Eclipse cycle - Knowledge

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the Sun. The mean anomaly of the Sun is a smooth function, increasing by about 10° when increasing inex by 1 in a saros series and decreasing by about 20° when increasing saros index by 1 in an inex series. This means it is almost constant when increasing inex by 1 and saros index by 2 (the "Unidos" interval of 65 years). The above graph showing the time of year of eclipses basically shows the solar anomaly, since the perihelion moves by only one day per century in the Julian calendar, or 1.7 days per century in the Gregorian calendar. The mean anomaly of the Moon is more complicated. If we look at the eclipses whose saros index is divisible by 3, then the mean anomaly is a smooth function of inex and saros values. Contours run at an angle, so that mean anomaly is fairly constant when inex and saros values increase together at a ratio of around 21:24. The function varies slowly, changing by only 7.4° when changing the saros index by 3 at a constant inex value. A similar smooth function obtains for eclipses with saros modulo 3 equal to 1, but shifted by about 120°, and for saros modulo 3 equal to 2, shifted by 120° the other way.

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as well as alternate between total and annular. Hence there is usually a maximum of one total or annular eclipse each in a given lunar year. (However, in the middle of an eight-semester series the hemispheres switch, and there is a switch during the series between whether the odd ones or the even ones are total.) It is possible to have two eclipses separated by a semester and a third eclipse one month before or after, so that two of the three are separated by seven months, but this only happens during certain centuries (see graph of inex versus date below). Because it is close to a half integer of anomalistic, draconic months, and tropical years, each lunar eclipse will usually alternate between edges of Earth's shadow each semester, as well as alternate between Lunar eclipses with the moon’s penumbral and umbral shadow difference less or greater than 1. Hence there is usually a maximum of one Lunar eclipse with Moon’s penumbral and umbral shadow difference less or greater than 1 each in a given lunar year.

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from apogee toward perigee. The time is also delayed because of the eccentricity of the Earth's orbit. Eclipses occur about four hours later in April and four hours earlier in October. This means that the delay varies from eclipse to eclipse in a series. The delay is the sum of two sine-like functions, one based on the time in the anomalistic year and one on the time in the anomalistic month. The periods of these two waves depends on how close the nominal interval between two eclipses in the series is to a whole number of anomalistic years and anomalistic months. In series like the "Immobilis" or the "Accuratissima", which are near whole numbers of both, the delay varies very slowly, so the interval is quite constant. In series like the octon, the Moon's anomaly changes considerably at least twice every three intervals, so the intervals vary considerably.

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shorter. The eccentricity of the Earth's orbit is presently decreasing at about one percent per 300 years, thus decreasing the effect of the sun's anomaly. Formulae for the Delaunay arguments show that the lengthening of the synodic month means that eclipses tend to occur later than they would otherwise proportionally to the square of the time separation from now, by about 0.32 hours per millennium squared. The other Delaunay arguments (mean anomaly of the Moon and of the sun and the argument of latitude) will all be increased because of this, but on the other hand the Delaunay arguments are also affected by the fact that the lengths of the draconic month and anomalistic month and year are changing. The net results are:

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position moves eastward by more than what it does for that change of day in year at other times. This means the Sun's position relative to the node doesn't change as much as for saros series giving eclipses at other times of the year. In the first half of the 21st century, solar saros series showing this slow rate of change of gamma include 122 (giving an eclipse on January 6, 2019), 132 (January 5, 2038), 141 (January 15, 2010), and 151 (January 4, 2011). Sometimes this phenomenon leads to a saros series giving a large number of central eclipses, for exammple solar saros 128 gave 20 eclipses with |γ|<0.75 between 1615 and 1958, whereas series 135 gave only nine, between 1872 and 2016.

3450:, for example, all produce mainly total eclipses when they are central, because the moon is close to perigee. In fact, at the solar eclipse of October 17, 1781, which was in saros series 130 and inex 50, was both very central and at perigee. But this repetition is not perfect. In about 2460 years, the above-mentioned series, 130, 133... (equivalent to 1 modulo 3) will give central solar eclipses that are annular, near apogee. In about 820 years central lunar eclipses, but not solar ones, will be near perigee every three saros series, and in around 1640 years the solar saros series with index equivalent to 2 modulo 3 will give central eclipses near perigee. 4028:

of draconic months) and longitude (because a period of three saros is always within a couple hours of being 19755.96 days long, which would change the longitude by about 13° eastward). If instead we increase the saros index at a constant inex index, the intervals are quite variable because the number of anomalistic months or years is not very close to a whole number. This means that although the latitude will be similar (but changing sign), the longitude change can vary by more than 180°. Moving by six inex (a de la Hire cycle) preserves the latitude fairly well but the longitude change is very variable because of the variation of the solar anomaly.

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Accuratissima will become exactly equal to a whole number of days or weeks in around AD 2100, meaning that an eclipse around AD 1200 will be repeated at the same time of day on the same day of the week 1841 years later. The Accuratissima is also useful for calculating the magnitude and character of eclipses. An Accuratissima plus a Tritrix plus a saros makes an eclipse cycle 1.8 days short of 2000 Julian years, or 13.2 days longer than 2000 Gregorain years. It is only half a day less than a whole number of anomalistic months, whereas the Accuratisssima is only 0.2 days short of a whole number of anomalistic months.

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of semester and Hipparchic cycle.) This means that at the time of the second eclipse same side of the earth will be facing the sun as at the first eclipse (but the value of gamma will be different). By comparing his own eclipse observations with Babylonian records from 345 years earlier, Hipparchus could verify the accuracy of the various periods that the Chaldeans used. Ptolemy points out that dividing it by 17 still gives a whole number of synodic months (251) and anomalistic months (269), but this is not an eclipse interval because it is not near a whole or half integer number of draconic months.

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occur at every full moon, a solar eclipse every new moon, and all solar eclipses would be the same type. In fact the distances between the Earth and Moon and that of the Earth and the Sun vary because both the Earth and the Moon have elliptic orbits. Also, both the orbits are not on the same plane. The Moon's orbit is inclined about 5.14° to Earth's orbit around the Sun. So the Moon's orbit crosses the ecliptic at two points or nodes. If a New Moon takes place within about 17° of a node, then a solar eclipse will be visible from some location on Earth.

58: 456:" of about 14 lunations in the timings and appearances of full (and new) Moons. The Moon moves faster when it is closer to the Earth (near perigee) and slower when it is near apogee (furthest distance), thus periodically changing the timing of syzygies by up to 14 hours either side (relative to their mean timing), and causing the apparent lunar angular diameter to increase or decrease by about 6%. An eclipse cycle must comprise close to an integer number of anomalistic months in order to perform well in predicting eclipses. 3417:, can produce at most two solar eclipses (both partial) and at most two lunar eclipses (both penumbral). The Callipic cycle is 20 octons, and series of octons often produce only 21 eclipses, so only the first and the last of such a series are separated by a Callipic cycle. Most eclipses are not followed by another eclipse 940 lunations later, but rather 939 lunations later (two inex and a saros), which comes near an integer number of draconic months, producing similar eclipses. This is called a Short Callippic Period. 3258: 3812: 186: 3874: 3899: 4032: 10209: 8268: 3921:, and in September/October further west than its mean longitude, the absolute values of gamma in the first and fourth eclipse are decreased, while the absolute values in the second and third are increased. The result is that all four gamma values are small enough to lead to total lunar eclipses. The phenomenon of the Moon "catching up" with the Sun (or the point opposite the Sun), which is usually not at its mean longitude, has been called a "stern chase". 3866: 3929: 4007: 3821: 8257: 3986:

perigee at the time of the eclipse, and therefore relatively large, favoring total eclipses. In the red area, the Moon is generally further from the Earth, and the eclipses are annular. We can also see the effect of the Sun's anomaly. Eclipses in July, when the Sun is further from the Earth, are more likely to be total, so the blue area extends over a greater range of inex index than for eclipses in January.

8245: 3968:, which is like a linear function of inex and saros but with a deviation that grows quadratically with distance from the reference time, amounting to about 19 minutes at a distance of 1000 years. The mean argument of latitude, F, is equivalent to 0° or 180° (depending on whether the saros index is even or odd) along the smooth curve going through the centre of the band of eclipses, where 370:(how far the Moon is north or south of the ecliptic during an eclipse) changes monotonically throughout any single saros series. The change in gamma is larger when Earth is near its aphelion (June to July) than when it is near perihelion (December to January). When the Earth is near its average distance (March to April or September to October), the change in gamma is average. 3265:

year. This means that the clusters slowly move forward to later dates. In a saros series, every 18 years the eclipse moves to the next later cluster. After 631 years (35 saros) it comes back to the original cluster, which by then has moved, in the Julian calendar, to a date about 13 or 14 days later, or about 18 days later in the Gregorian calendar.

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the node, and the eclipse year when the Sun returns to the node. These three 2-way relations are not independent (i.e. both the synodic month and eclipse year are dependent on the apparent motion of the Sun, both the draconic month and eclipse year are dependent on the motion of the nodes), and indeed the eclipse year can be described as the

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the diagram) occur after the Moon goes through its node (the beginning and end of a draconic month), while the later eclipses (in the lower part) occur before the Moon goes through its node. Every 18 years, the eclipse occurs on average about half a degree further west with respect to the node, but the progression is not uniform.

362:. In other words, a particular eclipse will be repeated only if the Moon will complete roughly an integer number of synodic, draconic, and anomalistic periods and the Earth-Sun-Moon geometry will be nearly identical. The Moon will be at the same node and the same distance from the Earth. This happens after the period called the 3964:

times when the inex value goes up by 1, and 358 times when the saros value goes up by 1. It is thus equivalent to 0°, by definition, at each combination of solar saros index and inex index, because solar eclipses occur when the elongation is zero. From D one can find the actual elapsed time from some reference time such as

424:. In other words, a particular eclipse will be repeated only if the Moon will complete roughly an integer number of synodic, draconic, and anomalistic periods (223, 242, and 239) and the Earth-Sun-Moon geometry will be nearly identical to that eclipse. The Moon will be at the same node and the same distance from the Earth. 3924:

Inex series move slowly through the year, each eclipse occurring about 20 days earlier in the year, 29 years later. This means that over a period of 18.2 inex cycles (526 years) the date moves around the whole year. But because the perihelion of Earth's orbit is slowly moving as well, the inex series

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Lunar eclipses can also be plotted in a similar diagram, this diagram covering 1000 AD to 2500 AD. The yellow diagonal band represents all the eclipses from 1900 to 2100. This graph immediately illuminates that this 1900–2100 period contains an above average number of total lunar eclipses compared to

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Saros and inex numbers are also defined for lunar eclipses. A solar eclipse of given saros and inex series will be preceded a fortnight earlier by a lunar eclipse whose saros number is 26 lower and whose inex number is 18 higher, or it will be followed a fortnight later by a lunar eclipse whose saros

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Saros and inex number can be calculated for an eclipse near a given date. One can also find the approximate date of solar eclipses at distant dates by first determining one in an inex series such as series 50. This can be done by adding or subtracting some multiple of 28.9450 Gregorian years from the

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An eclipse cycle where the number of solar years (365.371) closely matches (by chance) the number of days in 1 solar year (365.242). Lasting 365 years 4.5 months or 4519 lunations. It is the eighth convergent in the continued fractions development of the ratio between the eclipse year and the synodic

3543:

An eclipse cycle where the number of eclipse years (354.5) closely matches (by chance) the number of days in a lunar year (354.371). It equals approximately 336 years 5 months 6 days or 4161 lunations. It is a convergent in the continued fractions development of the ratio between the eclipse year and

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An eclipse cycle equal to 299 years and about ten and a half months, always occurring on the same node. Peter Macdonald found that a series of eclipses of especially long duration visible from Britain occurs with this interval in the period AD 1 to 3000. A Macdonald series has around ten eclipses and

