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Predicting total solar eclipses

Quamrul Haider
A total solar eclipse is a dramatic event. It occurs when the New Moon passes directly in front of the Sun. As totality approaches, the sky becomes dark, mid-day turns into dusk, and stars appear in the sky. In the words of Homer, "and the Sun has perished out of heaven, and an evil mist hovers overall."
The Moon's orbital plane is tilted by about 5 degrees to the Earth's ecliptic (orbital plane). The points where it crosses the ecliptic are known as the nodes. The Moon crosses the ecliptic twice in a lunar month (29.53 days). It spends half the lunar month above the ecliptic and the other half below. In addition to the tilt, Moon's orbital plane also wobbles, causing the line connecting the nodes to slowly precess. It takes 346.6 days for the line of nodes to go from one alignment to the next identical alignment. This time period is called the eclipse year.
Although the Moon crosses the nodes twice each month, episodes of total solar eclipses are rare. They occur only when the New Moon is at a node on the line of nodes between the Earth and the Sun. Furthermore, the Moon must be in the part of its elliptic orbit where it is closer to the Earth. If these conditions are not met, the long, narrow shadows of the Earth and Moon will miss their marks and no eclipseswill occur.
How can the Moon which is about 400 times smaller than the Sun completely block out the Sun from our view? It is a happy coincidence that the angular diameters of the Sun and Moon, or the angle subtended by them at the point of observation have the same value of half a degree. Thus when their orbital planes intersect and the distances align favorably, the New Moon can completely block the Sun.
Predicting the occurrence of a solar eclipse is quite simple. If there is an eclipse today, then to predict when the next one will occur, we need to know how many whole lunar months equal whole number of eclipse years. We can then calculate the time it will take for the next identical alignment of the Sun, Moon, and the line of nodes. By trial and error, it is found that 223 lunar months is equal to 19 eclipse years, because 223x29.53 = 19x346.6 = 6585 days (18 years, 11 days). A more accurate calculation yields the value 18 years, 11 1/3 days. This interval of time is called the Saros, Greek for "repetition".
An eclipse will repeat with surprising accuracy after one Saros cycle. However, because of the extra one-third day in the Saros cycle, it will not be visible from the same place as the previous one. After one Saros the Earth will rotate an additional one-third of a turn farther east, shifting the region of visibility west, causing the eclipse to occur 8 hours later in the day.
Eclipses separated by the Saros interval forms the eclipse series. How does one know when the series starts and when it ends? First, one has to find the very first eclipse of the series and the exact moment that eclipse occurred by back-tracking along the trail of eclipses within a given Saros series. Once the occurrence of the first eclipse is found, the rest in the series is a foregone conclusion.
There will be 71 to 73 solar eclipses in a series spread over a period of approximately 1300 years.
Every Saros series begins with a number of partial eclipses near one of the poles and ends with a group of partial eclipses near the opposite pole. We are now going through a number of series' beginning at 117. For this series, the first eclipse occurred on June 24,0792 and the last one will be on August 3,2054. The latest one was on July 1, 2000; the next one will be on July 13, 2018, and so on. Note they are all separated by the Saros cycle.
A Saros series returns to almost the same geographic region every three Saros periods (54 years and 34 days) of its earlier location. This triple Saros cycle is known as the Exeligmos, Greek for "turn of the wheel." Thanks to the Babylonians (Chaldeans), the Saros cycle is a clever and powerful tool for predicting solar eclipses.
The writer is a Professor of Physics at Fordham University, New York.