There is a point of confusion for many interested in eclipses. The term "Greatest Eclipse" appears on many eclipse maps. So does that mean it is the greatest place to see the eclipse? Or maybe the longest duration point of the eclipse path? Or maybe something else?
The term "Greatest Eclipse" is, in my opinion, a poor choice of words to describe a geometric point, one that is calculated. But one is pressed to come up with a better term and thus we keep using it. And every eclipse we need to clarify just what that means. So here goes....
Just for clarity, we are only talking about total solar eclipses and not annular or partial, although the same term applies in both (see Types of Eclipses). I want to focus on totality only since that is the "big show". Annular and partial eclipses are nice, but they are not really spectacular like a total solar eclipse.
The greatest eclipse point is where the shadow of the moon (a cone shaped shadow) is nearest to the center of the Earth. It is a calculated point using the geometry of the eclipse. This point may just coincide with the longest duration and could even coincide with the best place to be for an eclipse - but that is not always the case.
The longest duration is a function of the elevation, angle of the Earth towards the Sun, lunar profile and so on. Many times the greatest duration is found near to the Greatest Eclipse point, maybe just a few kilometers off. The computation of the greatest eclipse point is direct, the computation of the greatest duration is iterative. That means we calculate a heap of points to find the longest duration.
For example, this summer's eclipse across the continental USA, note that the Greatest Eclipse (in green) is east of the Greatest Duration (magenta). Map courtesy of NASA.
So where exactly is the really greatest place to see the total solar eclipse? Where ever the sky is clear at the time of totality! Oh, and inside the narrow path as seen in the map above!