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Eratosthenes's experiment

by Philippe Jeanjacquot last modified Jul 13, 2012 03:55 PM
This experiment takes place in the second session of our astronomy and philosophy course. It is made near the autumn equinox.

Eratosthenes (276-194 BC) succeeded in measuring with a very simple way the circumference of the Earth

The aim of this activity is to use a similar method to measure the circumference of the earth.

First challenge

 

Measure the height and the azimuth of the Sun as accurately as possible.

1. Knowing that we cannot look at the Sun directly, propose a simple experiment for viewing altitude and theazimuth(see definitionsin the dictionary). Make a list of the necessary equipment.

2. The teacher gives the following equipment: a polystyrene board, a stick wood, a compass, a level, a ruler, a piece of paper, a square, the experiment takes place in a yard with gravels.

a) Drafting a protocol for the measurement of the position of the Sun. Be verified by the teacher

b) Achieve the measure, noting also the time at which you have done it

c) What are the phenomena that make inaccurate measurement?

equipement
What do we need for this experiment.

 

Our experiment ready to use

The experiment ready to use on the ground.

Second challenge: Measuring the circunference of the Earth

Thanks to the shade of a stick, Eratosthenes was able to measure the circumference of the Earth. We work, with a similar method, on measurements carried out on the day of the Equinox.

 

1) Students from different countries decide to measure at the same time the position of the Sun in the shade of a stick. The experience is drawn below (the drawing is not to scale). Represent the shadow of the for sticks on the drawing below.

shadow and latitude

 

2) Features of the Equinox:

 

The Equinox in took place this year (2010) on September 23. Complete: On the Equinox, on the Earth, the duration of the day is ……….. that the duration of the night.

Another particularity of the Equinox: atsolar noon , the Sun is at the Zenith, i.e. to the vertical from the equator. What then is the length of the shadow of a stick placed vertically at the Equator?

globe
A model to explain the size of the shadow according to the latitude (during the equinox day)

 

 

3) In Décines (our school city), students plotted on the day of the Equinox the position of the end of the shadow of a vertical stick around solar noon.
The baton has a length L = 27, 6 cm. shade measure h = 28, 5 cm
We calculate angle α (assistance: in a triangle tan formula.jpg)
Our experiment with another equipment shadow.jpg
We plot the end of the shadow Details of the shadows
4) The Eratosthene's trick.
Determine the relationship between the angle determined previously and the angle between the radius of the Earth at the Equator and our school location in Décines (see the diagram on the right.) angle similitude.jpg

5) In the "Google Earth" software can measure the distance between the Equator and our school location in Décines, we find d=5070km

Using Google Earth distance between equator and our school.jpg

6) From the properties of the circle, determine the perimeter p of the Earth.

circle properties.jpg

Calculations for participants

Calculations

Links

La main à la Pâte

Eratosthenes

European Association for Astronomy in Education : Eratosthenes

Le site Eratosthène du Collège Antonin Perbosc de Lafrançaise

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