Solar Eclipse Maths and the Cosmic Coincidence of the Saros Cycle

There was a solar eclipse on the 20 March new and so I thought Id make a quick video of the mathematics behind predicting eclipses. I now regret that decision.\r
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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.\r
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NASA pages on the moons orbit and the Saros cycle:\r
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Photograph of the total eclipse is copyright Anthony Ayiomamitis and used with his kind permission.\r
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The paper on the long-term instabilities of planetary orbits is here:\r
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Fred Espenak is the eclipse dude:\r
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Music by Howard Carter\r
Design by Simon Wright\r
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MATT PARKER: Stand-up Mathematician\r
Website: \r
New book: \r
Nerdy maths toys: