Reinventing Eratosthenes’ method

At the end of the 3rd century BC the Greek polymath Eratosthenes of Cyrene made the most famous estimation of the Earth’s perimeter. For this he made use of the fact that the cities of Alexandria and Syene were approximately on the same meridian (same longitude), as well as the fact that on of the summer solstice (in the northern hemisphere) the Sun, at noon, is directly overhead in Syene. In the present work we generalized, in an approximate way, the method of Eratosthenes for the case which the localities are separated both in latitude and longitude. Furthermore, in the proposed model, it is not necessary to have the Sun, at local noon, directly overhead in any city. We carried out three experiments, that is, we worked with three pairs of cities: Goiânia and Juiz de Fora, Goiânia and Maraú and Goiânia and Bragança Paulista. We hope that the article will be used by teachers of Physics, Astronomy, Geography and/or Mathematics.

Keywords
Circumference of the Earth; Earth Radius; Posidonius of Apameia; Ancient Greece; Astronomy