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A triple saros, with the advantage that it has nearly an integer number of days, so the next eclipse will be visible at locations near the eclipse that occurred one exeligmos earlier, in contrast to the saros, in which the eclipse occurs about 8 hours later in the day or about 120° to the west of the

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At an average angular velocity of 0.99° per day, the Sun takes 34.5 days to cross the 34° wide eclipse zone centered on each node. Because the Moon's orbit with respect to the Sun has a mean duration of 29.53 days, there will always be one and possibly two solar eclipses during each 34.5-day interval

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Another thing to consider is that the motion of the Moon is not a perfect circle. Its orbit is distinctly elliptic, so the lunar distance from Earth varies throughout the lunar cycle. This varying distance changes the apparent diameter of the Moon, and therefore influences the chances, duration, and

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will experience a total number of 11,898 solar eclipses between 2000 BCE and 3000 CE. A particular solar eclipse will be repeated approximately after every 18 years 11 days and 8 hours (6,585.32 days) of period, but not in the same geographical region. A particular geographical region will experience

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The fact that the argument of latitude is decreased explains why one sees a curvature in the "Panorama" above. Central eclipses in the past and in the future are higher in the graph (lower inex number) than what one would expect from a linear extrapolation. This is because the ratio of the length of

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In terms of Delaunay arguments, the Sun is biggest at ascending-node solar eclipses and smallest at descending-node solar eclipses around when l'+D=F (modulo 360°), such as June, 2010. It is smallest at descending-node solar eclipses and biggest at ascending-node solar eclipses 9.3 years later, such

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Cosine of mean anomaly of moon at solar eclipses, 2001 through 2040. The curves connect eclipses that are 12 synodic months apart, but do not represent the anomaly between the eclipses. In each such series of four eclipses, the mean anomaly follows a sine wave. The moon is largest when the cosine of

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The time interval between two eclipses in an eclipse cycle is variable. The time of an eclipse can be advanced or delayed by up to ten hours due to the eccentricity of the Moon's orbit – the eclipse will be early when the Moon is going from perigee to apogee, and late when it is going

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Solar eclipses around the present time. Series of semesters, heptons, and octons are easily visible. Note that the hepton series tend to remain total or annular, because the interval is near a whole number of anomalistic months, whereas in the octon series the type of eclipse changes over a cycle of

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Equals 58 inex plus 7 saros (one saros more than a Heliotrope), which is 95 Metonic cycles, or 95 saros plus 95 lunar years, or 100 saros plus 25 lunations, or a bit over 1805 years, always occurring on the same node, and revealing the Metonic cycle's mismatch from 19 years as 95 repeats accumulates

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7 eclipse seasons, and one of the less noteworthy eclipse cycles. Each eclipse in a hepton is followed by an eclipse 3 saros series before, always occurring at alternating nodes. It is equal to 41 synodic months. The interval is nearly a whole number of weeks (172.96), so each eclipse is followed by

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Half a lunar year. Eclipses will repeat exactly one semester apart at alternating nodes in a cycle that lasts for 8 or 9 eclipses. Because it is close to a half integer of anomalistic, draconic months, and tropical years, each solar eclipse will (usually) alternate between hemispheres each semester,

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If the Earth had a perfectly circular orbit centered around the Sun, and the Moon's orbit was also perfectly circular and centered around the Earth, and both orbits were coplanar (on the same plane) with each other, then two eclipses would happen every lunar month (29.53 days). A lunar eclipse would

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If a solar eclipse occurs at one new moon, which must be close to a node, then at the next full moon the Moon is already more than 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, so it is less likely that there will

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Both the angular size of the Moon in the sky at eclipses at the ascending node and the size of the Sun at those eclipses vary in a sort of sine wave. The sizes at the descending node vary in the same way, but 180° out of phase. The Moon is large at an ascending-node eclipse when its perigee is near

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The "Panorama" can also be related to where on the Earth the shadow of the Moon falls at the central time of the eclipse. If this "maximum eclipse" for a given eclipse is at a particular location, eclipses three saros later will be at a similar latitude (because the saros is close to a whole number

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is near zero (around inex series 50 at present). F decreases as we go away from this curve towards higher inex series, and increases on the other side, by about 0.5° per inex series. When the inex value is too far from the centre, the eclipses disappear because the Moon is too far north or south of

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These four arguments are basically linear functions of time but with slowly varying higher-order terms. A diagram of inex and saros indices such as the "Panorama" shown above is like a map, and we can consider the values of the Delaunay arguments on it. The mean elongation, D, goes through 360° 223

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One can skew the graph of inex versus saros for solar or lunar eclipses so that the x axis shows the time of year. (An eclipse which is two saros series and one inex series later than another will be only 1.8 days later in the year in the Gregorian calendar.) This shows the 586-year oscillations as

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Equals 58 inex plus 9 saros (one saros more than an Immobilis), therefore 1841 years 1 month or 22771 lunations, which is presently about an hour more than a whole number of weeks, allowing eclipses to occur the same day of the week. Because of the slowing of the Earth's rotation, the length of the

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constructed it to closely match an integer number of synodic and anomalistic months, years (345), and days. Because of it being close to a whole number of both anomalistic months and anomalistic years, its length is always within about an hour of 126007 days and half an hour. (See graphs lower down

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A triple inex, with the advantage that it has nearly an integer number of anomalistic months, which makes the circumstances between two eclipses one Triad apart very similar, but at the opposite latitude. Almost exactly 87 calendar years minus 2 months. The triad means that every third saros series

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of dates of solar eclipses in 21st century. The dates form 35 clusters. Each cluster contains eclipses separated by Metonic cycles of 19 years. Each series contains four or five eclipses, and 46 or 65 or 84 years after the first one another series starts about a day and a half later in the (Julian)

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An eclipse "cycle" of at most 3 eclipses, but in fact meant as a period separating a pair of similar eclipses with opposite gamma values. Adding 1 lunation (for 112 synodic months) gives another period with the same property, the other half of a saros. The two surround a sar (half-saros). Named for

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6 eclipse seasons, and a fairly short eclipse cycle. Each eclipse in a hexon series (except the last) is followed by an eclipse whose saros series number is 8 lower, always occurring at the same node. It is equal to 35 synodic months, 1 less than 3 lunar years (36 synodic months). At any given time

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5.868831091 = Quotients Convergents SM/half EY decimal SM/full EY named cycle 5; 5/1 = 5 pentalunex 1 6/1 = 6 12/1 semester 6 41/7 = 5.857142857 hepton 1 47/8 =

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The lengths of the synodic, draconic, and anomalistic months, the length of the day, and the length of the anomalistic year are all slowly changing. The synodic and draconic months, the day, and the anomalistic year (at least at present) are getting longer, whereas the anomalistic month is getting

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The waviness seen in the graph is also due to the Sun's anomaly. In April the Sun is further east than if its longitude progressed evenly, and in October it is further west, and this means that in April the Moon catches up with the Sun relatively late, and in October relatively early. This in turn

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Time of year for solar eclipses between saros 90 and saros 210, but showing only the saros series whose index is divisible by 3. The time of year is related to the anomaly of the Sun. Two of the four eclipses of the year 2000 are indicated, with a line between them which shows (almost exactly) the

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which progresses smoothly from partial eclipses into total or annular eclipses and back into partials. Each graph row represents an inex series. Since a saros, of 223 synodic months, is slightly less than a whole number of draconic months, the early eclipses in a saros series (in the upper part of

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Eclipses between AD 1600 and 2400. One can fairly easily see six of the eclipse cycles mentioned in this article. During some periods there are (non-consecutive) eclipses seven lunar months apart (a change of 69 in inex index). The two eclipses are seen both near the Arctic Circle or both near the

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Equals 110 inex plus 7 saros, therefore 3310 years and about 2 months, always occurring on the same node. It is useful for calculating the timing and magnitudes of eclipses as they are approximately an integer number of draconic and anomalistic months and weeks apart (172,715.97 weeks), leading to

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cause the period for occurrence of tetrads to be variable, and it is currently about 565 years; see Meeus III (2004) for a detailed discussion. The Tetradia period also shows up in the distance between eras in which there are pairs of (non-consecutive) eclipses seven months apart, or eras in which

3504:

Equals 3 inex plus 6 saros, lasting 195 Julian years and 4 days or 2412 lunations, equaling 201 lunar years, always occurring at alternating nodes. Just two days over a whole number of anomalistic years and near a whole number of anomalistic months, which means the interval between two eclipses is

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Equals 3 inex plus 3 saros, which is 140 years 11 months or 1743 lunations, always occurring on alternating nodes. The tritrix is very close to a whole number of anomalistic months ((1867.9970) and close to a whole number of anomalistic years, which means the interval between two eclipses is quite

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Note that there are three main moving points: the Sun, the Moon, and the (ascending) node; and that there are three main periods, when each of the three possible pairs of moving points meet one another: the synodic month when the Moon returns to the Sun, the draconic month when the Moon returns to

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The upshot is that the properties vary slowly over the diagram in any of the three sets of saros series. The accompanying graph shows just the saros series that have saros index modulo 3 equal to zero. The blue areas are where the mean anomaly of the Moon is near 0°, meaning that the Moon is near

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Eclipses that occur when the earth is near perihelion (sun anomaly near zero) are in saros series in which the gamma value changes little every 18.03 years. The reason for this is that from one eclipse to the next in the saros series, the day in the year advances by about 11 days, but the Sun's

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by only 1.3 days (1.8 days over 65 average Gregorian years). Name suggested by Karl Palmen in that 2 saros are added over an inex. A period of three Unidos (195 years, a "Trihex") is quite close to both a whole number of anomalistic years and a whole number of anomalistic months, which means the

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Very convenient in the classification of eclipse cycles. One inex after an eclipse, another eclipse takes place at the opposite latitude. Inex series, after a sputtering beginning, go on for many thousands of years giving eclipses every 29 years minus 20 days, or 21 days if the last year has 366

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but not given this name), and one of the best for predicting eclipses, in which 223 synodic months equal 242 draconic months with an error of only 51 minutes. It is also very close to 239 anomalistic months, which makes the circumstances between two eclipses one saros apart very similar. Being a

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The number of days given is the average. The actual number of days and fractions of days between two eclipses varies because of the variation in the speed of the Moon and of the Sun in the sky. The variation is less if the number of anomalistic months is near a whole number, and if the number of

4317:

The fact that the day is getting longer means there are more revolutions of the Earth since some point in the past than what one might calculate from the time and date, and fewer from now to some future time. This effect means eclipses occur earlier in the day or calendar, going in the opposite

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Julian years. The inex cycle is the cycle that produces the highest number of eclipses while it lasts. Inex series 30 first produced a solar eclipse in saros series -245 (in 9435 BC), has been producing eclipses every 29 years since saros series -197 (in 8045 BC), and will continue long past AD

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The properties of eclipses, such as the timing, the distance or size of the Moon and Sun, or the distance the Moon passes north or south of the line between the Sun and the Earth, depend on the details of the orbits of the Moon and the Earth. There exist formulae for calculating the longitude,

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Therefore, at most new moons, Earth passes too far north or south of the lunar shadow, and at most full moons, the Moon misses Earth's shadow. Also, at most solar eclipses, the apparent angular diameter of the Moon is insufficient to fully occlude the solar disc, unless the Moon is around its

3994:

occurs too far to the east of the node, but more eclipses occur at high inex values in April because syzygy is not so far west of the node. The opposite applies to October. It also means that in April ascending-node solar eclipses will cast their shadow further north (such as the

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solar eclipse of 10 May, 2013, or 28.9444 Julian years from the Julian date of 27 April, 2013. Once such an eclipse has been found, others around the same time can be found using the short cycles. For lunar eclipses, the anchor dates May 4, 2004 or Julian April 21 may be used.

