Eclipses may occur repeatedly, separated by some specific interval of time: this interval is called an eclipse cycle. The series of eclipses is called an eclipse series. Total solar eclipse in Zambia, 2001 An eclipse (Greek verb: ecleipo = cease to exist) is an astronomical event that occurs when one celestial object moves into the shadow of another. ...

General explanation

Eclipse conditions

Eclipses may occur when the Earth and Moon are on one line with the Sun, and the shadow of one body cast by the Sun falls on the other. So at New Moon (or rather Dark Moon), when the Moon is in conjunction with the Sun, the Moon may pass in front of the Sun as seen from a narrow region on the surface of the Earth. At Full Moon, when the Moon is in opposition with the Sun, the Moon may pass through the shadow of the Earth, which is visible from the night half of the Earth. Total solar eclipse in Zambia, 2001 An eclipse (Greek verb: ecleipo = cease to exist) is an astronomical event that occurs when one celestial object moves into the shadow of another. ... Earth, also known as the Earth or Terra, is the third planet outward from the Sun. ... Crust composition Oxygen 43% Silicon 21% Aluminium 10% Calcium 9% Iron 9% Magnesium 5% Titanium 2% Nickel 0. ... A Sun is the star at the centre of a solar system. ... Traditionally, the lunar phase new moon begins with the first visible crescent of the Moon, after conjunction with the Sun. ... The dark moon is the time when the Moon is so close to the Sun in the sky that it cannot be seen even near sunset or sunrise. ... The Galileo spacecraft took this composite image on December 7, 1992 on its way to explore the Jupiter system in 1995-97. ...

Note: conjunction and opposition of the Moon together have a special name: syzygy (from Greek for "junction"), because of the importance of these lunar phases. Syzygy can refer to any of several different things: Astronomy In astronomy, a syzygy (Greek: yoked together) is a situation where three bodies are situated along a straight line. ... The Greek language (Greek Ελληνικά, IPA – Hellenic) is an Indo-European language with a documented history of some 3,000 years. ... In astronomy, a phase of the Moon is any of the aspects or appearances presented by the Moon as seen from Earth, determined by the portion of the Moon that is visibly illuminated by the Sun. ...

Now an eclipse does not happen at every New or Full Moon, because the plane of the orbit of the Moon around the Earth is tilted with respect to the plane of the orbit of the Earth around the Sun (the ecliptic). This inclination is on average about: For other meanings of the term orbit, see orbit (disambiguation) In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ... The plane of the Ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ... Inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit and is the angular distance of the orbital plane from the plane of the reference (usually planets equator or the ecliptic), stated in degrees. ...

I = 5°09'

Compare this with the relevant apparent mean diameters:

Sun: 32' 2"

Moon: 31'37" (as seen from the surface of the Earth right beneath the Moon)

and: 1°23' for the diameter of the shadow of the Earth at the position of the Moon.

So at most New Moons the Earth passes too much North or South of the shadow of the Moon, and at most Full Moons the Moon misses the shadow of the Earth. Also most of the time the Moon will not be able to fully cover the Sun, but because of the elliptic orbit it sometimes is nearer and looks bigger. In any case, the alignment must be close to perfect to cause an eclipse.

An eclipse can only occur when the Moon is close to the plane of the orbit of the Earth, i.e. when its ecliptic latitude is small. This happens when at the time of the syzygy, the Moon is near one of the two nodes of its orbit on the ecliptic. Of course the Sun is also near a node at that time: the same node in case of a solar eclipse, the opposite node in case of a lunar eclipse. A node is one of two points where a bodys orbit crosses the ecliptic, called the ascending node (when the body is moving northward) and descending node (when the body is moving southward). ...

Recurrence

Now the time it takes for the Moon to return to a node, the so-called draconic month, is less than the time it takes for the Moon to return to the Sun: the synodic month. The reason is that the orbit of the Moon precesses backward with respect to the ecliptic, and makes a full circle in somewhat less than 9 years. The difference in period between synodic and draconic month is about 2 + 1/3 days. Likewise, the Sun passes both nodes as it moves over the ecliptic. The period to return to the same node is called eclipse year, and is about 1/9th year shorter than a sidereal year because of the precession of the nodes of the Moon's orbit in about 9 years. In Egyptian mythology, Month is an alternate spelling for Menthu. ... In Egyptian mythology, Month is an alternate spelling for Menthu. ... Precession (also called gyroscopic precession) is the phenomenon by which the axis of a spinning object (e. ... A year is the time between two recurrences of an event related to the orbit of the Earth around the Sun. ... The sidereal year is the time for the Sun to return to the same position in respect to the stars of the celestial sphere. ...

So if a solar eclipse occurs at one New Moon, so close to a node, then at the next Full Moon the Moon is already over a day past its opposite node, and may or may not miss the Earth's shadow. By the next New Moon it is even further ahead of the node, and it is more unlikely that there will be a solar eclipse somewhere at Earth. By the next month, there will certainly be no event.

However, about 5 or 6 lunations later the New Moon will fall close to the opposite node. In that time (half an eclipse year) the Sun has moved to the opposite node too. Now the circumstances are suitable again for one or more eclipses.

So eclipses can occur in a one- or two-month period twice a year, around the time when the Sun is near the nodes of the Moon's orbit.

Periodicity

These are still rather vague predictions. However we know that if an eclipse occurred at some moment, then there will occur an eclipse again S synodic months later, if that interval is also D draconic months, where D is an integer number (return to same node), or an integer number + 1/2 (return to opposite node). So an eclipse cycle is any period P for which approximately holds:

P = S×(synodic month length) = D×(draconic month length)

Given an eclipse, then there is likely to be another eclipse after every period P. This remains true for some limited time, because the relation is only approximate.

Another thing to consider is that the motion of the Moon is not a perfect circle. Its orbit is distinctly elliptic, which means that the Moon's distance from the Earth varies. This changes the apparent diameter of the Moon, and therefore influences the chances, duration, and appearance of an eclipse. This orbital period is called the anomalistic month, and together with the synodic month causes the so-called "full moon cycle" of about 14 lunations in the timings and appearances of Full (and New) Moons. The perturbations of the orbit may change the times of the syzygies by up to 14 hours, and change the apparent diameter by about 6% in either direction. An eclipse cycle will have to be close to an integer number of anomalistic months for predicting eclipses well. In Egyptian mythology, Month is an alternate spelling for Menthu. ... The full moon cycle (the abbreviation fumocy was introduced by Karl Palmen in the CALNDR-L mailing list in October 2002) is a cycle of about 14 lunations over which full moons vary in apparent size. ...

Numerical values

SM = 29.53059 days (Synodic month)

DM = 27.21222 days (Draconic month)

AM = 27.55455 days (Anomalistic month)

EY = 346.620 days (Eclipse year)

Note that:

Good periods can be found from continued fractions:

half draconic months per synodic month:

 2.170391... = 2+1/ 2 5+1/ 11/5 1+1/ 13/6 semester 6+1/ 89/41 1+1/ 102/47 1+1/ 191/88 1+1/ 293/135 tritos 1+1/ 484/223 saros 1+1/ 777/358 inex 11+1/ 9031/4161 1+... 9808/4519 

synodic months per half eclipse year and per eclipse year yield the same series: The tritos is an eclipse cycle of 135 synodic months 146. ... A Saros cycle is a period of 6585 + 1/3 days (approximately 18 years 10 days and 8 hours) which can be used to predict eclipses of the sun and the moon. ... Eclipses may occur repeatedly, separated by some specific interval of time: this interval is called an eclipse cycle. ...

 5.868831... = 5+1/ 5 1+1/ 6 semester 6+1/ 41/7 1+1/ 47/8 47/4 1+1/ 88/15 1+1/ 135/23 tritos 1+1/ 223/38 223/19 saros 1+1/ 358/61 inex 11+1/ 4161/709 1+... 4519/770 4519/385 

Each of these is an eclipse period. Less accurate periods may be constructed by combination of these. The tritos is an eclipse cycle of 135 synodic months 146. ... A Saros cycle is a period of 6585 + 1/3 days (approximately 18 years 10 days and 8 hours) which can be used to predict eclipses of the sun and the moon. ... Eclipses may occur repeatedly, separated by some specific interval of time: this interval is called an eclipse cycle. ...

Eclipse cycles

Comments: In astronomy, an octaeteris is the period of eight solar years after which the moon phase occurs on the same day of the year plus one or two days. ... The tritos is an eclipse cycle of 135 synodic months 146. ... A Saros cycle is a period of 6585 + 1/3 days (approximately 18 years 10 days and 8 hours) which can be used to predict eclipses of the sun and the moon. ... The Metonic cycle or Enneadecaeteris in astronomy and calendar studies is a particular approximate common multiple of the tropical year and the synodic month. ... Eclipses may occur repeatedly, separated by some specific interval of time: this interval is called an eclipse cycle. ...

