
STADES, OR ABOUT 28,000 MILES
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SHADOWS: DISTANCE TO THE MOON
SHADOW OF THE EARTH IN SPACE
D
108 D
ARISTAUCHUS 250 BCE
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UMBRA AND PENUMBRA
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DURING A LUNAR ECLIPSE, THE MOON PASSES THROUGH THE SHADOW OF THE EARTH
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OBSERVATIONS
THE SHADOW IS 2 1/2 TIMES THE MOON’S DIAMETER
ANGULAR SIZE OF MOON = ANGULAR SIZE OF SUN
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THE PROBLEM HAS BEEN REDUCED TO GEOMETRY
d
2.5d
BC = 2.5 AB
AC = BC + AB = 2.5AB + AB =3.5 AB
AB = AC/3.5 = 108D/3.5 = 31D
B
A
CD
E
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MoonSun
Earth
900
ARISTARCHUS: DISTANCE TO THE SUN
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Date Astronomer Moon Distance Sun Distance -260 Aristarchus 9.5 180
-130 Hipparchus 33.7 1245
-70 Posidonius 26.2 6545
+150 Ptolemy 29.5 605
Modern Values 30.3 11,745
SUMMARY: GREEK DISTANCES IN EARTH
DIAMETERS
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ARISTARCHUS’ HELIOCENTRIC MODEL
SUN IS AT CENTER
EARTH ROTATES DAILY PRODUCINGTHE APPARENT DAILY MOTIONS
OF THE CELESTIAL OBJECTS
EARTH ORBITS SUN ONCE PER YEARPRODUCING THE PROGRESSION
THROUGH THE ZODIAC
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1. Lack of stellar parallax.
2. Required overthrowing a long-established conventional wisdom.
3. The earth feels like it is stationary. If we evaluate the earth’s orbital speed required by the heliocentric model, even using Aristarchus’ small value for the distance to the sun, we find v = 2R/365 = 25,000 miles/day. This was an unheard of speed, and we don’t notice it. Galileo was the first person to correctly address this question and to explain it.
4. Religious and cultural reasons. Accepting this radical change in world view would require changing the jobs of many of the gods (e.g. Zeus, who carried the Sun across the sky). It also displaces humans from the center of the universe.
SUMMARY