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third of a day more than a whole number of days, each succeeding eclipse is centered about 120° further west over the Earth. If the Earth's orbit around the sun were circular, the saros cycle would be very close to a periodic orbit that would repeat exactly every 223 months.ὤ

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The shortest cycle that gives eclipses on the same date (more or less) in both the Gregorian and in a 12-month lunar calendar, because it is almost exactly a whole number of Gregorian years (391.00029) as well as being exactly 403 12-month lunar years. Discovered by

3704:

are all similar, being equal to 52 inex periods plus up to two triads and various numbers of saros periods. This means they all have a near-whole number of anomalistic months. They range from 1505 to 1841 years, and each series lasts for many thousands of years.

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month, giving a series of eclipses one square year apart a life expectancy of thousands of years. Many eclipses of our day belong to "square year" series or selebit series that have been going for over 13,000 years, and many will continue for over 13,000 years.

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will be followed by a very central total lunar eclipse. A solar eclipse where the Moon's penumbra just barely grazes the southern limb of Earth will be followed half a saros later by a lunar eclipse where the Moon just grazes the southern limb of the Earth's

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For two solar eclipses to be almost identical, the geometric alignment of the Earth, Moon and Sun, as well as some parameters of the lunar orbit should be the same. The following parameters and criteria must be repeated for the repetition of a solar eclipse:

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series. The change in gamma is larger when Earth is near its aphelion (June to July) than when it is near perihelion (December to January). When the Earth is near its average distance (March to April or September to October), the change in gamma is average.

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As an example, from the solar eclipse of April, 1688 BC, to that of April, AD 1623, is 110 inex plus 7 saros (equivalent to a "Palaea-Horologia" plus a "tritrix", 3310.09 Julian years). According to the table above, the Delaunay arguments should change by:

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eclipses actually occur every three years on average, because there are also the ones at the descending node that occur in between the ones at the ascending node. At lunar eclipses the size of the Moon is 180° out of phase with its size at solar eclipses.

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means that the argument of latitude at the actual time of the eclipse will be raised higher in April and lowered in October. Eclipses (either partial or not) with low inex index (near the upper edge in the "Panorama" graph) fail to occur in April because

3757:

Equals 58 inex plus 6 saros, one saros more than a Proxima, therefore about 1787 years. Useful for calculating the longitudinal positions of the central lines of eclipses on Earth's surface near an integer number of years (1786.954 Julian years, 1786.991

3191:

of the Metonic cycle, and a fairly decent short eclipse cycle, but poor in anomalistic returns. Each octon in a series is 2 saros apart, always occurring at the same node. It is equal to 47 synodic months. At any given time there are eight octon series

3775:

Equals 58 inex plus 8 saros (one saros more than a Megalosaros), which is exactly 1879 lunar years. Always occurs on the same node. Very close to a whole number of anomalistic months, although 43 inex minus 5 saros (14279 months, 1154.5 years) is even

3495:

in his Tabularum Astronomicarum in 1687. It equals 6 inex periods, which is 173 years and around 8 months, or 2148 lunations, equaling 179 lunar years, always occurring on the same node at nearly an integer number of anomalistic months, as it equals 2

378:

For the repetition of a lunar eclipse, the geometric alignment of the Moon, Earth and Sun, as well as some parameters of the lunar orbit should be repeated. The following parameters and criteria must be repeated for the repetition of a lunar eclipse:

3290:

days. It is also 5 "octon" periods and close to 20 eclipse years, so it yields a short series of four or five eclipses on the same calendar date or on two calendar dates. It is equivalent to 110 "hollow months" of 29 days and 125 "full months" of 30

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there will be another eclipse: the Sun and Moon will have moved about 15° with respect to the nodes (the Moon being opposite to where it was the previous time), but the luminaries may still be within bounds to make an eclipse. For example, penumbral

3849:

When this is greater than 1, the integer part gives the year AD, but when it is negative the year BC is obtained by taking the integer part and adding 2. For instance, the eclipse in saros series 0 and inex series 0 was in the middle of 2884 BC.

642:

Since there may be an eclipse every half draconic month, we need to find approximations for the number of half draconic months per synodic month: so the target ratio to approximate is: SM / (DM/2) = 29.530588853 / (27.212220817/2) = 2.170391682

3748:

Equals 58 inex plus 5 saros, therefore a bit less than 1769 years, always occurring at the same node and toward an integer number of draconic and anomalistic months and weeks, making the circumstances of each eclipse a proxima apart similar in

3696:

Equals 12 "Short Callippic Periods" (each a month shorter than a Callipic cycle), or 12 Callippic cycles minus 1 lunar year, so therefore a bit over 911 years or 11268 lunations, which is 939 lunar years. First mentioned by Alexander Pogo in

3909:(see above) are more common at present than at other periods. Tetrads occur when four lunar eclipses occur at four lunar inex numbers, decreseing by 8 (that is, a semester apart), which are in the range giving fairly central eclipses (small 3299:

Equal to a whole number of weeks plus a hundredth of a day, so consecutive eclipses of the cycle are usually on the same day of the week. Each eclipse in this period is a member of a preceding saros series, always occurring on alternating

3917:), the inex numbers were 52, 44, 36, and 28, and the eclipses occurred in April and late September-early October. Normally the absolute value of gamma decreases and then increases, but because in April the Sun is further east than its 600: 4570:

2.170391682 = 2 + 0.170391682 ; 1/0.170391682 = 5 + 0.868831085... ; 1/0.868831085... = 1 +5097171...6237575... ; etc. ; Evaluating this 4th continued fraction: 1/6 + 1 = 7/6; 6/7 + 5 = 41/7 ; 7/41 + 2 =

3526:

lasts about 3000 years. All or most are on the same day of the week, since the interval is only about an hour less than a whole number of weeks and the length is fairly constant becauses the anomaly of the moon is almost constant.

3678:

found a period of 586 years. This happens to be an eclipse cycle; see Meeus (1997). The phenomenon is related to the elliptical orbit of the Earth, as explained below. Recently Tudor Hughes explained that secular changes in the

3102:, these values are different going from quarter moon to quarter moon. The shortest lunar fortnight between first and last quarter moons lasts only about 13 days and 12 hours, while the longest lasts about 16 days and 2 hours.) 4018:

Length of Hipparchic intervals ending in 2001-2050 on the same scale as above. The interval is quite constant because it is close to a whole number of anomalistic months (4573.002) and to a whole number of anomalistic years

653:

5 11/5 = 2.2 pentalunex 1 13/6 = 2.166666667 semester 6 89/41 = 2.170731707 hepton 1 102/47 = 2.170212766 octon 1 191/88 = 2.170454545

3576:

Known for returning toward the same day of the week and Gregorian calendar date, as approximately an integer number of years, months, and weeks, are achieved, usually moving only a quarter day later in the Gregorian

3534:

The seventh convergent in the continued fractions development between the ratio of the eclipse year and synodic month, if this ratio is approximated as between 2.17039173 and 2.17039179. Discussed by James Utting in

272:

later the new moon will fall close to the opposite node. In that time (half an eclipse year) the Sun will have moved to the opposite node too, so the circumstances will again be suitable for one or more eclipses.

4334:

a synodic month to the length of a draconic month is getting smaller. Although both are getting longer, the draconic month is doing so more quickly because the rate at which the node moves west is decreasing.

3458:

Named after Karl Palmen in that a saros is subtracted from 4 inex. Each eclipse is followed by an eclipse 4 saros series later, always occurring at the same node. It equals 97 years 9 months or 1209 lunations.

3119:

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

3728:

Equals 55 inex plus 4 saros, one saros more than a Palaea-Horologia, therefore over 1664 years, near an integer number of anomalistic months, therefore having similar properties, but at the opposite latitude.

4313:

Note that in this example, in terms of anomaly (position with respect to perigee) the moon returns to within 1% of an orbit (about 3.4°), rather than 3.2% as predicted using today's values of month lengths.

3224:

Includes an odd number of fortnights (223). As a result, eclipses alternate between lunar and solar with each cycle, occurring at the same node and with similar characteristics. A solar eclipse with small

3202:

Includes a half draconic month, so occurs at alternating nodes and alternates between hemispheres. Each consecutive eclipse is a member of preceding saros series from the one before. Equal to nearly ten

4168: 632:: the numerators and denominators then give the multiples of the two periods – draconic and synodic months – that (approximately) span the same amount of time, representing an eclipse cycle. 4322:. It cannot be calculated exactly but amounts to around 50 minutes per millennium squared. In our example above, this means that although the eclipse in 1688 BC was centred on March 16 at 00:15:31 in 4162:

The Sun is large at an ascending-node eclipse when its perigee (the direction toward the Sun when it is closest to the Earth) is near the ascending node, so the period for the size of the Sun is

3720:

Equals 55 inex plus 3 saros, which is over 1646 years. Useful for calculating the timing of eclipses. Close to a whole number of anomalistic months. A series lasts tens of thousands of years.

3098:. The shortest lunar fortnight between a new moon and a full moon lasts only about 13 days and 21.5 hours, while the longest such lunar fortnight lasts about 15 days and 14.5 hours. (Due to 464:

when the Sun passes through the nodal eclipse zones. These time periods are called eclipse seasons. Either two or three eclipses happen each eclipse season. During the eclipse season, the

4047: 27: 3712:

Equals 52 inex, therefore 1505 years and between 1 and 2 months. Eclipses in this period occur at a similar distance as nearly an integer number of anomalistic months are achieved.

3308:

This eclipse cycle is just over 36 tzolk'ins, lasting 317 lunations. Each eclipse in this period is followed by an eclipse 4 saros series' later, always occurring on the same node.

708:

Meeus (1997) Ch.9. More details are given in the comments below, and several notable cycles have their own pages. Many other cycles have been noted, some of which have been named.

3946:

latitude, and distance of the Moon and of the Sun using sine and cosine series. The arguments of the sine and cosine functions depend on only four values, the Delaunay arguments:

3688:

there are more pairs of eclipses one month apart, or eras in which there are saros series in which gamma is fairly constant for many decades, or eras with more low-gamma eclipses.

608:

Eclipse cycles have a period in which a certain number of synodic months closely equals an integer or half-integer number of draconic months: one such period after an eclipse, a

4146:(Note that a plus sign is used because the perigee moves eastward whereas the node moves westward.) A maximum of this is in 2024 (September), explaining why the ascending-node 135:): so as viewed from Earth, when the Moon appears nearest the Sun (at new moon) or furthest from it (at full moon), the three bodies are usually not exactly on the same line. 221:

of their orbit around the Sun: the Moon has to make up for this in order to come again into conjunction or opposition with the Sun. Secondly, the orbital nodes of the Moon

4848: 628:, and an eclipse can occur again. However, the synodic and draconic months are incommensurate: their ratio is not an integer number. We need to approximate this ratio by 3171:

another that is usually on the same day of the week (moving backwards irregularly by an average of a quarter day). At any given time there are seven hepton series active.

3740:. George van den Bergh first mentioned a period of 55 inex plus 5 saros (over 1682 years) before mentioning a period of 95 inex plus 11 saros (over 2948 years) in 1951. 10149: 3413:

days. In the table, taken as 940 synodic months, equivalent to 441 hollow months and 499 full months. This cycle, though useful for example in the calculation of the

3128:

5 synodic months. Successive solar or lunar eclipses may occur 1, 5 or 6 synodic months apart. When two solar eclipses are one month apart, one will be seen near the

304:

a particular solar eclipse in every 54 years 34 days period. Total solar eclipses are rare events, although they occur somewhere on Earth every 18 months on average.

3479:

constant. Two tritrix minus a saros (3263 lunations) is even closer to a whole number of anomaalistic months (3497.0018), being exactly thirteen seventeenths of the

9065: 536: 177:. Of course, to produce an eclipse, the Sun must also be around a node at that time – the same node for a solar eclipse or the opposite node for a lunar eclipse. 243:

days. Likewise, as seen from the Earth, the Sun passes both nodes as it moves along its ecliptic path. The period for the Sun to return to a node is called the

3913:), and furthermore the eclipses take place around halfway between the Earth's perihelion and aphelion. For example, in the tetrad of 2014-2015 (the so-called 3666:

noticed that there are eras when such tetrads occur comparatively frequently, interrupted by eras when they are rare. This variation takes about 6 centuries.

5491: 5456: 3618:. George van den Bergh called it the "Long Babylonian Period" or the "Old Babylonian Period", but there is no evidence that the Babylonians were aware of it. 4909: 3517:

in 1765. (The "Lambert I cycle is what we also call the inex.) Very close to a half-integer number of draconic months. It equals about 278 and a half years.

3470:, so that eclipses synchronize with the timing of Mercury's position in its orbit during each period, equaling 112 years minus one week or 1385 lunations. 5471: 3216:

William B. Hibbard who identified it in 1956. One lunar year less than a Hibbardina, 99 lunations, is only about a day and a half more than eight years.

4041:

the ascending node, so the period for the size of the Moon is the time it takes for the angle between the node and the perigee to go through 360°, or

7321: 6541: 4603: 704:

This table summarizes the characteristics of various eclipse cycles, and can be computed from the numerical results of the preceding paragraphs;

5541: 3634:(521 anomalistic years minus 5 days), and weeks (27185 weeks plus 0.1 day), leading to eclipses on the same day of the Julian calendar and week. 5451: 4920:

S. Newcomb (1882): On the recurrence of solar eclipses. Astron.Pap.Am.Eph. vol. I pt. I . Bureau of Navigation, Navy Dept., Washington 1882

3793:

Equals 76 inex plus 9 saros, therefore 2362 years and about a month, always occurring on the same node. Mentioned by A. Mackay in the 1800's.

3767:

the mismatch to about three years. The extra 25 lunations are needed because 100 saros cycles exceeds the life expectancy of a saros series.

4326:, it actually occurred before midnight and therefore on March 15 (using time based on the location of present-day Greenwich, and using the 3886:

number is 12 higher and whose inex number is 43 lower. As with solar eclipses, the Gregorian year of a lunar eclipse can be calculated as:

211:. The main reason is that during the time that the Moon has completed an orbit around the Earth, the Earth (and Moon) have completed about 649:

2.170391682 = : Quotients Convergents half DM/SM decimal named cycle (if any) 2; 2/1 = 2

5486: 200:

An eclipse does not occur every month, because one month after an eclipse the relative geometry of the Sun, Moon, and Earth has changed.

3238:

Equal to an inex minus a saros. A triple tritos is close to an integer number of anomalistic months and so will have similar properties.

8380: 8370: 8365: 5481: 5476: 5466: 5140: 5135: 5130: 5125: 5120: 5115: 5110: 639:: this arithmetical technique provides a series of progressively better approximations of any real numeric value by proper fractions. 5461: 5102: 4261:{\displaystyle {\frac {1}{1/{\text{period of node}}-1/{\text{period of perigee}}}}={\frac {1}{1/18.60+1/41{\text{ million}}}}=18.60} 3276:

Nearly 6940 days, but as an eclipse cycle can be taken as 235 synodic months. This is just an hour and a half less than 19 years of

8304: 5027: 4935:

G. van den Bergh (1955): Periodicity and Variation of Solar (and Lunar) Eclipses, 2 vols. Tjeenk Willink & Zn NV, Haarlem 1955

3360:

mentions it after discussing what we now call the saros, and says that it is called the exeligmos (ἐξελιγμός, meaning "unrolling").

10251: 8395: 8339: 5161: 4745: 3658:

Sometimes 4 total lunar eclipses occur in a row with intervals of 6 lunations (one semester) between them, and this is called a

4585: 162:, i.e. nearer Earth and apparently larger than average. In any case, the alignment must be almost perfect to cause an eclipse. 4010:

Length of "semester" interval. The length varies considerably, depending on the lunar and solar anomalies of the two eclipses.

4496: 3153:

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

4729: 530:

of the synodic and draconic months (i.e. the period of the difference between the synodic and draconic months); in formula:

197:, a one- or two-month period that happens twice a year, around the time when the Sun is near the nodes of the Moon's orbit. 693:

11 4161/709 = 5.868829337 selebit 1 4519/770 = 5.868831169 4519/385 square year ...

189:

A symbolic orbital diagram from the view of the Earth at the center, showing the Moon's two nodes where eclipses can occur.

8729: 4929:

A. Pannekoek (1951): Periodicities in Lunar Eclipses. Proc. Kon. Ned. Acad. Wetensch. Ser.B vol.54 pp. 30..41 (1951)

3853:

A "panorama" of solar eclipses arranged by saros and inex has been produced by Luca Quaglia and John Tilley showing 61775

9636: 8105: 7855: 7825: 7782: 7752: 7572: 7512: 7467: 7397: 7140: 7070: 6967: 6907: 6902: 6842: 6520: 6485: 6420: 6415: 6350: 6032: 5962: 5932: 5857: 5852: 5772: 5147: 5097: 146:

diameter of the Sun (32′ 2″), the Moon as viewed from Earth's surface directly below the Moon (31′ 37″), and

3207:. Every third tzolkinex in a series is near an integer number of anomalistic months and so will have similar properties. 8080: 8035: 8030: 7990: 7985: 7965: 7955: 7935: 7910: 7905: 7860: 7787: 7772: 7732: 7712: 7697: 7687: 7662: 7622: 7607: 7547: 7532: 7497: 7457: 7447: 7427: 7402: 7377: 7362: 7342: 7295: 7290: 7260: 7245: 7225: 7185: 7180: 7120: 7115: 7040: 7012: 7007: 7002: 6947: 6942: 6862: 6827: 6792: 6787: 6772: 6752: 6712: 6707: 6692: 6647: 6637: 6622: 6617: 6582: 6577: 6557: 6525: 6465: 6455: 6395: 6365: 6335: 6295: 6290: 6280: 6265: 6260: 6222: 6192: 6162: 6142: 6092: 6087: 6072: 6067: 6022: 6002: 5967: 5902: 5797: 5777: 5742: 5722: 5692: 5687: 5657: 5647: 5627: 92:

with the Sun, the Moon may pass in front of the Sun as viewed from a narrow region on the surface of Earth and cause a

4796: 225:

westward in ecliptic longitude, completing a full circle in about 18.60 years, so a draconic month is shorter than a

10184: 8204: 8110: 8095: 8070: 8055: 8015: 8005: 7970: 7940: 7890: 7885: 7875: 7850: 7845: 7830: 7812: 7777: 7742: 7717: 7707: 7647: 7632: 7592: 7577: 7562: 7542: 7482: 7472: 7407: 7382: 7357: 7300: 7275: 7265: 7235: 7230: 7210: 7175: 7170: 7165: 7150: 7125: 7105: 7100: 7050: 7045: 7027: 6982: 6977: 6972: 6917: 6912: 6892: 6887: 6852: 6822: 6747: 6717: 6682: 6642: 6612: 6567: 6500: 6495: 6430: 6400: 6330: 6227: 6197: 6157: 6132: 6127: 6062: 6057: 6027: 6007: 5992: 5987: 5957: 5942: 5937: 5922: 5892: 5867: 5862: 5832: 5822: 5787: 5757: 5617: 5607: 4971: 4957: 4943: 4135:{\displaystyle {\frac {1}{1/{\text{period of node}}+1/{\text{period of perigee}}}}={\frac {1}{1/18.60+1/8.85}}=5.997} 3736:

One saros more than a Hybridia. The name for eclipse cycles useful for calculating the magnitudes of eclipses in the

4309:

40940.998 synodic months, 44429.006 draconic months, 43876.990 anomalistic months, 3310.007 anomalistic years, resp.

4289:

the mean anomaly of the Moon is increased by 1.1° per millennium squared, corresponding to 0.0030 anomalistic months

4286:

the mean argument of latitude is decreased by 0.16° per millennium squared, corresponding to 0.00045 draconic months

8209: 8050: 8045: 7920: 7870: 7802: 7797: 7757: 7682: 7642: 7617: 7517: 7507: 7477: 7442: 7392: 7372: 7337: 7200: 7110: 7085: 7080: 7035: 6962: 6937: 6922: 6882: 6877: 6857: 6847: 6812: 6782: 6777: 6702: 6697: 6677: 6627: 6490: 6480: 6460: 6435: 6390: 6385: 6360: 6320: 6315: 6245: 6212: 6147: 6097: 5997: 5927: 5897: 5847: 5827: 5792: 5782: 5737: 5732: 5727: 5677: 5672: 5587: 5582: 5567: 4151: 108:

is visible from the night half of Earth. The conjunction and opposition of the Moon together have a special name:

8075: 8010: 7995: 7980: 7960: 7930: 7915: 7820: 7807: 7747: 7737: 7702: 7602: 7567: 7557: 7537: 7502: 7462: 7310: 7305: 7280: 7270: 7240: 7205: 7145: 6997: 6932: 6872: 6867: 6837: 6802: 6797: 6762: 6737: 6732: 6722: 6662: 6657: 6592: 6587: 6475: 6425: 6410: 6380: 6375: 6345: 6325: 6305: 6300: 6275: 6270: 6250: 6232: 6202: 6177: 6172: 6107: 6102: 5887: 5817: 5812: 5752: 5747: 5697: 5682: 5667: 5652: 5557: 4716: 4692: 3925:

that are now producing tetrads will again be halfway between Earth's perihelion and aphelion in about 586 years.

715:

Any eclipse cycle, and indeed the interval between any two eclipses, can be expressed as a combination of saros (

4760:"Do periodic consolidations of Pacific countercurrents trigger global cooling by equatorially symmetric La Niña" 4638:"Do periodic consolidations of Pacific countercurrents trigger global cooling by equatorially symmetric La Niña" 4301:

40941 synodic months, 44429.003 draconic months, 43877.032 anomalistic months, 3310.007 anomalistic years, resp.

8329: 8100: 8090: 8085: 8040: 7950: 7925: 7900: 7895: 7865: 7840: 7835: 7792: 7727: 7677: 7672: 7657: 7652: 7637: 7612: 7582: 7552: 7527: 7492: 7487: 7452: 7437: 7432: 7417: 7412: 7387: 7367: 7347: 7285: 7255: 7220: 7215: 7195: 7190: 7155: 7130: 7095: 7075: 7022: 7017: 6952: 6817: 6807: 6767: 6742: 6727: 6687: 6667: 6652: 6632: 6607: 6602: 6597: 6572: 6530: 6470: 6355: 6310: 6285: 6255: 6237: 6207: 6187: 6182: 6167: 6152: 6137: 6122: 6117: 6112: 6082: 6077: 6052: 6047: 6042: 6037: 6012: 5977: 5972: 5907: 5872: 5802: 5707: 5702: 5662: 5642: 5632: 5622: 5612: 5577: 5572: 4147: 3996: 3585:

Equal to six Unidos or two Trihex. Useful for giving accurate calculations of the timing of lunisolar syzygies.

3136:. When they are five months apart, they are both seen near the Arctic Circle or both near the Antarctic Circle. 3091: 4798:

The Strategic Role of Perigean Spring Tides in Nautical History and North American Coastal Flooding, 1635-1976

10108: 8334: 8065: 8025: 8020: 8000: 7975: 7945: 7880: 7767: 7762: 7722: 7692: 7667: 7627: 7587: 7522: 7422: 7250: 7160: 7135: 7090: 7060: 7055: 6992: 6987: 6957: 6927: 6897: 6832: 6672: 6562: 6515: 6510: 6505: 6445: 6440: 6405: 6370: 6340: 6217: 6017: 5982: 5952: 5947: 5917: 5912: 5877: 5842: 5837: 5767: 5762: 5712: 5637: 5602: 5592: 4318:

direction relative to the effect of the lengthening synodic month already mentioned. This effect is known as

3670:(1951) offered an explanation for this phenomenon and found a period of 591 years. Van den Bergh (1954) from 3976: 9935: 9865: 9780: 9755: 9710: 9685: 9610: 9515: 9505: 9430: 9387: 9302: 9297: 9222: 9217: 9142: 9102: 9087: 8989: 8961: 8911: 8297: 8060: 7597: 7352: 7065: 6757: 6450: 5882: 5807: 5717: 5597: 5562: 5020: 4759: 4637: 10093: 10078: 10063: 10038: 10018: 9993: 9978: 9960: 9940: 9910: 9895: 9885: 9870: 9845: 9815: 9800: 9775: 9730: 9715: 9670: 9565: 9555: 9495: 9475: 9450: 9440: 9417: 9367: 9357: 9352: 9327: 9287: 9277: 9272: 9262: 9237: 9207: 9197: 9182: 9157: 9147: 9132: 9122: 9019: 9009: 8951: 8921: 8871: 8826: 8811: 8771: 8756: 4932:

G. van den Bergh (1954): Eclipses in the second millennium B.C. Tjeenk Willink & Zn NV, Haarlem 1954

3684: 3544:

the synodic month, giving a series of eclipses one selebit apart a life expectancy of thousands of years.

408:

The Earth will be nearly the same distance from the Sun, and tilted to it in nearly the same orientation.

342:

The Earth will be nearly the same distance from the Sun, and tilted to it in nearly the same orientation.

10246: 10131: 10121: 10116: 10048: 10023: 10008: 9945: 9920: 9850: 9830: 9825: 9760: 9740: 9705: 9690: 9665: 9600: 9550: 9540: 9530: 9520: 9485: 9470: 9460: 9402: 9392: 9377: 9337: 9317: 9307: 9257: 9247: 9227: 9192: 9177: 9167: 9117: 9107: 9039: 9024: 8974: 8956: 8906: 8131: 3599: 207:, is less than the time it takes for the Moon to return to the same ecliptic longitude as the Sun: the 151: 4292:

the mean anomaly of the sun is decreased by 0.002° per millennium squared, which is fairly negligible.

3646: 696:

Each of these is an eclipse cycle. Less accurate cycles may be constructed by combinations of these.

10144: 10058: 9988: 9930: 9905: 9860: 9795: 9750: 9725: 9680: 9585: 9560: 9480: 9347: 9267: 9187: 9044: 8994: 8969: 8941: 8916: 8866: 8861: 8816: 8796: 8761: 8344: 8229: 8141: 8136: 4983: 4462: 4327: 3081:

Half a synodic month (29.53 days). When there is an eclipse, there is a fair chance that at the next

670:

11 9031/4161 = 2.170391732 selebit 1 9808/4519 = 2.170391679 square year ...

712:

anomalistic years is near a whole number. (See graphs lower down of semester and Hipparchic cycle.)

10136: 10126: 10088: 10083: 10053: 10043: 10013: 9970: 9925: 9890: 9855: 9820: 9785: 9745: 9700: 9675: 9660: 9655: 9545: 9510: 9500: 9465: 9455: 9435: 9425: 9382: 9372: 9342: 9292: 9252: 9212: 9172: 9162: 9137: 9097: 9077: 9054: 8936: 8891: 8886: 8846: 8841: 8791: 8786: 8746: 8741: 8156: 8151: 4036:

the anomaly is 1. On average every 3 years there is a "super moon" eclipse, with anomaly near zero.

10212: 10073: 10033: 10028: 10003: 9983: 9955: 9950: 9900: 9880: 9840: 9835: 9810: 9790: 9770: 9765: 9720: 9695: 9620: 9615: 9595: 9590: 9575: 9570: 9525: 9445: 9397: 9362: 9312: 9282: 9232: 9152: 9112: 9049: 9034: 9029: 9004: 8999: 8984: 8979: 8946: 8931: 8926: 8901: 8896: 8876: 8856: 8851: 8831: 8821: 8806: 8801: 8766: 8751: 8321: 8290: 8271: 8146: 5082: 5013: 3627: 3514: 3385: 3343:

15,000, by which time it will have produced 707 consecutive eclipses. The name was introduced by

3320: 3095: 465: 101: 89: 165:

An eclipse can occur only when the Moon is on or near the plane of Earth's orbit, i.e. when its

10098: 10068: 9998: 9965: 9915: 9875: 9805: 9735: 9625: 9605: 9580: 9535: 9490: 9412: 9407: 9332: 9322: 9242: 9202: 9127: 9092: 9082: 9014: 8881: 8836: 8781: 8776: 8126: 3595: 3087: 4819:"Numerical expressions for precession formulae and mean elements for the Moon and the planets" 4704: 3376:. With 1385 fortnights, eclipses alternate between lunar and solar in 56 years minus 3.5 days. 34:. The interval between successive eclipses in the series is one saros, approximately 18 years. 5525: 4597: 4583: 4376: 3663: 4833: 595:{\displaystyle {\mbox{EY}}={\frac {{\mbox{SM}}\times {\mbox{DM}}}{{\mbox{SM}}-{\mbox{DM}}}}} 265:

be a solar eclipse somewhere on Earth. By the next month, there will certainly be no event.

8219: 5507: 4926:

A.C.D. Crommelin (1901): The 29-year eclipse cycle. Observatory xxiv nr.310, 379, Oct-1901

4859: 4829: 4774: 4652: 4475: 3680: 3671: 3426:

will be similar (central eclipses mostly total or mostly annular for example). Solar saros

3344: 412:

These conditions are related with the three periods of the Moon's orbital motion, viz. the

4891: 4515: 4511: 3890:

year = 28.945 × number of the saros series + 18.030 × number of the inex series − 2454.564

8: 8261: 8224: 8187: 4014: 3845:

year = 28.945 × number of the saros series + 18.030 × number of the inex series − 2882.55

3492: 3257: 636: 346:

These conditions are related to the three periods of the Moon's orbital motion, viz. the

139: 41:

may occur repeatedly, separated by certain intervals of time: these intervals are called

4938:

Jean Meeus (1991): Astronomical Algorithms (1st ed.). Willmann-Bell, Richmond VA 1991;

4877: 4863: 4778: 4656: 4319: 448:

type (partial, annular, total, mixed) of an eclipse. This orbital period is called the

4531: 3991: 3906: 3838: 3659: 3082: 609: 481: 174: 109: 45:. The series of eclipses separated by a repeat of one of these intervals is called an 4527: 4154:, is near apogee and annular. Although this cycle is about a day less than six years, 10241: 5519: 5157: 4967: 4953: 4939: 4492: 4343: 3667: 3243: 3176: 1308: 1087: 663: 501: 469: 449: 429: 417: 363: 351: 282: 166: 147: 124: 57: 3999:), and descending-node eclipses further south. The opposite is the case in October. 3953:

F, the mean argument of latitude (the angle between the Moon and the ascending node)

3898: 3873: 8249: 5513: 5060: 5050: 4892:"Five Millennium Catalog of Solar Eclipses -1699 to -1600 ( 1700 BCE to 1601 BCE )" 4782: 4680: 4660: 3914: 3631: 3549: 3480: 3467: 3133: 2111: 677:

5.875 47/4 octon 1 88/15 = 5.866666667

527: 359: 222: 128: 4908:

given by calculations – see p. 59 of Schaefer, B. E. (March 1990).

4031: 10189: 8718: 8713: 8708: 8703: 8698: 8693: 8688: 8683: 8678: 8673: 8668: 8663: 8658: 8653: 8648: 8643: 8638: 8633: 8628: 8623: 8618: 8613: 8608: 8603: 8598: 8593: 8588: 8583: 8578: 8573: 8568: 8563: 8558: 8553: 8548: 8543: 8538: 8533: 8528: 8523: 8518: 8513: 8508: 8503: 8498: 8493: 8488: 8483: 8478: 8473: 8468: 8463: 8458: 8453: 8448: 8443: 8438: 8433: 8428: 8423: 8418: 8413: 8408: 8403: 8177: 5435: 5430: 5425: 5420: 5415: 5410: 5405: 5400: 5395: 5390: 5385: 5380: 5375: 5370: 5365: 5360: 5355: 5350: 5345: 5340: 5335: 5330: 5325: 5320: 5315: 5310: 5305: 5300: 5295: 5290: 5285: 5280: 5275: 5270: 5265: 5260: 5255: 5250: 5245: 5240: 5235: 5230: 5225: 5220: 5215: 5210: 5205: 5200: 5195: 5190: 5185: 5180: 5175: 5170: 5070: 3969: 3910: 3447: 3443: 3439: 3435: 3431: 3427: 3394: 3226: 1655: 1217: 629: 453: 425: 367: 31: 3937:

oscillations that go up around perihelion and down around aphelion (see graph).

3513:

An eclipse cycle in which eclipses occur in similar circumstances, according to

229:. In all, the difference in period between synodic and draconic month is nearly 203:

As seen from the Earth, the time it takes for the Moon to return to a node, the

10179: 8199: 5065: 4905: 4901: 3918: 3737: 3414: 3106: 442: 421: 355: 226: 204: 194: 113: 3857:

from 11001 BC to AD 15000 (see below). Each column of the graph is a complete

3399:

Originally defined as 4 Metonic cycles minus one day or precisely 76 years of

123:

An eclipse does not occur at every new or full moon, because the plane of the

10235: 10194: 8313: 8214: 8172: 5036: 5000: 4995: 4741: 3928: 3854: 3270: 3129: 3114: 1352: 833: 413: 347: 292: 258: 208: 105: 93: 62: 84:, and the shadow of one body projected by the Sun falls on the other. So at 10169: 8182: 5055: 4876:

Based on the length of a century increasing by 62 seconds per century (see

4787: 4665: 4323: 3830: 3820: 3811: 3369: 402: 398: 336: 332: 244: 185: 4584:

Giovanni Valsecchi, Ettore Perozzi, Archie Roy, Bonnie Steves (Mar 1993).

673:

The ratio of synodic months per half eclipse year yields the same series:

3877:

Saros and inex values for solar eclipses calculated from approximate date

3858: 3650:

Inex and saros for tetrads between AD 1000 and 2500, showing the tetradia

3204: 686: 650: 296: 117: 17: 4846: 4305:

But because of the changing lengths of these, they actually changed by:

4989: 4155: 3615: 3555: 3373: 621: 170: 3865: 3319:

days. Eighteen inex cycles (see "Basic period") are equal to 520.9996

26: 4006: 3261: 3197: 1524: 1131: 678: 655: 617: 497: 97: 3642:

Equals 18 inex plus 2 saros, therefore 557 years plus about 1 month.

3611: 3357: 3249: 3099: 625: 613: 605:

as can be checked by filling in the numerical values listed above.

269: 132: 85: 4923:

J.N. Stockwell (1901): Eclips-cycles. Astron.J. 504 , 14-Aug-1901

3956:

l, the mean anomaly of the Moon (how far the Moon is from perigee)

3950:

D, the mean elongation (angle between the Sun and Moon longitudes)

8282: 5005: 387: 321: 104:

to the Sun, the Moon may pass through the shadow of Earth, and a

69: 38: 4486: 1265: 682: 659: 391: 325: 169:

is low. This happens when the Moon is around either of the two

142:

is on average about 5° 9′, much larger than the apparent

3932:

Time of year for solar eclipses between saros 90 and saros 210

4962:

Jean Meeus (2004): Mathematical Astronomy Morsels III, Ch.21

4912:. Royal Astronomical Society Quarterly Journal, 31(1), 53–67. 3965: 3384:

Very close to 65 years. Equals 67 lunar years and exceeds 65

493: 477: 300: 159: 73: 30:

Paths of partiality, annularity, hybridity, and totality for

452:, and together with the synodic month causes the so-called " 4693:

How often does a solar eclipse happen on the March equinox?

3834: 3313: 1480: 690: 667: 77: 436: 4948:

Jean Meeus (1997): Mathematical Astronomy Morsels , Ch.9

4705:

Eminent Lives in Twentieth-century Science & Religion

473: 81: 3356:

eclipse that occurred one saros earlier. Ptolemy in the

723:) intervals. These are listed in the column "formula". 4966:(pp. 123..140). Willmann-Bell, Richmond VA 2004; 4904:

of given moments of an eclipse are different from the

3825:

Antarctic Circle. The next such period begins in 2098.

3816:

3, since the anomaly changes by around 130° each time.

3702:

The next nine cycles, Cartouche through Accuratissima,

583: 573: 564: 554: 541: 4171: 4050: 646:

The continued fractions expansion for this ratio is:

539: 4952:(pp. 49..55). Willmann-Bell, Richmond VA 1997; 4150:, is near perigee and total and the descending-node 3368:

Named for the calculation of eclipses measured with

127:

around Earth is tilted with respect to the plane of

116:

for "junction"), because of the importance of these

4487:Littmann, Mark; Fred Espenak; Ken Willcox (2008). 4260: 4134: 594: 4847:T. C. van Flandern & K. F. Pulkkinen (1979). 3959:l', the mean anomaly of the Sun (or of the Earth) 10233: 4849:"Low-precision formulae for planetary positions" 4816: 3389:interval between two eclipses is quite constant. 3806: 3248:The best known eclipse cycle (described in the 373: 307: 295:in succession, which will be either 1, 5, or 6 3802:similar eclipses in character and week timing. 689:1 358/61 = 5.868852459 716/61 685:1 223/38 = 5.868421053 223/19 681:1 135/23 = 5.869565217 635:These fractions can be found by the method of 492:These are the lengths of the various types of 8298: 5021: 518:AM = 27.55454988 days (Anomalistic month) 4757: 4635: 4602:: CS1 maint: multiple names: authors list ( 4579: 4577: 3837:series. The year of a solar eclipse (in the 3466:Equals approximately 353 synodic periods of 428:changes monotonically throughout any single 4794: 4615: 4613: 4586:"Periodic orbits close to that of the Moon" 3626:Achieves nearly an integer number (521) of 496:as discussed above (according to the lunar 8305: 8291: 5028: 5014: 4996:Eclipses, Cosmic Clockwork of the Ancients 4456: 4454: 4452: 4450: 4448: 4446: 4444: 4442: 4440: 4438: 4436: 4434: 4432: 4430: 4428: 4426: 4424: 4422: 4420: 4418: 4416: 4414: 4412: 4410: 4408: 4406: 4404: 515:DM = 27.212220817 days (Draconic month) 4786: 4664: 4574: 4402: 4400: 4398: 4396: 4394: 4392: 4390: 4388: 4386: 4384: 3940: 512:SM = 29.530588853 days (Synodic month) 193:Up to three eclipses may occur during an 4889: 4812: 4810: 4808: 4610: 4460: 4030: 4013: 4005: 3975: 3927: 3897: 3872: 3864: 3819: 3810: 3645: 3256: 521:EY = 346.620076 days (Eclipse year) 261:because of the precession of the nodes. 184: 56: 25: 4856:Astrophysical Journal Supplement Series 4631: 4629: 4627: 4625: 4480: 4362:properly, these are periods, not cycles 3829:Any eclipse can be assigned to a given 437:Eclipses would not occur in every month 10234: 4817:Jean-Louis Simon; et al. (1994). 4381: 3554:Not a long-lasting eclipse cycle, but 247:: about 346.6201 days, which is about 23:Calculation and prediction of eclipses 10221:symbol denotes next eclipse in series 8286: 5009: 4805: 4372: 4370: 4368: 3981:slope of simultaneity in this graph. 3869:Solar eclipses from –11000 to +15000. 52: 4990:Search 5,000 years worth of eclipses 4910:Lunar visibility and the crucifixion 4622: 4986:(more comprehensive than the above) 4619:See Panorama of Quaglia and Tilley. 4276: 3598:in a speculative interpretation of 666:1 777/358 = 2.170391061 662:1 484/223 = 2.170403587 658:1 293/135 = 2.170370370 487: 480:become aligned straight enough (in 173:on the ecliptic at the time of the 13: 8312: 5035: 4950:Solar Eclipses: Some Periodicities 4377:NASA Periodicity of solar eclipses 4365: 3841:) is then given approximately by: 3610:Fourteen inex plus two saros. The 3162:there are six hexon series active. 14: 10263: 10185:Eclipses in mythology and culture 8205:Eclipses in mythology and culture 4977: 4671:See especially Figures 10 and 13. 3905:This is related to the fact that 699: 10208: 10207: 9635: 9064: 8728: 8267: 8266: 8255: 8243: 8210:List of films featuring eclipses 7320: 6540: 5540: 4528:Five Millennium Catalog of Lunar 4152:solar eclipse of October 2, 2024 291:is the interval between any two 4883: 4870: 4840: 4767:Climate of the Past Discussions 4751: 4735: 4722: 4710: 4698: 4686: 4674: 4645:Climate of the Past Discussions 4564: 4555: 4463:"A Catalogue of Eclipse Cycles" 383:The Moon must be in full phase. 10252:Technical factors of astrology 4730:Saros, Inex and Eclipse cycles 4546: 4537: 4532:Solar Eclipses: -1999 to +3000 4521: 4505: 4469: 4356: 4148:solar eclipse of April 8, 2024 3997:solar eclipse of April 8, 2024 3096:lunar eclipse of June 24, 2002 3092:solar eclipse of June 10, 2002 317:The Moon must be in new phase. 276: 180: 1: 4984:A Catalogue of Eclipse Cycles 4758:John H. Duke (May 20, 2010). 4636:John H. Duke (May 20, 2010). 4534:, Fred Espenak and Jean Meeus 4489:Totality: Eclipses of the Sun 4349: 3088:lunar eclipse of May 26, 2002 394:of the Moon must be the same. 328:of the Moon must be the same. 289:periodicity of solar eclipses 5051:Baily's beads (diamond ring) 3807:Saros series and inex series 3491:A sextuple inex, adopted by 374:Repetition of lunar eclipses 308:Repetition of solar eclipses 299:. It is calculated that the 7: 4992:between 2000 BC and AD 3000 4746:Solar eclipse panaorama.xls 4681:SE Newsletter February 1999 4491:. Oxford University Press. 4337: 3090:is followed by the annular 624:of the Moon's orbit on the 620:) takes place again near a 484:) for an eclipse to occur. 10: 10268: 4826:Astronomy and Astrophysics 4590:Astronomy and Astrophysics 3895:other adjacent centuries. 500:ELP2000-85, valid for the 440: 280: 15: 10203: 10162: 10107: 9648: 9634: 9063: 8727: 8391: 8353: 8320: 8238: 8230:Solar eclipses in fiction 8165: 8119: 7319: 6539: 5539: 5500: 5444: 5156: 5090: 5081: 5043: 4552:Meeus (1991) ch. 49 p.334 4476:Solar Eclipses: 2011–2020 4328:proleptic Julian calendar 3614:attributes this cycle to 3105:For more information see 8340:Historically significant 8335:Total penumbral eclipses 3072: 245:eclipse or draconic year 16:Not to be confused with 8322:Lists of lunar eclipses 8262:Solar System portal 4834:1994A&A...282..663S 4561:Meeus (1991) form. 48.1 4543:Meeus (1991) form. 47.1 3515:Johann Heinrich Lambert 3132:and the other near the 8330:Central total eclipses 5001:The Saros and the Inex 4788:10.5194/cpd-6-905-2010 4666:10.5194/cpd-6-905-2010 4262: 4136: 4037: 4020: 4011: 3982: 3941:Properties of eclipses 3933: 3902: 3878: 3870: 3826: 3817: 3676:Canon der Finsternisse 3651: 3596:Henry Grattan Guinness 3590:Grattan Guinness cycle 3266: 2281:Grattan Guinness cycle 596: 268:However, about 5 or 6 190: 100:, when the Moon is in 88:, when the Moon is in 66: 35: 32:Solar Saros Series 136 5546:Total/hybrid eclipses 4896:NASA Eclipse Web Site 4717:29-Year-Eclipse-Cycle 4465:. Utrecht University. 4263: 4137: 4034: 4017: 4009: 3979: 3931: 3901: 3876: 3868: 3823: 3814: 3664:Giovanni Schiaparelli 3649: 3260: 597: 504:J2000.0; taken from ( 397:The longitude of the 331:The longitude of the 188: 80:are aligned with the 60: 29: 8250:Astronomy portal 8220:Magnitude of eclipse 4795:Fergus Wood (1976). 4512:Periodicity of Lunar 4273:as September, 2019. 4169: 4048: 3672:Theodor von Oppolzer 3493:Phillippe de la Hire 3455:Quarter Palmen cycle 3345:George van den Bergh 2445:tetradia (Meeus III) 1737:quarter Palmen cycle 537: 257:year shorter than a 131:around the Sun (the 8188:Eclipse photography 4864:1979ApJS...41..391V 4779:2010CliPD...6..905D 4742:Saros-Inex Panorama 4657:2010CliPD...6..905D 3550:Cycle of Hipparchus 3481:Cycle of Hipparchus 3181:8 eclipse seasons, 2112:Cycle of Hipparchus 637:continued fractions 9641:Penumbral eclipses 5526:Muhammad's eclipse 4258: 4132: 4038: 4021: 4012: 3983: 3934: 3903: 3879: 3871: 3839:Gregorian calendar 3827: 3818: 3652: 3273:or enneadecaeteris 3267: 2487:tetradia (Meeus I) 592: 587: 577: 568: 558: 545: 508:) Meeus (1991) ): 472:is low, hence the 191: 67: 53:Eclipse conditions 36: 10247:Time in astronomy 10229: 10228: 10222: 10158: 10157: 8280: 8279: 8225:Planetary transit 5551:next total/hybrid 5535: 5534: 5520:Eclipse of Thales 5508:Mursili's eclipse 5083:Lists of eclipses 4498:978-0-19-953209-4 4344:Saros (astronomy) 4250: 4247: 4208: 4205: 4204:period of perigee 4189: 4124: 4087: 4084: 4083:period of perigee 4068: 3668:Antonie Pannekoek 3632:anomalistic years 3070: 3069: 590: 586: 576: 567: 557: 544: 450:anomalistic month 418:anomalistic month 405:must be the same. 386:The longitude of 