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There are a couple of factors which affect the duration of a total solar eclipse. To see these you need to start by thinking of the Moon's shadow in three dimensions. The umbral shadow is the true shadow, the fully black shadow, the region where the disk of the Sun is completely blocked by the Moon. Within the umbral shadow the eclipse is total. The umbral shadow is actually a long cone that begins at the Moon where it has the diameter of the Moon, over 2000 miles across, and then narrows down to a single point, which, by luck, happens to fall very close to the Earth's distance from the Moon. Picture that in your head: a long dark cone extending from the Moon to a distance about 235,000 miles from it where it ends at a point. Now set the Moon in motion around the Earth. That long cone will extend out to the Earth, and if the Moon is close enough at the time of the eclipse, the tip of the cone will intersect the Earth. At any instant of time, a small oval region will be within the shadow on the Earth's surface. You can see that the cone will intersect more deeply if the the observer's location on the Earth is closer to the Moon, further up the cone away from the pointy tip. As the Moon travels, the amount of time that any point spends within the umbral shadow will be greater if it is further up the shadow cone away from the tip, or in other words, closer to the Moon. In addition, if the Moon is high in the sky, the shadow will be intersecting the surface of the Earth in a nearly perpendicular fashion, so as the shadow cone sweeps across the Earth's surface it will  spend more time at one observer's location. On the other hand, if the Moon is low in the sky, the shadow cone is sweeping across at a glancing angle. There are other issues related to the rotation of the Earth and the orientation relative to the Moon's orbit, but these are the principal factors that affect the duration on the ground.

There's some bickering among towns near the center of the eclipse next summer for the claim to longest eclipse. Over a broad region in southern Illinois and western Kentucky, there is essentially no practical difference. Small differences in models of the Moon's limb (the shape of mountain ranges and valleys) can affect the outcome. Traditional limb models have been used for some calculations while models based on laser-ranging data from spacecraft currently in lunar orbit have been used for other calculations. Supposedly this has been a significant component of some of the small disagreements.

If we can all agree on a model, it is, however, possible to be exceedingly exact in these calculations thanks to a unique property of the Sun: it has a sharply-defined edge. That sharp "limb" that we depend on in celestial navigation, too, is an accident of Nature. Stars like the Sun have unique atmospheric properties that lead to a sharp transition from the opaque, glowing photosphere to the transparent atmosphere just above it. There is no sudden change in density despite the illusion of a surface. It's a change in opacity of the solar atmosphere driven largely by an ion that sounds like it shouldn't exist: the H- ion, a hydrogen atom with an extra electron loosely bound to it. It's as if we're looking a stable layer of clouds when we see the Sun's limb. Like clouds, there's no real difference in density, but unlike clouds there's no phase change --no "droplets" in the air, just a modest change in the density of the ions that scatter light. It's enough to make the Sun transition from almost completely opaque to almost completely transparent in a tiny fraction of the Sun's actual diameter.

Frank Reed