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 [i]Sandreckoner [/i]1.19 conveys.

In order to measure the Moon’s distance, set the time slider [i]t [/i]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 [i]t [/i]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 [i]t [/i]the Moon’s centre needs to do so and use it in the given equations to find the angular width [i]α [/i]of the Earth’s shadow (in orange), and then the distance [i]M [/i]to the Moon (in white).