Why are not solar eclipses separated by one saros cycle visible from the same location on Earth﹖?
Question:
Answer:
Any two eclipses separated by one saros cycle share very similar geometries. They occur at the same node with the Moon at nearly the same distance from Earth and at the same time of year. Because the saros period is not equal to a whole number of days, its biggest drawback is that subsequent eclipses are visible from different parts of the globe. The extra 1/3 day displacement means that Earth must rotate an additional ~8 hours or ~120º with each cycle. For solar eclipses, this results in the shifting of each successive eclipse path by ~120º westward. Thus, a saros series returns to about the same geographic region every 3 saroses (54 years and 34 days).
Because it isn't an exact number of days long.
KDR is right. The Saros cycle only works for latitude, not longitude. With each cycle, the moon returns to roughly the same latitude (but not exactly the same -- with each cycle, the moon's shadow continues to track a little further to the north (for a northward-moving Saros) or a little further to the south of the time before.
But each cycle is about (not exactly) eight hours off from the time before. The earth turns an extra 8 hours, bringing the eclipse one-third of the way around the world from the last one.
Because the saros cycle is not exactly the right length of time, it is just close to the right length. It would be a wildly improbably coincidence if it was exact. It is pretty remarkable that it is as close as it is.
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