Oxford Mathematician Dr Tom Crawford visits Jantar Mantar in Jaipur, India, and explains the ancient calculations of Aristarchus of Samos in his seminal work “On the Sizes and Distances (of the Sun and Moon)”.

The video begins with a history of Jantar Mantar in Jaipur, and a tour of the many instruments used for astronomical measurements. We then look at the history of heliocentrism and the begin an exploration of the work of Aristarchus.

The first calculation relates to the relative distances of the Sun and the Moon from the Earth. Using simple trigonometry at a ‘Half-Moon’ we obtain the same estimates for the distances as Aristarchus.

The second calculation is more involved and looks at the relative sizes of the Sun and Moon in comparison to the Earth. This requires the use of the properties of similar triangles during a Lunar Eclipse. We also use the fact that during a total eclipse, the sun and moon take up the same proportion of the sky, which means the ratios of their sizes relative to the Earth, is the same as that of their distances from Earth.

Finally, we end with a discussion of the translation of the work of Aristarchus and how his calculations may in fact have been much more accurate than first thought…