Measuring How Far the Sun Is Compared to the Moon — Aristarchus' Half-Moon Method

Around 270 BC Aristarchus of Samos worked out that the Sun is far more distant than the Moon — and did it with pure geometry. His key idea: when the Moon is exactly half-lit, the Sun, Moon and Earth form a right angle at the Moon. Measure the angle in the sky between the half-Moon and the Sun, and trigonometry gives the ratio of their distances. This blueprint reproduces his method with a simple sighting instrument. It also shows, honestly, why his answer of '19 times' fell short of the true 390 — the geometry is perfect, but the angle is almost impossible to measure by eye. From it Aristarchus argued the Earth goes round the Sun, eighteen centuries before Copernicus.