The Eratosthenes Experiment. International collaboration

The Eratosthenes Experiment

International collaboration

Odense 26.september 2005Odense 26.september 2005

A short HistoryA short History

The size of the Earth was The size of the Earth was determined already more determined already more than 2000 years ago. than 2000 years ago. This is quite impressive, This is quite impressive, but was due to a clever but was due to a clever observation. The director observation. The director of the famous library in of the famous library in Alexandria in Egypt, the Alexandria in Egypt, the geographer Eratosthenes geographer Eratosthenes (about 276-195 BC.) did (about 276-195 BC.) did the historic achievement. the historic achievement.


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.


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 betweenSyene and Aleksandria = measured anglecircumference of the earth 360°


Eratosthenes mapEratosthenes map


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


How do we do it today?How do we do it today?


You measure the solar shadow angle at solar noon

a

b

tanα = b/aSUN

αa

b

tanα = b/aSUN

a

b

tanα = b/aSUN

tanα = b/aSUN

tanα = b/aSUNSUN

α


The

GLOBE

way!


And use the result from another school and do the calculations

School 1

School 2X

X

Distance between latitudes

School 1

School 2X

X


School 1

School 2X

XSchool 1

School 2X

XSchool 1

School 2X

X



Sun rays

The Earth

α-β

α

β

α

β

N

S

The Equator

Sun rays

The Earth

α-β

α

β

α

β

N

S

The Equator

The Earth

α-β

α

β

α

β

N

S

The Equatorα-β

α

β

α

β

α-β

α

β

α

β

N

S

The EquatorThe Equator

Both schools with shadow to the North:D/C = (α - β)/360 Find C.

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.


When and howWhen and how

Register for the experimentFind a partner school Conduct Experiment at

Wednesday May 25 +- 2 daysWednesday September 21 +-2 days

After the Experiment you register your results


Results Results

28 countries 28 countries 98 schools98 schools Average value 41179 kmAverage value 41179 km


HungaryHungary


RomaniaRomania


Deutsche Schule Abu Dhabi Deutsche Schule Abu Dhabi Vereinigte Arabische EmirateVereinigte Arabische Emirateaa


Puerto RicoPuerto Rico


The Czech RepublicThe Czech Republic


South KoreaSouth Korea


Where to registerWhere to register

www.naturfagsenteret.no/fysikk/eratosthenes/index.htmlor

www.globe-europe.org

Join the project!


FYSIKKÅRET ER TID FOR FYSIKKÅRET ER TID FOR FYSIKKSTUNT!FYSIKKSTUNT!


POTETKANON


PÅ STRAM LINEPÅ STRAM LINE


DEI UNGE ER BEST!DEI UNGE ER BEST!


Bøndar og fysikkBøndar og fysikk


Bemanna vannrakettBemanna vannrakett


LYKKE TIL!LYKKE TIL!

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The Eratosthenes Experiment. International collaboration