The Minus 10 Or 11 Day Jump

The effect of the saros is that eclipses repeat on intervals of 18 years plus 10 or 11 days. But if you look at a tabulation of past eclipses you will find that there are sequences with interstitial periods of a year minus 10 or 11 days, with three or four eclipses in a row. For example:

February 15, 1961; February 5, 1962; January 25, 1963;

January 14, 1964 (total, total, annular, partial eclipses of the Sun);

July 17, 1981; July 6, 1982; June 25,1983 (partial, total, partial eclipses of the Moon);

September 2, 1997; August 22, 1998; August 11, 1999; July 31, 2000 (partial, annular, total, partial eclipses of the Sun).

The reason for this is easy to see. Solar eclipses occur at conjunction, and conjunctions are spaced by synodic months; similarly for lunar eclipses at opposition. Twelve synodic months last for 354.37 days on average, which is 10.88 days short of a solar year.

On that basis one might expect eclipses to recur spaced by 354/355 days, but for how long could the sequence continue? The answer is given again by the lengths of the eclipse seasons, and the spacing between them. The longest eclipse season lasts for just over 37 days. The spacing of the eclipse season centers is equal to the eclipse year, 346.62 days, which is 18.62 days short of a solar year of close to 365.24 days. Therefore the eclipse seasons step backwards through the solar year in jumps of 18.62 days. At the same time the twelfth conjunction is stepping back by 10.88 days every year, producing a relative change of 18.62 - 10.88 = 7.74 days. Within a 37-day partial eclipse season one might get a sequence of a maximum of five solar eclipses in consecutive years (i.e., four steps of 7.74 days, equal to just below 31 days), usually less. Using the more stringent limits for total eclipses, a lower number of events appear in such a chain. These chains of eclipses just arrive consecutively 10 or 11 days earlier on the calendar (equivalent to 355/354 days later).

Turning to lunar eclipses, the ecliptic limits are more restricted, and as a result only pairs or trios with this spacing are identified. This is the reason for the patterns seen in Figures 15-5 and 15-6.

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