Fortnight

When there is an eclipse, there is a fair chance that at the next syzygy there will be another eclipse: the Sun and Moon have moved about 15° w.r.t. the nodes (the Moon opposite to where it was the first time), but the luminaries may still be within bounds to make an eclipse
For example, the total lunar eclipse of 15 May 2003 was followed by the partial solar eclipse of 31 May 2003.

Month

Similarly, two events one month apart have the Sun and Moon at two positions on either side of the node, 29° apart: both may cause a partial eclipse.

Semester

or "eclipse season". After 6 (or sometimes 5 or 7) months, the Sun is at the other node, and eclipses may again occur.

Lunar year

Twelve (synodic) months. A little longer than an eclipse year: the Sun has returned to the node, so more eclipses may occur.

Octon

This is a fairly decent short eclipse cycle, but poor in anomalistic returns. One octon after an eclipse from some saros series, an eclipse from the saros series with the next higher number occurs.

Octaeteris

Eight years of 365 days, equals 99 lunations to within 3.5 days.

Tritos

a mediocre cycle, relates to the saros like the inex.

Saros

The most well known, and one of the best, eclipse cycles. After this interval, the Moon's eclipses recur with respect to the lunar calendar. 223 synodic months equals 242 draconitic months to within 51 min.

Metonic cycle or Enneadecaeteris

This is nearly equal to 19 tropical years, but is also 5 "octon" periods and close to 20 eclipse years: so it yields a short series of eclipses on the same calendar date. It consists of 110 hollow months and 125 full months; thus precisely 19 years of 365 days, and equals 235 lunations to within 7.5 h.

Inex

In itself a poor cycle, it is very convenient in the classification of eclipse cycles. After a saros series dies, a new one begins 1 inex later (hence its name: in-ex). It is the interval after which the Moon's eclipses recur at the same longitudes as the previous cycle but at the opposite latitudes.

Exeligmos

3 saroses: the benefit is, that it is nearly an integer number of days. So the next eclipse will be visible from a location close to the first one; in contrast to the saros, when the eclipse occurs ca. 8h later on the day and about 120° West of the first one. It is the interval after which the Moon's eclipses recur with respect to the lunar calendar and at the same longitudes as the previous cycle.

Callippic cycle

441 hollow months and 499 full months; thus 4 Metonic Cycles minus one day or precisely 76 years of 365 1/4 days. It equals 940 lunations to within 5.9 h.

Hipparchic cycle

Not a very remarkable eclipse cycle, but Hipparchos constructed it to closely match an integer number of anomalistic months, years (345), and days. By comparing his own eclipse observations with Babylonian records from 345 years earlier, he could verify the accuracy of the various periods that the Chaldeans used. It is equal to four Callippic cycles minus one day, and equals 3760 lunations to within 15.5 min.

Babylonian

The ratio 5923 returns to latitude in 5458 months was used by the Chaldeans in their astronomical computations.

May 15 is the 135th day of the year in the Gregorian Calendar (136th in leap years). ... 2003 is a common year starting on Wednesday of the Gregorian calendar, and also: The International Year of Freshwater The European Disability Year Events January January 1 - Luíz Inácio Lula Da Silva becomes the 37th President of Brazil. ... May 31 is the 151st day of the year in the Gregorian calendar (152nd in leap years), with 214 days remaining, as the last day of May. ... 2003 is a common year starting on Wednesday of the Gregorian calendar, and also: The International Year of Freshwater The European Disability Year Events January January 1 - Luíz Inácio Lula Da Silva becomes the 37th President of Brazil. ... A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). ... For the Athenian tyrant, see Hipparchus (son of Pisistratus). ...

Frequency

number of eclipses per year; tetrads.

Saros and inex

saros×inex; conjunction points; lifecycles; very long periods.

External links

Search 5,000 years worth of eclipses at: http://www.hermit.org/Eclipse/when_search.shtml

A comprehensive page with eclipse cycles is at: http://www.phys.uu.nl/~vgent/calendar/eclipsecycles.htm

Literature

• S. Newcomb (1882): On the recurrence of solar eclipses. Astron.Pap.Am.Eph. vol.I pt.I . Bureau of Navigation, Navy Dept., Washington 1882
• J.N. Stockwell (1901): Eclips-cycles. Astron.J. 504 [vol.xx1(24)], 14-Aug-1901
• A.C.D. Crommelin (1901): The 29-year eclipse cycle. Observatory xxiv nr.310,379, Oct-1901
• G. van den Bergh (1954): Eclipses in the second millennium B.C. Tjeenk Willink & Zn NV, Haarlem 1954
• G. van den Bergh (1955): Periodicity and Variation of Solar (and Lunar) Eclipses, 2 vols. Tjeenk Willink & Zn NV, Haarlem 1955