# Aristarchos’ measurement of the Moon's distance

It is possible to get a fair approximation to the Moon’s distance by timing how long the Moon's centre takes to cross the Earth’s shadow during a Moon eclipse. The method illustrated in this file might have been used by Aristarchos of Samos to find the distance of 60 Earth-radii to the Moon that the ratio 11-to-1148 in

*Sandreckoner*1.19 conveys.In order to measure the Moon’s distance, set the time slider

*t*to zero and drag the Moon’s centre to a position where it just touches the limb of (and is about to get into) the Earth’s shadow. Then move the time slider*t*until the Moon’s centre has crossed the whole breadth of the Earth’s shadow and is just about to leave it. Read the time*t*the Moon’s centre needs to do so and use it in the given equations to find the angular width*α*of the Earth’s shadow (in orange), and then the distance*M*to the Moon (in white).