## The Frequencies Of Eclipses

What is the maximum and minimum numbers of eclipses that can occur in any one calendar year? The matter of the minimum number is the easiest to address. The ecliptic limit pertaining to certainty of at least a partial solar eclipse is 15.35 degrees, producing a range in longitude of 30.7 degrees. The Sun appears to move along the ecliptic at just less than 1 degree per day (360 degrees to move and almost 365.26 days in a sidereal year). Therefore it takes just over 31 days to traverse the zone in which eclipses can occur, the seasons that recur twice per eclipse year when the lunar nodes are close to the solar direction. Because 31 days is longer than the nodical month, there must be at least one solar eclipse of some description in each eclipse season, making two each year. The eclipse year of 346.6 days most often is phased such that there are only two eclipse seasons in a calendar year, so that every calendar year must contain a minimum of two solar eclipses.

In contrast, partial lunar eclipses are certain only within ecliptic limits of 9.5 degrees, a range of 19 degrees in all, which the Sun takes just over 19 days to traverse, considerably less than a nodical month. Therefore it is possible for the Moon to avoid being eclipsed, in fact to avoid such ignominy in both eclipse seasons within a certain calendar year.

In consequence the minimum number of eclipses in any calendar year is two: both solar. Next we turn to the maximum.

The ecliptic limit rendering the possibility of partial solar eclipses is 18.5 degrees, making for a range of 37 degrees, which the Sun takes 37.5 days to traverse. One could get a solar eclipse at one conjunction, and then another at the following conjunction about 29.5 days later, both within that one eclipse season. Not only that, but a lunar eclipse between times is also feasible.

One can imagine, then, getting one lunar and two solar eclipses in an eclipse season, and in the next such season half an eclipse year later the same thing occurs, making six.

Is that the maximum? No, it's not quite. If the first eclipse season were centered on about January 15, the initial trio of eclipses would be in January with the lunar eclipse on that date and the initial solar eclipse on the first or second day of the month. The next set of three would be centered on July 8. Such a phasing allows for a third eclipse season partially lying within the calendar year, starting on December 12. A solar eclipse might occur soon thereafter, making seven in all within the calendar year, five solar and two lunar. In this scenario there cannot be a third lunar eclipse within the year, because twelve synodic months last for 354 days, and that period counted after January 15 puts any possible lunar eclipse twelve full moons later, on about January 4 of the following year.

A similar wrangling with dates allows one to ascertain that it is feasible to get four solar and three lunar eclipses in a year, again a total of seven. For this to occur one needs a lunar eclipse early in January followed by a solar eclipse at the next conjunction, then a solar/lunar/solar trio straddling the middle of the year, and finally in December a solar eclipse and paired lunar eclipse at the following opposition.

The bottom line is that in any calendar year there are at least two eclipses, both solar, but there may be up to a total of seven, split either 5:2 or 4:3 as solar:lunar. Nowadays that's of interest on a trivial level only, though, because such eclipses may be a mixture of partial, annular, and total, and for scientific purposes (and indeed public enthusiasm) it is really only the total eclipses that inspire. On the other hand, the mere keeping of records of when eclipses of any variety occurred would have allowed ancient civilizations to unravel the secrets of the cycles of the Moon. Our discussion of those cycles will have given you some inkling of how that could have been achieved.

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