Terence Tao on how we measure the cosmos | The Distance Ladder Part 1

The Cosmic Distance Ladder, how we learned distances in the heavens.
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Artwork by Kurt Bruns
Thanks to Paul Dancstep for several animations, such as the powers of 10 zoom out and the simulations of shadows on the moon.

Corrections:
Terry has kindly cataloged many of the added nuances, including a few corrections, in this post:
https://terrytao.wordpress.com/2025/0...

As an additional one, the portrait shown for Kepler, despite being somewhat widespread, actually turns out not to be Kepler. See this article by Václav Pavlík https://ui.adsabs.harvard.edu/abs/202...

Also, although the earth is about 4 times as wide as the moon, as it happens you would not see this with the lunar eclipse composites, since the umbra of Earth's shadow from the sun is sufficiently smaller than the earth out where the moon is.

Moon composite shot by Reddit user _wanderloots:   / partial_lunar_eclipse_composite  
   / @wanderloots  

Thanks to Tanya Klowden for helpful conversations about the history of the distance ladder.

Argument for why if every shadow of a convex shape is a circle, it must be a sphere: https://mathoverflow.net/questions/39...

Timestamps:
0:00 - About Terence Tao and the Distance Ladder
2:02 - Earth
8:07 - Moon
11:15 - Sun
15:45 - Heliocentrism in Antiquity
18:27 - Kepler’s genius
27:16 - Where this leaves us


SEV #5:    • Secret Endscreen Vlog #5  

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https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/

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The music is by Vincent Rubinetti.
https://www.vincentrubinetti.com
https://vincerubinetti.bandcamp.com/a...
https://open.spotify.com/album/1dVyjw...

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