An explanation for Aristarchus’ measurement of the sun’s distance

Aristarchus of Samos determined the angular distance between moon and sun at half-moon as 87°, from which he deduced that the sun’s distance is “between 18 and 20 times that of the moon”. In this study, we show that his result can be reproduced and understood when it is assumed that the observation was made when, apart from being perceived as straight, the shadow edge over the moon’s surface was vertical. A measurement could then have been done with instruments that were available at the time: the gnomon and the quadrant. An example that might have been observed by Aristarchus himself is presented and analyzed.