The Eratosthenes activity

Two locations (B and E) on the same longitude are the distance p apart (green arc element). At each location, the height angle is measured. The difference angle of the two height angles, allows the calculation of the radius r.

Procedure for participation:
1) Measure your local height angle with a shadow stick at astronomical noon time (shortest shadow).
- Measure the length of the shadow stick.
- Measure the length of the shadow at astronomical noon
- Use the GeoGebra applet http://www.xplora.org/downloads/Erathostenes/erathostenes.html to get the height angle
2) Email the following data to your project partners:
- The geographical coordinates of your location
- Length of shadow stick.
- Length of shadow at astronomical noon.
- Height angle
3) Move two locations and (yours and that of at least one project partner) to the same longitude (e.g. Greenwich meridian) in a map which shows both locations. The names of these two locations are B and E.
4) Take the real distance of the two locations B and E from the map. You must use the scale of the map.
5) Use the formula below to calculate the radius of the earth.

Karl Sarnow, 1.3.2006, Created with GeoGebra