### Project Eratosthenes

Eratosthenes of Cyrene lived in Egypt between 280 BC and 190 BC. He was a Greek mathematician, astronomer, and the father of geography. Today, he is famous for his experiment to measure the radius of the earth by measuring shadows at two different latitudes, and for an original method to find prime numbers, the Sieve of Eratosthenes. For more details, please consult this webpage.

We are trying to measure the radius of the earth by reproducing Eratosthenes experiment, but this time, between Paris and Grahamstown: this is a bigger challenge since we change hemisphere, and we are not at the same longitude! Of course, what we are really trying to measure is the ratio of the radius of the earth and the distance between our two locations.

In Grahamstown, the project is supervised by myself and Mr S. Johnson, science teacher at Ntsika Secondary school, and involves 6 grade 11 students: Simamkele, Thobeka, Ekhona, Anesipho, Anelisa and Ntsikelelo. We acknowlegde support from The Community Engagement Office of Rhodes University, and the staff of Ntsika Secondary School. Here are the students, around the gnomon they built:

Here they are during their measurements on the 23rd of April 2013:

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The team in Paris is a group of members of the astronomy club of ENSTA. Dr J. Perez coordinates the project on that side.

Here are their gnomon in front of the new ENSTA building:

On the second of May, we managed to get a common measurement in both sites.

The following figure represents the situation, with the sun on the left. Note that we neglect, in first approximation, the difference in longitude:

Our measurements on the second of May 2013 gave: αp=33o and αG=48o. Therefore θ=81o. Hence, if we call D the distance between Paris and Grahamstown, we found, R/D=0.7. We verified that taking into account the difference in longitude does not alter this result, which means that our measurement is clearly dominated by systematic errors made while aquiring the data. Taking a distance between Paris and Grahamstown of D=9412 km (from http://www.timeanddate.com/worldclock/distances.html?n=2246), we get R=6722 km. An estimate of the equatorial radius of the earth is given by R=6 378 km (from http://en.wikipedia.org/wiki/Earth_radius), thus an error of 5% between the equatorial radius and our estimate! Not bad, for an experiment that used a coat hanger and a broom stick!