Reinventing the Aristarchus method

The greek mathematician and astronomer Aristarchus of Samos, 3rd century BC, was the first person to systematize a method to estimating relative distances and sizes between Earth, Sun and Moon. He was also the first to propose that the Earth revolves around the Sun. In the present work, we carried out a review, in modern language, of the method proposed by Aristarchus to estimate the distance from the Sun to the Earth, S, in relation to the distance from the Moon to the Earth, L. After that we present the model proposed by us to do the experimental determination of the ratio S/L and the angular diameter of the Sun and Moon, as well as the experimental setup used. We performed two experiments, one with the Crescent Moon and one with the Waning Moon. We emphasize that our main objective is to deal with calculating astronomical distances with the use of geometric models. We expect that teachers of mathematics, physics and astronomy will use this material in their classes and presentations, discussing with students the technical and historical difficulties and the physical and geometric aspects involved. And, if possible, that they reproduce the measures.

Keywords
Aristarchus; Heliocentrism; Astronomy