# why do total solar eclipses vary in length?

For the 2017 eclipse, the duration of totality will last between 20 seconds (over Kansas City, Kansas) to a maximum of two minutes and 40 seconds (over Carbondale, Illinois). The 2024 eclipse by comparison will average just under 4 minutes (4 minutes 27 seconds in Texas) along the path of totality.

My question is... why would the maxmium length of totality vary?

Your quote gives two variations in eclipse length, which aren't really related to each other.

The duration of a particular eclipse varies depending on how far the observer is from the center of the line of totality. If you have a look at the interactive map, you can see that the dot marked "Kansas City" was near the boundary between total and partial eclipse, while the dot marked "Carbondale" is quite close to the centerline (and also quite close the the marker "GD", for "greatest duration"). Another interactive map (which runs more slowly because it loads more information) will, if you click on the right way, show you the Moon's shadow as an oval stretching across the band of totality; folks near the edge have a smaller chord across the oval to spend in total eclipse.

I was surprised at how rapidly totality goes from brief to long as you move across the band: I was only three miles from the southern edge of the shadow, but had totality for about a minute. A friend a mile to the northeast had several seconds more than I did. This is because the Moon's shadow is approximately a circle, and the slope of a circle near its edge is very steep.

I think that "20 seconds of totality in Kansas City" ignores that Kansas City has a finite size and doesn't reflect the observing experience people had there.

The second reason is more interesting: the duration of totality also depends on the distance between the Earth and the Moon, which varies because the Moon is on an elliptical orbit. For 2024, the Moon will be closer to perigee during the eclipse than it was this year, so it will look bigger in the sky and its shadow will take longer to cross a particular point on the ground. You can see this by comparing path maps for this week's eclipse and the next one: in 2024 the shadow is clearly fatter.

(images from NASA via Wikipedia; click to embiggen)

Note that if the Moon is too far from the Earth during an eclipse, its apparent size is smaller than the Sun's apparent size, its umbra does not touch the ground, an you get an annular eclipse.