## The Distribution Of Eclipses

The average numbers of eclipses per century were mentioned in Chapter 2. The figures used were based on a monumental work by the nineteenth-century Viennese astronomer Theodor von Oppolzer, published posthumously in 1887. Using detailed theories for the orbits of the Sun and Moon, Oppolzer calculated by hand the circumstances for all eclipses between 1208 B.C. and A.D. 2161, a total of 3,368 years providing in all 8,000 solar and 5,200 lunar eclipses. From this compendium are derived the averages of 238 solar and 154 lunar eclipses per century.

These may further be subdivided into partial and total events, and so on. Easiest to analyze are the lunar eclipses: over a hundred years about 71 total and 83 partial lunar eclipses may be expected.

Turning to solar eclipses, the 238 per century break down as 84 partial, 66 total, 77 annular, and 11 partly annular and partly total.

How could a particular eclipse event be both? Consider Figure 2-1 again. The nearest part of the Earth's surface to the Moon, around the noon meridian, may be only just close enough to be within the umbra (the conical lunar shadow), so that observers there experience a very brief total eclipse. Further to the east and the west the observers are a few thousand miles more distant, putting them beyond the vertex of the umbral cone, so that they witness only an annular eclipse. The track of the eclipse drawn across the globe would start in the west as an annular phenomenon, become total as the point of greatest eclipse is approached, and then become annular again as the track proceeds east. This may be termed a hybrid eclipse.

If there are 66 total eclipses per century, then such an opportunity presents itself somewhere around the world once every 18 months on average. If you were clever enough to take advantage of one of the 11 hybrid eclipses by placing yourself within the portion of the ground track achieving totality, then with an unlimited travel budget you might manage one total eclipse every 15 or 16 months, on average. They are not smoothly distributed in time, though.

Unfortunately many total solar eclipses have paths unfavorable for potential viewers, and a track traversing an accessible location with a good chance of clear weather occurs only about once every three years. Nevertheless, many is the keen eclipse watcher who has spent an enormous amount of time and money getting to a well-considered prime spot, only to be stymied by an unseasonably cloudy day.

These numbers of eclipses per century are all averages, such as would result if they happened randomly in time. But we know that is not reality. They repeat on regular cycles. Total solar eclipse tracks perform consistent geographical steps within a saros, as in Figure 2.2, and there are systematic trends in other eclipse sequences.

There is another geographical effect that we have yet to mention, although it was alluded to at the start of this book. Taking into account the summed area of a track of totality across the surface of the Earth, and the average occurrence rate, for any random point on the planet a total solar eclipse might be expected about once per 410 years. But just as they are not randomly distributed in time, so they do not occur randomly in terms of geography.

A total solar eclipse is more likely to happen while the Earth is near aphelion than when near perihelion, because while we are further from the Sun its apparent diameter is minimized, presenting less of a target area for the Moon to obscure. This means that more total solar eclipses occur between May and August (straddling aphelion in early July) than between November and February (bracketing perihelion in early January), at least in the present epoch. Over the next six or seven millennia the date of perihelion will move much later in the year, eventually reversing this trend.

This implies that more total eclipses occur during the Northern Hemisphere summer than its winter. Summer is the time when the Northern Hemisphere is tipped over towards the Sun (that's why it is summer), as in Figure A-3, presenting a larger sunward area than the Southern Hemisphere. Overall the effect is that the north gets more total solar eclipses. Averaged over the globe the rate is about one per 410 years for a random location, but a random location chosen in the Northern Hemisphere gets one total eclipse every 330 years or so, whereas in the Southern Hemisphere it is less frequent, once per 540 years.

As the bulk of the population lives in the Northern Hemisphere, a person picked at random from the whole of humankind has an enhanced probability of experiencing a total solar eclipse without needing to chase after one. Lifetimes average to about 80 years in the developed world, such as in North America, Europe, or Japan. A randomly chosen person from such a country therefore has about a one-in-four chance of happening to be crossed by a total solar eclipse track during his or her lifetime.

That probability can be turned into a certainty by going in chase of such an event. I hope this book will have persuaded you that this is an attractive idea.

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