352:anomalistic month 339:must be the same. 320:The longitude of 283:Saros (astronomy) 167:ecliptic latitude 10259: 10220: 10219: 10211: 10210: 10143: 9977: 9646: 9645: 9639: 9424: 9068: 8968: 8734:Partial eclipses 8732: 8307: 8300: 8293: 8284: 8283: 8270: 8269: 8260: 8259: 8258: 8248: 8247: 8246: 7819: 7330: 7326:Partial eclipses 7324: 7034: 6550: 6546:Annular eclipses 6544: 6244: 5550: 5544: 5514:Assyrian eclipse 5088: 5087: 5061:Solar prominence 5030: 5023: 5016: 5007: 5006: 4913: 4899: 4887: 4881: 4878:ΔT (timekeeping) 4874: 4868: 4867: 4853: 4844: 4838: 4837: 4823: 4814: 4803: 4802: 4792: 4790: 4764: 4755: 4749: 4739: 4733: 4726: 4720: 4714: 4708: 4702: 4696: 4690: 4684: 4678: 4672: 4670: 4668: 4642: 4633: 4620: 4617: 4608: 4607: 4601: 4593: 4581: 4572: 4568: 4562: 4559: 4553: 4550: 4544: 4541: 4535: 4525: 4519: 4509: 4503: 4502: 4484: 4478: 4473: 4467: 4466: 4458: 4379: 4374: 4363: 4360: 4277:Long-term trends 4267: 4265: 4264: 4259: 4251: 4249: 4248: 4245: 4240: 4226: 4214: 4209: 4207: 4206: 4203: 4201: 4190: 4187: 4185: 4173: 4141: 4139: 4138: 4133: 4125: 4123: 4119: 4105: 4093: 4088: 4086: 4085: 4082: 4080: 4069: 4066: 4064: 4052: 3915:Four Blood Moons 3717:Palaea-Horologia 3510:Lambert II cycle 3488:de la Hire cycle 3412: 3411: 3407: 3404: 3341: 3339: 3338: 3335: 3332: 3328: 3289: 3288: 3284: 3281: 3221:Sar (half saros) 3190: 3189: 3185: 3134:Antarctic Circle 2609:Palaea-Horologia 1943:Lambert II cycle 1863:de la Hire cycle 1579: 1578: 1574: 1230: 1229: 1225: 1218:sar (half saros) 798: 797: 793: 790: 726: 725: 630:common fractions 601: 599: 598: 593: 591: 589: 588: 584: 578: 574: 570: 569: 565: 559: 555: 551: 546: 542: 488:Numerical values 360:anomalistic year 256: 255: 251: 242: 241: 237: 234: 220: 219: 215: 154:(1° 23′). 10267: 10266: 10262: 10261: 10260: 10258: 10257: 10256: 10232: 10231: 10230: 10225: 10217: 10199: 10154: 10141: 10103: 9975: 9642: 9640: 9630: 9422: 9071: 9069: 9059: 8966: 8735: 8733: 8723: 8393: 8387: 8355: 8349: 8316: 8311: 8281: 8276: 8256: 8254: 8244: 8242: 8234: 8178:Eclipse chasing 8161: 8115: 7817: 7328: 7327: 7325: 7315: 7032: 6548: 6547: 6545: 6535: 6242: 5548: 5547: 5545: 5531: 5496: 5440: 5152: 5077: 5071:helmet streamer 5039: 5034: 4980: 4917: 4916: 4888: 4884: 4875: 4871: 4851: 4845: 4841: 4821: 4815: 4806: 4762: 4756: 4752: 4740: 4736: 4727: 4723: 4715: 4711: 4703: 4699: 4691: 4687: 4679: 4675: 4640: 4634: 4623: 4618: 4611: 4595: 4594: 4582: 4575: 4569: 4565: 4560: 4556: 4551: 4547: 4542: 4538: 4526: 4522: 4510: 4506: 4499: 4485: 4481: 4474: 4470: 4459: 4382: 4375: 4366: 4361: 4357: 4352: 4340: 4279: 4244: 4236: 4222: 4218: 4213: 4202: 4197: 4186: 4181: 4177: 4172: 4170: 4167: 4166: 4115: 4101: 4097: 4092: 4081: 4076: 4065: 4060: 4056: 4051: 4049: 4046: 4045: 3943: 3809: 3693:Hyper exeligmos 3683:of the Earth's 3600:Revelation 9:15 3522:Macdonald cycle 3505:quite constant. 3409: 3405: 3402: 3400: 3395:Callippic cycle 3336: 3333: 3330: 3329: 3326: 3324: 3286: 3282: 3279: 3277: 3187: 3183: 3182: 3075: 2529:hyper exeligmos 1985:Macdonald cycle 1656:Callippic cycle 1576: 1572: 1571: 1227: 1223: 1222: 795: 791: 788: 786: 769: 764: 759: 754: 749: 744: 739: 702: 694: 671: 582: 572: 571: 563: 553: 552: 550: 540: 538: 535: 534: 490: 454:full moon cycle 445: 439: 403:descending node 376: 337:descending node 310: 285: 279: 253: 249: 248: 239: 235: 232: 230: 217: 213: 212: 183: 72:may occur when 61:A diagram of a 55: 24: 21: 12: 11: 5: 10265: 10255: 10254: 10249: 10244: 10227: 10226: 10224: 10223: 10215: 10204: 10201: 10200: 10198: 10197: 10192: 10187: 10182: 10180:Eclipse season 10177: 10172: 10166: 10164: 10160: 10159: 10156: 10155: 10153: 10152: 10147: 10139: 10134: 10129: 10124: 10119: 10113: 10111: 10105: 10104: 10102: 10101: 10096: 10091: 10086: 10081: 10076: 10071: 10066: 10061: 10056: 10051: 10046: 10041: 10036: 10031: 10026: 10021: 10016: 10011: 10006: 10001: 9996: 9991: 9986: 9981: 9973: 9968: 9963: 9958: 9953: 9948: 9943: 9938: 9933: 9928: 9923: 9918: 9913: 9908: 9903: 9898: 9893: 9888: 9883: 9878: 9873: 9868: 9863: 9858: 9853: 9848: 9843: 9838: 9833: 9828: 9823: 9818: 9813: 9808: 9803: 9798: 9793: 9788: 9783: 9778: 9773: 9768: 9763: 9758: 9753: 9748: 9743: 9738: 9733: 9728: 9723: 9718: 9713: 9708: 9703: 9698: 9693: 9688: 9683: 9678: 9673: 9668: 9663: 9658: 9652: 9650: 9643: 9632: 9631: 9629: 9628: 9623: 9618: 9613: 9608: 9603: 9598: 9593: 9588: 9583: 9578: 9573: 9568: 9563: 9558: 9553: 9548: 9543: 9538: 9533: 9528: 9523: 9518: 9513: 9508: 9503: 9498: 9493: 9488: 9483: 9478: 9473: 9468: 9463: 9458: 9453: 9448: 9443: 9438: 9433: 9428: 9420: 9415: 9410: 9405: 9400: 9395: 9390: 9385: 9380: 9375: 9370: 9365: 9360: 9355: 9350: 9345: 9340: 9335: 9330: 9325: 9320: 9315: 9310: 9305: 9300: 9295: 9290: 9285: 9280: 9275: 9270: 9265: 9260: 9255: 9250: 9245: 9240: 9235: 9230: 9225: 9220: 9215: 9210: 9205: 9200: 9195: 9190: 9185: 9180: 9175: 9170: 9165: 9160: 9155: 9150: 9145: 9140: 9135: 9130: 9125: 9120: 9115: 9110: 9105: 9100: 9095: 9090: 9085: 9080: 9074: 9072: 9070:Total eclipses 9061: 9060: 9058: 9057: 9052: 9047: 9042: 9037: 9032: 9027: 9022: 9017: 9012: 9007: 9002: 8997: 8992: 8987: 8982: 8977: 8972: 8964: 8959: 8954: 8949: 8944: 8939: 8934: 8929: 8924: 8919: 8914: 8909: 8904: 8899: 8894: 8889: 8884: 8879: 8874: 8869: 8864: 8859: 8854: 8849: 8844: 8839: 8834: 8829: 8824: 8819: 8814: 8809: 8804: 8799: 8794: 8789: 8784: 8779: 8774: 8769: 8764: 8759: 8754: 8749: 8744: 8738: 8736: 8725: 8724: 8722: 8721: 8716: 8711: 8706: 8701: 8696: 8691: 8686: 8681: 8676: 8671: 8666: 8661: 8656: 8651: 8646: 8641: 8636: 8631: 8626: 8621: 8616: 8611: 8606: 8601: 8596: 8591: 8586: 8581: 8576: 8571: 8566: 8561: 8556: 8551: 8546: 8541: 8536: 8531: 8526: 8521: 8516: 8511: 8506: 8501: 8496: 8491: 8486: 8481: 8476: 8471: 8466: 8461: 8456: 8451: 8446: 8441: 8436: 8431: 8426: 8421: 8416: 8411: 8406: 8400: 8398: 8392:Lunar eclipses 8389: 8388: 8386: 8385: 8384: 8383: 8375: 8374: 8373: 8368: 8359: 8357: 8354:Lunar eclipses 8351: 8350: 8348: 8347: 8342: 8337: 8332: 8326: 8324: 8318: 8317: 8314:Lunar eclipses 8310: 8309: 8302: 8295: 8287: 8278: 8277: 8275: 8274: 8264: 8252: 8239: 8236: 8235: 8233: 8232: 8227: 8222: 8217: 8212: 8207: 8202: 8200:Eclipse season 8197: 8192: 8191: 8190: 8185: 8175: 8169: 8167: 8163: 8162: 8160: 8159: 8154: 8149: 8144: 8139: 8134: 8129: 8123: 8121: 8117: 8116: 8114: 8113: 8108: 8103: 8098: 8093: 8088: 8083: 8078: 8073: 8068: 8063: 8058: 8053: 8048: 8043: 8038: 8033: 8028: 8023: 8018: 8013: 8008: 8003: 7998: 7993: 7988: 7983: 7978: 7973: 7968: 7963: 7958: 7953: 7948: 7943: 7938: 7933: 7928: 7923: 7918: 7913: 7908: 7903: 7898: 7893: 7888: 7883: 7878: 7873: 7868: 7863: 7858: 7853: 7848: 7843: 7838: 7833: 7828: 7823: 7815: 7810: 7805: 7800: 7795: 7790: 7785: 7780: 7775: 7770: 7765: 7760: 7755: 7750: 7745: 7740: 7735: 7730: 7725: 7720: 7715: 7710: 7705: 7700: 7695: 7690: 7685: 7680: 7675: 7670: 7665: 7660: 7655: 7650: 7645: 7640: 7635: 7630: 7625: 7620: 7615: 7610: 7605: 7600: 7595: 7590: 7585: 7580: 7575: 7570: 7565: 7560: 7555: 7550: 7545: 7540: 7535: 7530: 7525: 7520: 7515: 7510: 7505: 7500: 7495: 7490: 7485: 7480: 7475: 7470: 7465: 7460: 7455: 7450: 7445: 7440: 7435: 7430: 7425: 7420: 7415: 7410: 7405: 7400: 7395: 7390: 7385: 7380: 7375: 7370: 7365: 7360: 7355: 7350: 7345: 7340: 7334: 7332: 7317: 7316: 7314: 7313: 7308: 7303: 7298: 7293: 7288: 7283: 7278: 7273: 7268: 7263: 7258: 7253: 7248: 7243: 7238: 7233: 7228: 7223: 7218: 7213: 7208: 7203: 7198: 7193: 7188: 7183: 7178: 7173: 7168: 7163: 7158: 7153: 7148: 7143: 7138: 7133: 7128: 7123: 7118: 7113: 7108: 7103: 7098: 7093: 7088: 7083: 7078: 7073: 7068: 7063: 7058: 7053: 7048: 7043: 7038: 7030: 7025: 7020: 7015: 7010: 7005: 7000: 6995: 6990: 6985: 6980: 6975: 6970: 6965: 6960: 6955: 6950: 6945: 6940: 6935: 6930: 6925: 6920: 6915: 6910: 6905: 6900: 6895: 6890: 6885: 6880: 6875: 6870: 6865: 6860: 6855: 6850: 6845: 6840: 6835: 6830: 6825: 6820: 6815: 6810: 6805: 6800: 6795: 6790: 6785: 6780: 6775: 6770: 6765: 6760: 6755: 6750: 6745: 6740: 6735: 6730: 6725: 6720: 6715: 6710: 6705: 6700: 6695: 6690: 6685: 6680: 6675: 6670: 6665: 6660: 6655: 6650: 6645: 6640: 6635: 6630: 6625: 6620: 6615: 6610: 6605: 6600: 6595: 6590: 6585: 6580: 6575: 6570: 6565: 6560: 6554: 