The Eratosthenes Challenge

An activity proposal for IYA-2009

Sergio Torres Arzayús


As we commemorate 400 years since Galileo awoke humanity to a new cosmic reality by bringing the gods of the Greeks and the Romans closer to us and exposing their earthly defects that his telescope revealed it is time to remind our children the most important of Galileo’s lessons, namely: the immense universe out there can be studied, can be explained and can be understood.

One of the most common questions that I get asked when giving presentations about cosmology and the universe is "how can you study objects and processes so remote in distance and time and of such large scales when compared to the human scale". To prove that objects much larger than the human scale can be comprehended and measured using methods within our reach, I proposed my 11 year old daughter to measure the Earth. We did it using rulers, sticks and the elementary geometry that she had already studied in school. It was a huge success: (see project page). We replicated Erastosthenes’ measurement done more than 2,200 years ago. In the process we realized that, although a simple concept, it cannot be done in isolation, the measurement requires the coordination with students in another country in order to cover an arc along the Earth sufficiently long to expose the Earth’s curvature. Briefly, Eratosthenes method consists of measuring the distance between two cities (same longitude) and the angle (from the center of the Earth) subtended by the arc joining these two cities. The angle is estimated by looking at the shadows projected by sticks. Details are provided in the link above.

The Challenge

Eratosthenes measured the size of the Earth; a natural extension of his work would be to prove that the shape of the Earth is not spherical and to measure the Earth’s eccentricity. All these, of course, using sticks and shadows! Because of the very small difference between the polar and equatorial radius (21.4 Km) this measurement is extremely difficult, hence the challenge! To achieve this goal it would require a coordinated effort between at least 4 groups (possibly in 4 different countries) that perform measurements of the local radius at two locations (one close to the equator, the other far from the equator). Students need to understand the errors and work diligently to reduce measurement errors and to use their creativity to develop ways to improve the measurements. A separate document with error estimation and details of the 4-group approach is provided here.

UNICEF should fund a contest for [middle to high school] students to develop a creative solution to perform the measurement of Earth’s eccentricity (using sticks and shadows). The team that demonstrates the oblateness of the Earth and measures it with the highest precision is the winner. A project web site could be set up so that interested groups can find and contact partners.



© Copyright 2008. Derechos reservados, Sergio Torres Arzayús   (30 Octubre, 2008)