The Eratosthenes Experiment
Encouraged by our teachers of the Comenius "Maths for Europe" group, we repeated the Eratosthenes Experiment on the autumnal equinox of Wednesday September 22, 1999.
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At 13h29,in Sint-Niklaas (with Irene Verdiesen, Jonathan De Graeve, Bert Van De Putte, Marijke Rottiers, Sarah Spooren, Heike Rombaut and physics teacher Mrs Simonne Van Aken) when the sun was at the highest point,we measured the shortest shadow being 148 cm casted by a vertical stick with length 120 cm
At the time, in Egypt, Eratosthenes(Greek geographer about 276 to 194 B.C.) made a remarkably precise computation of the size of the circumference of earth. He knew that, at the summer solstice and at noon, the sun shone directly into a well at Syene(now Aswan). In Alexandria, 5000 stadia(now about 787 km) north of Syene, the sun was not directly overhead at noon on the same day because a vertical object casted a shadow. From this shadow he could find the angle of inclination of the sun's rays : 7.12 °. With these measurements he computed the circumference of the earth (his result :250 000 stadia) using the same reasoning as described below.
We repeated the experiment of Eratosthenes in the different partnerschools looking for our own angle of inclination with respect to the equator on the autumnal equinox September 1999 because on the equinox the vertical rays of the sun are directly over the equator (like the well at Syene). On the playground Antigone of our school OLVP in Sint-Niklaas, inside Sarah's car, we could read the latitude of our location : 51°10'04" NL.
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Left to right : Sarah Vermeiren and Marieken Linthout
If we take also the same assumptions as
Eratothenes made : the earth is round and the sun rays are essentially parallel,
then we can take for the length of an arc corresponding to an angle of 1° latitude : 111,
133 km. From the shadow we measured and the latitude we could
read on the dashbord in the car we can calculate resp. the angle between
the sun rays' and the vertical direction : Arctan(148/120) = 50,9645° and our shortest
distance on the globe to the equator : d = 51, 1677 x 111, 133 km = 5686,43 km.
Calculating D from the previous equation, we
get for the circumference of our planet 40 167 km
By e-mail we got the results and pictures from the experiment, done in the same period, by
the students of our partnerschools :
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Greåker with
physics teacher Mr
Jens Olaf Hvalgård : at 59,2751°NL the students measured a shadowlength of 183cm, starting from a vertical stick of
1m, which leads to 38658 km
We must mention that they had to wait for a sunny day until September 29,thus the
sunrays were not quite parallel to the equator.
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Mikkeli : at 61,69° NL with a sunny solar noon on September 23, they found 39 973 km, which is very close to the exact value
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Vittorio Veneto : at 46° NL shadowlength 105cm starting from a vertical stick of 1m leads to : 39 665 km
More information
*on Eratosthenes and the flattening at the poles of our
planet, you'll find more on the website of our Finnish partnerschool
http://www.mikkeli.fi/opetus/myk/pv/
*http://www.ed.uiuc.edu/Projects/noon-project/spreadsheet-description.html
*we used the computerprogramme CABRI for the drawings
