From: F. Espenak: Fifty Year Canon of solar eclipses 1986 - 2035, NASA Ref. Pub # 1178 rev. July 1987
ECLIPSE FREQUENCY AND RECURRANCE
Having established the preliminary geometry for solar eclipses a question immediately arises. Why doesn't a solar eclipse occur at every new Moon? Since the Moon cycles through its phases every 29 1/2 days or one synodic month, one would expect an eclipse to occur during each conjunction with the Sun. If the Moon's orbit around the Earth were in the same plane as the Earth's around the Sun, this is precisely what would happen. However, the Moon's orbit is inclined 5° to the Earth's. Our planet's natural satellite passes through the ecliptic only twice a month at a pair of points called the nodes. The rest of the time the Moon is either above or below the plane of the Earth's orbit. Since an eclipse can only occur when the Sun, Moon and Earth lie in the same plane, these conditions are met when new Moon takes place at one of the nodes. Contrary to popular belief, solar eclipses are not at all rare. In fact, they're more common than lunar eclipses. An examination of the exterior tangents which delineate the Earth's umbra will substantiate this claim. An eclipse is possible only when the Moon is within that section of its orbit inscribed by the exterior tangents. However, the sunward arc of the Moon's orbit is clearly longer than the anti-sunward arc which passes through the shadow. The number of solar and lunar eclipses that occur are proportional to the lengths of these two arcs. Thus, solar eclipses out number lunar eclipses by almost 5 to 3. In this argument, the Earth's penumbral shadow has been ignored since penumbral lunar eclipses are essentially unobservable. In any one calendar year, there are at least two and as many as five solar eclipses. On the other hand, there can be no more than three lunar eclipses per year and it's quite possible to have none at all. Combining both solar and lunar eclipses, it's possible for one calendar year to contain a maximum of seven eclipses. However, they can only occur in the combinations of five solar and two lunar or four solar and three lunar. In either case, the solar eclipses must all be partial. As a point of interest, 1982 happened to be one of the rare years containing seven eclipses. What made it even more remarkable was the fact that all three lunar eclipses were total. This will not happen again until the year 2485 AD.
The previous discussion contradicts common experience because lunar eclipses are observed more frequently than solar eclipses. The conflict is resolved since solar eclipses are only visible from isolated regions of the Earth while lunar eclipses are visible from the entire night time hemisphere of our planet. An examination of the geometry of the nodes yields further clues on the subject of eclipse recurrence. Since the Sun and Moon both subtend significant angles, neither one has to be exactly at the nodes for an eclipse to occur. In addition, an observer's position on the surface of the Earth introduces a sizable parallax of 2° in ecliptic latitude. These factors make a solar eclipse possible whenever the Sun is within 18.5° of a node. The Sun travels along the ecliptic at about 1° per day and requires about 37 days to cross through the eclipse zone centered on each node. New Moon occurs every 29 1/2 days and thus guarantees at least one eclipse during each of the Sun's node crossings. The period during which the Sun is near a node is called an eclipse season and there are two eclipse seasons each year.
If the line of nodes were fixed in space, then eclipse seasons would occur six months apart and at the same time each year. Actually, the line of nodes slowly drifts westward at the rate of 19 degrees per year. As a result, eclipse seasons occur every 173.3 days. Two eclipse seasons constitute an eclipse year of 346.6 days. This is 18.6 days short of a solar year and is equal to the time required by the Sun to cross the same node twice. In order to find a periodicity in the mechanics of solar eclipses, we must search for a commensurability between the synodic month and the eclipse year. Fortunately, 19 eclipse years are almost exactly equal to 223 synodic months; they differ by only 11 hours. The coincidence is all the more remarkable when compared to a period known as the anomalistic month. This is the time required for the Moon to pass from perigee to perigee and is approximately 27 1/2 days. The anomalistic month is important because the Moon's geocentric distance is the primary factor determining the annular or total nature of a solar eclipse. As unlikely as it may seem, 239 anomalistic months are also equal to 223 synodic months to within 6 hours. This is the origin of the famous Saros cycle of 6585 1/3 days or 18 years. 11 days and 8 hours. Any two eclipses separated by one Saros cycle share very similar mechanical characteristics. They occur at the same node with the Moon at the same distance from Earth and at the same time of year. Because the Saros does not contain an integral number of days, its biggest drawback is that subsequent eclipses are visible from different parts of the globe. Although the 1/3 day displacement shifts the eclipse path 120° westward with each cycle, the series returns to the same geographic region every 3 Saroses or 56 years and 34 days.
A Saros series doesn't last indefinitely because the various periods are not perfectly commensurate with one another. In particular, 19 eclipse years are 1/2 day longer than the Saros. As a result, the node shifts eastward by about 0.5° with each cycle. A typical Saros series begins when new Moon occurs about 18 degrees east of a node. If the first eclipse occurs at the Moon's decending node, the Moon's umbral shadow will pass 3500 km below the Earth and a partial eclipse will be visible from the south polar region. On the following return, the umbra will pass about 300 km closer to the Earth and a partial eclipse of slightly larger magnitude will result. After ten or eleven Saros cycles (about 200 years), the first central eclipse will occur near the south pole of the Earth. Over the course of the next 950 years, a central eclipse will occur at each Saros but will be displaced northward by an average of 300 km. Halfway through this period, eclipses of long duration will occur near the equator. The last central eclipse of the series will occur near the north pole. The next ten eclipses will be partial with successively smaller magnitudes. Finally, the Saros series will end some 13 centuries after it began at the opposite pole. A typical series may be comprised of 70 to 80 eclipses, about 50 of which are central.
If a Saros series begins near the ascending node, the first eclipse will be partial from the northern polar region and the previous sequence of events is reversed. Since at least two solar eclipses occur every year, there are obviously many different Saros series in progress simultaneously. For instance, during the later half of the twentieth century, there are 41 individual series and 26 of them are producing central eclipses. As old series terminate, new ones are always beginning and take their places. To illustrate, the total solar eclipses of 1925, 1943. 1961, 1979, 1997, 2015 and 2033 are all members of Saros 120. The series began with a partial eclipse at the south pole in 915 AD. The 2033 event is the last central eclipse of the series. Note that the paths of the last four eclipses grow progressively broader as the umbral shadow cone passes closer to the limb of the Earth. The next eclipse in the series will be a partial eclipse in 2051. Saros 120 will end with a partial eclipse near the north pole in 2195.
Posted for the WWW by Dr. Wolfgang Strickling
Back to Wolfgang's solar eclipse links (German language)
Other links to (solar) eclipse cycles:
A catalogue of eclipse cycles most comprehensive explanation, eclipse cycle calculator, large referece collection
The Metonic Cycle and the Saros short introduction to Metonic and Saros cycles
Saros, Inex and Eclipse cycles good mathematic explanation and survey
URL of this article: http://www.strickling.net/saros.htm