Repeat On Repeating Eclipses

Referring again to Figure 2-2, the eclipses depicted all occurred around the middle of the year—shifting with forward steps of 10 or 11 days from May 18, 1901 to July 11, 1991, in accord with the saros—but are otherwise noteworthy because of the duration of totality. Most total solar eclipses last for only two or three minutes; the six eclipses shown each had totality lasting for about seven minutes. No natural solar eclipse will present such an opportunity again until the year 2150. One can increase the duration of totality by artificial means, by flying along the eclipse path as fast as you can in a supersonic aircraft, although even that cannot keep pace with the eclipse for much more than ten minutes.

When we first met the saros we merely noted that there was another near-coincidence with its length—that is, 239 anomalistic months last for 6,585.54 days, just 0.22 days longer than the saros— but we did not take that observation further at that stage.

The anomalistic month is the cycle time of the angular diameter of the Moon, altering between 0.548 degrees (at perigee) and 0.491 degrees (at apogee). At the end of a saros the Moon still has 0.22 days to go before it returns to the geocentric distance at which it began. If it started the saros precisely at perigee then at the end it has another 5 hours and 17 minutes to go before next passing through perigee. That is only one part in 125 of an orbit, the result being that the angular size of the Moon changes by very little, if measurements at start and completion of a saros are compared.

Now what about the apparent size of the Sun? That also affects whether or not an eclipse is going to total. The apparent solar diameter varies with the heliocentric distance of the Earth, and we saw earlier that it oscillates between 0.542 and 0.524 degrees during a complete orbit, or a full year. But we are not concerned with a full year. The saros lasts for 18.03 years implying that, compared with its beginning, at the end of a saros the Earth has traveled just 3 percent more than 18 complete orbits. Therefore the angular size of the Sun will not be much different from what it was at the start.

There is another remarkable coincidence, then. The apparent sizes of both Sun and Moon are close to being duplicated from one saros to the next. The eclipses in Figure 2-2 are a good example. Equally well the eclipses coupled with that of August 11, 1999, in saros 145 (those of July 31, 1981, and August 21, 2017, plus several others before and after) are also total eclipses, just shifted in steps west by 115 degrees and south by about 4 degrees. In the case of the 2017 eclipse this places the route beautifully across breadth of the contiguous United States, given that the 1999 event tracked over Europe and the Middle East.

Let us summarize what we have learned above. The saros enables us to predict repeating eclipses every 18.03 years, due to the fact that 223 synodic months happen to last for close to 242 nodical months. It also happens that 239 anomalistic months have essentially the same total duration, making the apparent size of the Moon not alter much after a saros, and the saros being not greatly different from 18 whole years results in the Sun also being near its original apparent diameter. These facts result not only in eclipses repeating, but also they repeat in basic character, a fact that was foreshadowed in Chapter 2 but not completely explained there.

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