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The diameter of the path of totality is only about 100 miles, because it's only the umbra of the shadow. This is 20x smaller than the moon diameter. But, a 1km moon bump is a 1km bump on the umbra as well, magnifying it's effect by the mentioned 20x and leading to a much different appearance.



I hadn't thought about this effect! You're absolutely right. Thanks very much.

(For others:) A diagram of the umbra makes this clear:

https://c.tadst.com/gfx/750x500/total-solar-eclipse-com.png?...

If you draw a few triangles, you can get an analytic expression.




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