Circumference of the Earth
The Greeks knew that the earth was spherical and derived estimates of its
circumference.
Eudoxus of Cnidos (408355 BC) was supposed to have estimated the
circumference of the earth to be 400,000 stades (circa 40,000 miles).
The most famous of
these estimates was given by Eratosthenes (276196 BC).
When he was in Syene in
Cyrene he observed that the sun was directly overhead at midday during the summer
solstice.
He knew that in Alexandria, some 5000 stades directly north, the sun was not
directly overhead.
In Alexandria, a shadow equal to one fiftieth of a circle was cast.
Assuming that the rays coming from the sun at both locations are parallel, the
angle
!
is determined by the curvature of the earth.
In radian measure the circumference
is given by
1
tan
"
5000 stades
=
50
"
5000 stades
=
250,000 stades
=
25,000 miles
.
This
is a fairly good estimate compared to the current accepted value of 24,902 miles at the
equator.
Relative Distances to Moon and Sun
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 Spring '08
 BLOCK
 Calculus, Astronomical unit, Alexandria, Syene

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