The
Eratosthenes
Experiment
International collaboration
A short History
The size of the Earth was
determined already more
than 2000 years ago.
This is quite impressive,
but was due to a clever
observation. The director
of the famous library in
Alexandria in Egypt, the
geographer Eratosthenes
(about 276-195 BC.) did
the historic achievement.
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Eratosthenes had learned a
fascinating fact about the city of
Syene in southern Egypt, not far
from Aswan: When the Sun was
at its highest in the sky in this
city on the longest day of the
year (today we call it summer
solstice), the Sun did not cast
any shadows. Actually, the Sun
shined into deep wells. The
story says that nobody dared to
stare into the wells since they
could become blinded by the
intense light reflected by the
water deep down.
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In Syene the Sun therefore had to be in the
zenith at this time. In Alexandria, further north
in Egypt, Eratosthenes knew from his own
experience that the shadow at the same time
was 7.2 degrees (see drawings to the right).
He could then calculate the circumference of
the earth by this simple ratio:
Distance between
Syene and Aleksandria
circumference of the earth
= measured angle
360°
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Eratosthenes map
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He could not measure the distance between the cities
directly, but estimates of people travelling between the
cities and the time they spent, gave a distance of about
5000 stadions. The circumference of the Earth therefore
had to be 250 000 stadia.
circumference of the earth = 5000*360/7.2 = 250000
A stadium (plural stadia) is a Greek measure of distance
equal to 600 Greek feet. Today we don't know the exact
length of one stadium. Opinions vary about how long it
actually was, with estimates varying from 154 to 215
metres. If we choose 160 m we get that 250 000 stadia
correspond to 40000 kilometers. This is close to the correct
value, which is 40 074 kilometers!
Anyway, the method is correct and can be applied even
today to estimate the size of our Earth
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How do we do it today?
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SUN
tanα = b/a
You measure
the solar
shadow angle
at solar noon
a
α
b
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The
GLOBE
way!
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And use the result from
another school and do the
calculations
School 1
X
X
School 2
Distance between latitudes
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Both schools with shadow to the
North:
D/C = (α - β)/360
Find C.
Sun rays
Both schools with shadow to the
South:
D/C = (β - α)/360
Find C.
One school with shadow to the North
and one school with shadow to the
South:
D/C = (α + β)/360
Find C.
N
α
β
α-β
α
The Equator
β
S
The Earth
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When and how
Register for the experiment
Find a partner school
Conduct Experiment at
Wednesday May 25 +- 2 days
Wednesday September 21 +-2 days
After the Experiment you register your
results
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Results
 28 countries
 98 schools
 Average value 41179 km
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Hungary
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Romania
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Deutsche Schule Abu Dhabi
Vereinigte Arabische Emiratea
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Puerto Rico
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The Czech Republic
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South Korea
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Where to register
www.naturfagsenteret.no/fysikk/eratosthenes/index.html
or
www.globe-europe.org
Join the project!
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FYSIKKÅRET ER TID FOR
FYSIKKSTUNT!
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POTETKANON
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PÅ STRAM LINE
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DEI UNGE ER BEST!
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Bøndar og fysikk
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Bemanna vannrakett
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LYKKE TIL!
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