I was hoping some SDoper could explain in simple terms the difference between max eclipse and max totality? For this solar eclipse, max eclipse occurred over Carbondale, IL; however, max totality occurred over Hopkinsville, KY.
As I understand it, max eclipse has something to do with the fact that the moon’s shadow becomes normal to the earth’s surface (where as places like Matras, OR has a slightly oblique shadow). When the shadow becomes normal, the shadow slows down. Hence, the longest eclipse. As for Hopkinsville, I can’t explain the difference. I know they had the longest duration, but…? I can’t straighten out the difference in my mind. Can anyone set me straight?
This page seems to have a more or less decent explanation, though the details of the calculation are not shown.
Your understanding is absolutely correct in that the “max eclipse” occurs when the shadow passes closest to the centre of the Earth (the only nitpick is that it might not always be quite normal to the surface-- think of an eclipse that just grazes the Earth near a pole, like this one). The longest duration is just what it sounds like.
Why a difference? Because of the Earth’s oblateness and the relative motion of the Moon’s shadow with respect to the equator, and also the latitude of the observation point on the spinning Earth (closer to the equator gives you more surface velocity eastward). These factors interact in a slightly more complicated way than the simple geometric “greatest-magnitude eclipse” description, but according to the first link above numerical calculations show the difference to be about 0.1 seconds on average and a few tenths of a second at most, so practically speaking it will not make much difference: the hills and valleys of the Moon’s profile can account for 2-3 seconds difference from the above computations which assume a smooth lunar disc (in fact, the “longest totality”, in southern Illinois, was all of about 1.5 seconds longer than the eclipse in Kentucky).