FREQUENCY

    Total solar eclipses are rare events. Although they occur somewhere on Earth approximately every 18 months, it has been estimated that they recur at any given place only once every 370 years, on average. Then, after waiting so long, the total eclipse only lasts for a few minutes, as the Moon's umbra moves eastward at over 1700 km/h. Totality can never last more than 7 min 40 s, and is usually much shorter: during each millennium there are typically fewer than 10 total solar eclipses exceeding 7 minutes. The last time this happened was June 30, 1973. Observers aboard a Concorde aircraft were able to stretch totality to about 74 minutes by flying along the path of the Moon's umbra. The next eclipse of comparable duration will not occur until June 25, 2150. The longest total solar eclipse during the 8,000-year period from 3000 BC to 5000 AD will occur on July 16, 2186, when totality will last 7 min 29 s.
    If the date and time of any solar eclipse are known, it is possible to predict other eclipses using eclipse cycles. Two such cycles are the Saros and the Inex. The Saros cycle is probably the best known, and one of the most accurate, eclipse cycles. The Inex cycle is itself a poor cycle, but it is very convenient in the classification of eclipse cycles. After a Saros cycle finishes, a new Saros cycle begins one Inex later, hence its name: in-ex. A Saros cycle lasts 6,585.3 days (a little over 18 years), which means that after this period a practically identical eclipse will occur. The most notable difference will be a shift of 120° in longitude (due to the 0.3 days) and a little in latitude. A Saros series always starts with a partial eclipse near one of Earth's polar regions, then shifts over the globe through a series of annular or total eclipses, and ends at the opposite polar region. A Saros lasts 1226 to 1550 years and 69 to 87 eclipses, with about 40 to 60 central.

Saros cycle

    The Saros cycle is an eclipse cycle with a period of about 18 years 11 days 8 hours (approximately 6585.3 days) that can be used to predict eclipses of the Sun and Moon. One Saros after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, and a nearly identical eclipse will occur.
    The Saros cycle of 18 years 11 days 8 hours (6585.3 days) is very useful for predicting the times at which nearly identical eclipses will occur, and is intimately related to three periodicities of the lunar orbit:

the synodic month (29.530 588 days = 29 d 12 h 44 min 2.8 s, or about 29 ? days),

the draconic month (27.212 220 days = 27 d 5 h 5 min 35.8 s, or about 27 1/5 days),

the anomalistic month (27.554 551 days = 27 d 13 h 18 min 33.2 s, or about 27 1/2 days).

    For an eclipse to occur, either the Moon must be located between the Earth and Sun (as for a solar eclipse) or the Earth must be located between the Sun and Moon (as for a lunar eclipse). This can happen only when the Moon is new or full, and repeat occurrences of these lunar phases are controlled by the Moon's synodic period, which is about 29.53 days. Most of the times during a full and new moon, however, the shadow of the Earth or Moon falls to the north or south of the other body. Thus, if an eclipse is to occur, the three bodies must also be nearly in a straight line. This condition occurs only when the Moon passes close to the ecliptic plane and is at one of its two nodes (the ascending or descending node). The period of time for two successive passes of the ecliptic plane at the same node is given by the draconic month, which is 27.21 days. Finally, if two eclipses are to have the same appearance and duration, then the distance between the Earth and Moon must be the same for both events. The time it takes the Moon to orbit the Earth once and return to the same distance is given by the anomalistic month, which has a period of 27.55 days.
    The origin of the Saros cycle comes from the recognition that 223 synodic months is approximately equal to 242 draconic months, which is approximately equal to 239 anomalistic months (this approximation is good to within about 2 hours). What this means is that after one Saros cycle, the Moon will have completed an integer number of synodic, draconic, and anomalistic months, and the Earth-Sun-Moon geometry will be nearly identical: the Moon will have the same phase, be at the same node, and have the same distance from the Earth. If one knew the date of an eclipse, then one Saros later, a nearly identical eclipse should occur. It should be noted that the Saros cycle (18.031 years) is not equal to the precessional period of the lunar orbit (18.60 years). Therefore, even though the relative geometry of the Earth-Sun-Moon system will be nearly identical, the Moon will be in a different position with respect to the fixed stars.
    A complication with the Saros cycle is that its period is not an integer number of days, but contains a fraction of 1/3 days. Thus, as a result of the Earth's rotation, for each successive Saros cycle, an eclipse will occur about 8 hours later in the day. In the case of an eclipse of the Sun, this means that the region of visibility will shift westward one third of the way around the globe by 120°, and the two eclipses will thus not be visible from the same place on Earth. In the case of an eclipse of the Moon, the next eclipse might still be visible from the same location as long as the Moon is above the horizon. However, if one waits three Saros cycles, the local time of day of an eclipse will be nearly the same. This period of three Saros cycles (54 years 1 month, or almost 19756 full days), is known as a Triple Saros or exeligmos (Greek: "turn of the wheel").

