Eclipse math can be totally mind-boggling

Check the stats, city by city
Without retracing these computations, there is perhaps another way to check the validity of these answers.

In the table below is a listing of 25 cities. Twenty-three are in North America, plus two others: Honolulu, on the Hawaiian island of Oahu, and Hamilton, the capital of Bermuda. Using two computer programs designed to scan through the centuries for eclipses, I first searched for the date of the most recent total solar eclipse that was visible from each city, then searched for the date when the next total eclipse for that city would take place.

It should be stressed that the nearly four-century wait is merely a statistical average. Indeed, over a much shorter span of time, the paths of different eclipses can sometimes criss-cross over a specific place, so in some cases the wait might not be so long at all. In fact, a 40-mile (64-kilometer) stretch of the Atlantic coast of Angola, just north of Lobito, experienced a total solar eclipse on June 21, 2001, and was treated to another on Dec. 4, 2002, after less than 18 months!

On the other hand, as Meeus recently discovered, some spots on Earth’s surface may not see a total solar eclipse for 36 centuries ("Though this must be exceedingly rare," he notes).

On our listing of 25 selected cities, how close would we come to the computed mean-frequency of nearly 400 years between total eclipses?

Here is the list:

A single asterisk (*) denotes that either the northern or southern limit of the moon’s umbral shadow only grazes a specific city; only part of that metropolitan area will see a total eclipse, while the other part sees a partial eclipse. A double asterisk (**) indicates a date when the now-defunct Julian calendar was in effect.

The average number of years between eclipses turned out to be nearly 534 years. Considering our relatively small survey of 25 cities, this is reasonably close to the once-in-almost-four-century rule.

A botched opportunity
All of us who enjoy eclipses should be indebted to those astronomers who pioneered doing these extensive calculations; otherwise we would not know exactly where to position ourselves for the big event. Prussian astronomer Friedrich Bessel introduced a group of mathematical formulas in 1824 (now called "Besselian Elements") that greatly simplified the calculation of the position of the sun, moon and Earth.

It is too bad that Bessel’s procedures were not available in the late 18th century, when Samuel Williams, a professor at Harvard, led an expedition to Penobscot Bay, Maine, to observe the total solar eclipse of Oct. 27, 1780. As it turned out, this eclipse took place during the Revolutionary War, and Penobscot Bay lay behind enemy lines. Fortunately, the British granted the expedition safe passage, citing the interest of science above political differences.

And yet in the end, it was all for naught.

Williams apparently made a fatal error in his computations and inadvertently positioned his men at Islesboro — outside the path of totality — likely finding this out with a heavy heart when the waning crescent of sunlight slid completely around the dark edge of the moon and started thickening!

Joe Rao serves as an instructor and guest lecturer at New York's Hayden Planetarium. He writes about astronomy for The New York Times and other publications, and he is also an on-camera meteorologist for News 12 Westchester, New York.

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