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. 

llerak.jpg (18022 bytes)

simk.jpg (18436 bytes)

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

sunera1.gif (3495 bytes)

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.

sunerasint.gif (3749 bytes)

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.

marieken.jpg (24082 bytes)

GPSdichtak.jpg (14655 bytes)

   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.

sunera2c.gif (5393 bytes)

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 :

------------------------------------------------------------------------------------------------------------------------------------------------------------------

eratom1k.jpg (20394 bytes)

eratom4k.jpg (23890 bytes)

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 sun
rays were not quite parallel to the equator.

---------------------------------------------------------------------------------------------------------------------------------------------------------------------

Er2fk.jpg (21684 bytes)

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 

----------------------------------------------------------------------------------------------------------------------------------------------------------------------

Vittorio Veneto : at 46° NL shadowlength 105cm starting from a vertical stick of 1m leads to : 39 665 km

aarde.jpg (12394 bytes)

 

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

 

BACK to OLVP page