Saros cycle

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The Saros cycle is an eclipse cycle with a period of about 18 years 11 days 8 hours (approximately 6585⅓ 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.

[edit] History

The Saros cycle was discovered by the Chaldeans (ancient Babylonian astronomers) several centuries BC, and was later known to Hipparchus, Pliny (Naturalis Historia II.10[56]) and Ptolemy (Almagest IV.2), but under different names. The Sumerian/Babylonian word "SAR" was a unit of measure, and as a number appears to have had a value of 3600. The name "saros" was first given to the eclipse cycle by Edmund Halley in 1691, who took it from the Suda, a Byzantine lexicon of the 11th century. Although Halley's naming error was pointed out by Guillaume Le Gentil in 1756, the name continues to be used.

[edit] Description

The Saros cycle of 18 years 11 days 8 hours 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, the draconic month, and the anomalistic month. 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 ⅓ 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").

[edit] Saros Series

Lunar eclipses occurring near the Moon's descending node are given odd Saros series numbers. The first eclipse in these series pass through the southern edge of the Earth's shadow, and the Moon's path is shifted northward each successive Saros cycle.

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.^{[1] [2]} 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.^[3][4] 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.

[edit] Example: Lunar Saros 131

As an example of a single Saros series, the accompanying table gives the dates of lunar eclipses for Saros series 131. This eclipse series began in 1427 AD with a partial eclipse at the southern edge of the Earth's shadow when the Moon was close to its descending node. Each successive Saros cycle, the Moon's orbital path is shifted northward with respect to the Earth's shadow, and the first total eclipse occurred in 1950. For the following 252 years, total eclipses occur, with the central eclipse being predicted to occur in 2078. The first partial eclipse is predicted to occur in the year 2220, and the final partial eclipse of the series will occur in 2707. The total lifetime of the lunar Saros series 131 is 1280 years.

Because of the ⅓ fraction of days in a Saros cycle, the visibility of each eclipse will differ for an observer at a given fixed locale. For the lunar Saros series 131, the first total eclipse of 1950 will not be visible to viewers in North America, as it will take place during the day, and is here labeled as down in the table. The following eclipse in the series will occur ⅓ day later, and is labelled as rising, as it will occur in the early evening. The third total eclipse occurs ⅓ day later, in the early morning, as is labelled as setting. This cycle of three (down, rising, setting) repeats from the initiation to termination of the series.

[edit] See also

• Eclipse cycle
• Solar eclipse
• Lunar eclipse
• Metonic cycle

[edit] References

Cited references

1. ^ Meeus (2004). Ch. 18 "About Saros and Inex series" in: Mathematical stronomy Morsels III. Willmann-Bell, Richmond VA, USA. 
2. ^ Espenak, Fred; Jean Meeus (Oct 2006). Five Millennium Canon of Solar Eclipses, Section 4 (NASA TP-2006-214141 (PDF). NASA STI Program Office. Retrieved on 2007-01-24.
3. ^ G. van den Bergh (1955). Periodicity and Variation of Solar (and Lunar) Eclipses (2 vols.). H.D. Tjeenk Willink & Zoon N.V., Haarlem. 
4. ^ Bao-Lin Liu and Alan D. Fiala (1992). Canon of Lunar Eclipses, 1500 B.C. to A.D. 3000. Willmann-Bell, Richmond VA. 

General refernces

• Jean Meeus and Hermann Mucke (1983)Canon of Lunar Eclipses. Astronomisches Büro, Vienna.
• Theodor von Oppolzer (1887). Canon der Finsternisse. Vienna.

[edit] External links

• NASA eclipse home page: Eclipses and the Saros
• Eclipses and the Saros Cycle
• Eclipse Search -- here one can search 5,000 years of eclipse data by type, magnitude, Saros number or simply by year.
• Saros series 131 table