Uploaded June 2024 | Updated September 2026, 2 weeks ago
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...
Useful links for more information / resources:
Zij-i-Muhammed Shahi: raymondm.co.uk/20005abd_143.pdf
Geocentric model animation: youtube.com/watch?v=VSeN6ZB1wqA
Translation of Aristarchus' work: archive.org/details/aristarchusofsam00heatuoft/page/414/mode/2up?view=theater
Measuring the relative size of the Earth and the Moon at home: https://websites.umich.edu/~lowbrows/astrophotos/alway/lunareclipse.html#:~:text=And%20the%20angular%20size%20of,%2B%202%20%3D%204.8%20Moon%20diameters
Produced by Dr Tom Crawford at the University of Oxford. Tom is Public Engagement Lead at the Oxford University Department of Continuing Education: conted.ox.ac.uk/profiles/tom-crawford
For more maths content check out Tom's website tomrocksmaths.com
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths
Get your Tom Rocks Maths merchandise here: beautifulequation.com/collections/tom-rocks-maths
With thanks to
Chuck Creager Jr.
Scritch314
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...
Useful links for more information / resources:
Zij-i-Muhammed Shahi: raymondm.co.uk/20005abd_143.pdf
Geocentric model animation: youtube.com/watch?v=VSeN6ZB1wqA
Translation of Aristarchus' work: archive.org/details/aristarchusofsam00heatuoft/page/414/mode/2up?view=theater
Measuring the relative size of the Earth and the Moon at home: https://websites.umich.edu/~lowbrows/astrophotos/alway/lunareclipse.html#:~:text=And%20the%20angular%20size%20of,%2B%202%20%3D%204.8%20Moon%20diameters
Produced by Dr Tom Crawford at the University of Oxford. Tom is Public Engagement Lead at the Oxford University Department of Continuing Education: conted.ox.ac.uk/profiles/tom-crawford
For more maths content check out Tom's website tomrocksmaths.com
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths
Get your Tom Rocks Maths merchandise here: beautifulequation.com/collections/tom-rocks-maths
With thanks to
Chuck Creager Jr.
Scritch314
