Solar Eclipse Maths and the Cosmic Coincidence of the Saros Cycle

There was a solar eclipse on the 20 March 2015 and so I thought I'd make a quick video of the mathematics behind predicting eclipses. I now regret that decision.

EDIT: I over-simplified the elliptical orbit of the moon but not putting the Earth at one of the foci, which messes with the closest and nearest points at 3:40. Elliptical orbits are not that simple.

NASA pages on the moon's orbit and the Saros cycle:
http://eclipse.gsfc.nasa.gov/SEhelp/m...
http://eclipse.gsfc.nasa.gov/SEsaros/...

Photograph of the total eclipse is copyright Anthony Ayiomamitis and used with his kind permission.
https://www.flickr.com/photos/ayiomam...

The paper on the long-term instabilities of planetary orbits is here:
http://www.nature.com/nature/journal/...

Fred Espenak is the eclipse dude:
http://www.mreclipse.com/MrEclipse.html

Music by Howard Carter
Design by Simon Wright

MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
New book: http://makeanddo4D.com/
Nerdy maths toys: http://mathsgear.co.uk/