Saros Series

If the date and time of any solar eclipse are known, it is possible to predict other eclipses using eclipse cycles. Two such cycles are the Saros and the Inex. The Saros cycle is probably the best known, and one of the most accurate, eclipse cycles. The Inex cycle is itself a poor cycle, but it is very convenient in the classification of eclipse cycles. After a Saros cycle finishes, a new Saros cycle begins one Inex later, hence its name: in-ex. A Saros cycle lasts 6,585.3 days (a little over 18 years), which means that after this period a practically identical eclipse will occur. The most notable difference will be a shift of 120° in longitude (due to the 0.3 days) and a little in latitude. A Saros series always starts with a partial eclipse near one of Earth's polar regions, then shifts over the globe through a series of annular or total eclipses, and ends at the opposite polar region. A Saros lasts 1226 to 1550 years and 69 to 87 eclipses, with about 40 to 60 central.
    As described above, the Saros cycle is based on the recognition that 223 synodic months is to a good approximation equal to 242 draconic months and 239 anomalistic months. However, as this relationship is not perfect, the geometry of two eclipses separated by one Saros cycle will differ slightly. In particular, the place where the Sun and Moon come in conjunction shifts westward by about 0.5° with respect to the Moon's nodes every Saros cycle, and this gives rise to a series of eclipses, called a Saros series, that slowly change in appearance.
    Each Saros series starts with a partial eclipse, and each successive Saros cycle the path of the Moon is shifted either northward (when near the descending node) or southward (when near the ascending node). At some point, eclipses will no longer be possible and the series terminates. For solar eclipses the statistics for the complete Saros series within the era between 2000 BCE and 3000 CE are as follows. The series last between about 1226 to 1550 years, which corresponds to 69 to 87 eclipses; most series have 71 or 72 eclipses. From 39 to 59 (mostly about 43) eclipses in a given series will be central (that is, total, annular, or hybrid annular-total). Lunar eclipse series are not as long-lived. At any given time, approximately 40 different Saros series will be in progress.
    Saros series are numbered according to the type of eclipse (solar or lunar) and whether they occur at the Moon's ascending or descending node. Odd numbers are used for solar eclipses occurring near the ascending node, whereas even numbers are given to descending node solar eclipses. For lunar eclipses, this numbering scheme is reversed. The ordering of these series is determined by the time at which each series peaks, which corresponds to when an eclipse is closest to one of the lunar nodes. For solar eclipses, (in 2003) the 39 series numbered between 117 to 155 are active, whereas for lunar eclipses, there are now 41 active Saros series.

Inex cycle

    The inex is an eclipse cycle of about 29 years. The cycle was first described by Crommelin in 1901, but was named by G. van den Bergh who studied it half a century later.
    An inex is 358 lunations (synodic months) long: this is almost exactly equal to 388.5 draconitic months or 30.5 eclipse years. This means that if there is a solar eclipse (or lunar eclipse), then after one inex a New Moon (resp. Full Moon) will take place at the opposite node of the orbit of the Moon, and under these circumstances another eclipse can occur.
    An inex also is close (within 70 min.) to an integer number of days (10,571.95) so solar eclipses tend to take place at about the same geographical longitude at successive events, although at opposite geographical latitudes because the eclipses occur at opposite nodes. This is in contrast to the better known saros cycle, which has a period of about 6585 + 1/3 days, so successive solar eclipses tend to take place about 120° in longitude apart on the globe (although at the same node and hence at about the same geographical latitude).
    Unlike the saros, the inex is not close to an integer number of anomalistic months so successive eclipses are not very similar in their appearance and characteristics. Indeed, unlike the saros, an inex series is not unbroken: at the begin and end of a series, eclipses may fail to occur. However once settled down, inex series are very stable and run for a long time.
    The significance of the inex cycle is not in the prediction, but in the organization of eclipses: any eclipse cycle, and indeed the interval between any two eclipses, can be expressed as a combination of saros and inex intervals. Also when a saros series has terminated, then often one inex after the last eclipse of that saros series, the first eclipse of a new saros series occurs. This in-coming and ex-iting of saros series separated by an interval of 29 years suggested the name for this cycle.

Solar eclipse. In Wikipedia, The Free Encyclopedia.
http://en.wikipedia.org/w/index.php?title=Solar_eclipse&oldid=116220081