6552: 6537: 6536: 6534: 6533: 6528: 6523: 6518: 6513: 6508: 6503: 6498: 6493: 6488: 6483: 6478: 6473: 6468: 6463: 6458: 6453: 6448: 6443: 6438: 6433: 6428: 6423: 6418: 6413: 6408: 6403: 6398: 6393: 6388: 6383: 6378: 6373: 6368: 6363: 6358: 6353: 6348: 6343: 6338: 6333: 6328: 6323: 6318: 6313: 6308: 6303: 6298: 6293: 6288: 6283: 6278: 6273: 6268: 6263: 6258: 6253: 6248: 6240: 6235: 6230: 6225: 6220: 6215: 6210: 6205: 6200: 6195: 6190: 6185: 6180: 6175: 6170: 6165: 6160: 6155: 6150: 6145: 6140: 6135: 6130: 6125: 6120: 6115: 6110: 6105: 6100: 6095: 6090: 6085: 6080: 6075: 6070: 6065: 6060: 6055: 6050: 6045: 6040: 6035: 6030: 6025: 6020: 6015: 6010: 6005: 6000: 5995: 5990: 5985: 5980: 5975: 5970: 5965: 5960: 5955: 5950: 5945: 5940: 5935: 5930: 5925: 5920: 5915: 5910: 5905: 5900: 5895: 5890: 5885: 5880: 5875: 5870: 5865: 5860: 5855: 5850: 5845: 5840: 5835: 5830: 5825: 5820: 5815: 5810: 5805: 5800: 5795: 5790: 5785: 5780: 5775: 5770: 5765: 5760: 5755: 5750: 5745: 5740: 5735: 5730: 5725: 5720: 5715: 5710: 5705: 5700: 5695: 5690: 5685: 5680: 5675: 5670: 5665: 5660: 5655: 5650: 5645: 5640: 5635: 5630: 5625: 5620: 5615: 5610: 5605: 5600: 5595: 5590: 5585: 5580: 5575: 5570: 5565: 5560: 5554: 5552: 5537: 5536: 5533: 5532: 5530: 5529: 5523: 5517: 5511: 5504: 5502: 5498: 5497: 5495: 5494: 5489: 5484: 5479: 5474: 5469: 5464: 5459: 5454: 5448: 5446: 5442: 5441: 5439: 5438: 5433: 5428: 5423: 5418: 5413: 5408: 5403: 5398: 5393: 5388: 5383: 5378: 5373: 5368: 5363: 5358: 5353: 5348: 5343: 5338: 5333: 5328: 5323: 5318: 5313: 5308: 5303: 5298: 5293: 5288: 5283: 5278: 5273: 5268: 5263: 5258: 5253: 5248: 5243: 5238: 5233: 5228: 5223: 5218: 5213: 5208: 5203: 5198: 5193: 5188: 5183: 5178: 5173: 5167: 5165: 5154: 5153: 5151: 5150: 5145: 5144: 5143: 5138: 5133: 5128: 5123: 5118: 5113: 5105: 5100: 5094: 5092: 5085: 5079: 5078: 5076: 5075: 5074: 5073: 5066:Stellar corona 5063: 5058: 5053: 5047: 5045: 5041: 5040: 5037:Solar eclipses 5033: 5032: 5025: 5018: 5010: 5004: 5003: 4998: 4993: 4987: 4979: 4978:External links 4976: 4975: 4974: 4960: 4946: 4936: 4933: 4930: 4927: 4924: 4921: 4915: 4914: 4906:Ephemeris Time 4902:Universal Time 4890:Fred Espenak. 4882: 4869: 4839: 4804: 4750: 4734: 4721: 4709: 4697: 4685: 4673: 4651:(3): 928–929. 4621: 4609: 4573: 4563: 4554: 4545: 4536: 4520: 4518:, Fred Espenak 4516:Solar Eclipses 4504: 4497: 4479: 4468: 4461:Rob van Gent. 4380: 4364: 4354: 4353: 4351: 4348: 4347: 4346: 4339: 4336: 4311: 4310: 4303: 4302: 4294: 4293: 4290: 4287: 4278: 4275: 4270: 4269: 4257: 4254: 4243: 4239: 4235: 4232: 4229: 4225: 4221: 4217: 4212: 4200: 4196: 4193: 4188:period of node 4184: 4180: 4176: 4144: 4143: 4131: 4128: 4122: 4118: 4114: 4111: 4108: 4104: 4100: 4096: 4091: 4079: 4075: 4072: 4067:period of node 4063: 4059: 4055: 3961: 3960: 3957: 3954: 3951: 3942: 3939: 3919:mean longitude 3892: 3891: 3855:solar eclipses 3847: 3846: 3808: 3805: 3804: 3803: 3799: 3795: 3794: 3791: 3787: 3786: 3782: 3778: 3777: 3773: 3769: 3768: 3764: 3760: 3759: 3755: 3751: 3750: 3746: 3742: 3741: 3738:3rd millennium 3734: 3730: 3729: 3726: 3722: 3721: 3718: 3714: 3713: 3710: 3699: 3698: 3694: 3690: 3689: 3656: 3644: 3643: 3640: 3636: 3635: 3624: 3620: 3619: 3608: 3604: 3603: 3591: 3587: 3586: 3583: 3579: 3578: 3574: 3570: 3569: 3565: 3561: 3560: 3552: 3546: 3545: 3541: 3537: 3536: 3532: 3528: 3527: 3523: 3519: 3518: 3511: 3507: 3506: 3502: 3498: 3497: 3489: 3485: 3484: 3476: 3472: 3471: 3464: 3460: 3459: 3456: 3452: 3451: 3423: 3419: 3418: 3415:date of Easter 3397: 3391: 3390: 3382: 3378: 3377: 3366: 3362: 3361: 3353: 3349: 3348: 3323:so an inex is 3316: 3310: 3309: 3306: 3302: 3301: 3297: 3293: 3292: 3274: 3255: 3254: 3246: 3240: 3239: 3236: 3232: 3231: 3222: 3218: 3217: 3213: 3209: 3208: 3200: 3194: 3193: 3179: 3173: 3172: 3168: 3164: 3163: 3159: 3155: 3154: 3151: 3147: 3146: 3142: 3138: 3137: 3126: 3122: 3121: 3117: 3111: 3110: 3107:eclipse season 3103: 3094:and penumbral 3079: 3074: 3071: 3068: 3067: 3064: 3061: 3058: 3055: 3052: 3049: 3046: 3043: 3040: 3030: 3026: 3025: 3022: 3019: 3016: 3013: 3010: 3007: 3004: 3001: 2998: 2988: 2984: 2983: 2980: 2977: 2974: 2971: 2968: 2965: 2962: 2959: 2956: 2946: 2942: 2941: 2938: 2935: 2932: 2929: 2926: 2923: 2920: 2917: 2914: 2904: 2900: 2899: 2896: 2893: 2890: 2887: 2884: 2881: 2878: 2875: 2872: 2862: 2858: 2857: 2854: 2851: 2848: 2845: 2842: 2839: 2836: 2833: 2830: 2820: 2816: 2815: 2812: 2809: 2806: 2803: 2800: 2797: 2794: 2791: 2788: 2778: 2774: 2773: 2770: 2767: 2764: 2761: 2758: 2755: 2752: 2749: 2746: 2736: 2732: 2731: 2728: 2725: 2722: 2719: 2716: 2713: 2710: 2707: 2704: 2694: 2690: 2689: 2686: 2683: 2680: 2677: 2674: 2671: 2668: 2665: 2662: 2652: 2648: 2647: 2644: 2641: 2638: 2635: 2632: 2629: 2626: 2623: 2620: 2610: 2606: 2605: 2602: 2599: 2596: 2593: 2590: 2587: 2584: 2581: 2578: 2572: 2568: 2567: 2564: 2561: 2558: 2555: 2552: 2549: 2546: 2543: 2540: 2530: 2526: 2525: 2522: 2519: 2516: 2513: 2510: 2507: 2504: 2501: 2498: 2488: 2484: 2483: 2480: 2477: 2474: 2471: 2468: 2465: 2462: 2459: 2456: 2446: 2442: 2441: 2438: 2435: 2432: 2429: 2426: 2423: 2420: 2417: 2414: 2404: 2400: 2399: 2396: 2393: 2390: 2387: 2384: 2381: 2378: 2375: 2372: 2366: 2362: 2361: 2358: 2355: 2352: 2349: 2346: 2343: 2340: 2337: 2334: 2324: 2320: 2319: 2316: 2313: 2310: 2307: 2304: 2301: 2298: 2295: 2292: 2282: 2278: 2277: 2274: 2271: 2268: 2265: 2262: 2259: 2256: 2253: 2250: 2240: 2236: 2235: 2232: 2229: 2226: 2223: 2220: 2217: 2214: 2211: 2208: 2198: 2194: 2193: 2190: 2187: 2184: 2181: 2178: 2175: 2172: 2169: 2166: 2156: 2152: 2151: 2148: 2145: 2142: 2139: 2136: 2133: 2130: 2127: 2124: 2114: 2108: 2107: 2104: 2101: 2098: 2095: 2092: 2089: 2086: 2083: 2080: 2070: 2066: 2065: 2062: 2059: 2056: 2053: 2050: 2047: 2044: 2041: 2038: 2028: 2024: 2023: 2020: 2017: 2014: 2011: 2008: 2005: 2002: 1999: 1996: 1986: 1982: 1981: 1978: 1975: 1972: 1969: 1966: 1963: 1960: 1957: 1954: 1944: 1940: 1939: 1936: 1933: 1930: 1927: 1924: 1921: 1918: 1915: 1912: 1902: 1898: 1897: 1894: 1891: 1888: 1885: 1882: 1879: 1876: 1873: 1870: 1864: 1860: 1859: 1856: 1853: 1850: 1847: 1844: 1841: 1838: 1835: 1832: 1822: 1818: 1817: 1814: 1811: 1808: 1805: 1802: 1799: 1796: 1793: 1790: 1780: 1776: 1775: 1772: 1769: 1766: 1763: 1760: 1757: 1754: 1751: 1748: 1738: 1734: 1733: 1730: 1727: 1724: 1721: 1718: 1715: 1712: 1709: 1706: 1700: 1696: 1695: 1692: 1689: 1686: 1683: 1680: 1677: 1674: 1671: 1668: 1658: 1652: 1651: 1648: 1645: 1642: 1639: 1636: 1633: 1630: 1627: 1624: 1615: 1611: 1610: 1607: 1604: 1601: 1598: 1595: 1592: 1589: 1586: 1583: 1565: 1561: 1560: 1557: 1554: 1551: 1548: 1545: 1542: 1539: 1536: 1533: 1527: 1521: 1520: 1517: 1514: 1511: 1508: 1505: 1502: 1499: 1496: 1493: 1488: 1477: 1476: 1473: 1470: 1467: 1464: 1461: 1458: 1455: 1452: 1449: 1439: 1435: 1434: 1431: 1428: 1425: 1422: 1419: 1416: 1413: 1410: 1407: 1397: 1393: 1392: 1389: 1386: 1383: 1380: 1377: 1374: 1371: 1368: 1365: 1355: 1349: 1348: 1345: 1342: 1339: 1336: 1333: 1330: 1327: 1324: 1321: 1316: 1305: 1304: 1301: 1298: 1295: 1292: 1289: 1286: 1283: 1280: 1277: 1268: 1262: 1261: 1258: 1255: 1252: 1249: 1246: 1243: 1240: 1237: 1234: 1220: 1214: 1213: 1210: 1207: 1204: 1201: 1198: 1195: 1192: 1189: 1186: 1176: 1172: 1171: 1168: 1165: 1162: 1159: 1156: 1153: 1150: 1147: 1144: 1134: 1128: 1127: 1124: 1121: 1118: 1115: 1112: 1109: 1106: 1103: 1100: 1090: 1084: 1083: 1080: 1077: 1074: 1071: 1068: 1065: 1062: 1059: 1056: 1046: 1042: 1041: 1038: 1035: 1032: 1029: 1026: 1023: 1020: 1017: 1014: 1004: 1000: 999: 996: 993: 990: 987: 984: 981: 978: 975: 972: 962: 958: 957: 954: 951: 948: 945: 942: 939: 936: 933: 930: 920: 916: 915: 912: 909: 906: 903: 900: 897: 894: 891: 888: 878: 874: 873: 870: 867: 864: 861: 858: 855: 852: 849: 846: 836: 830: 829: 826: 823: 820: 817: 814: 811: 808: 805: 802: 779: 775: 774: 771: 766: 761: 756: 751: 746: 741: 736: 733: 730: 701: 700:Eclipse cycles 698: 675: 648: 603: 602: 581: 562: 549: 523: 522: 519: 516: 513: 489: 486: 443:Eclipse season 441:Main article: 438: 435: 422:draconic month 410: 409: 406: 399:ascending node 395: 384: 375: 372: 356:draconic month 344: 343: 340: 333:ascending node 329: 318: 309: 306: 297:synodic months 293:solar eclipses 278: 275: 227:sidereal month 205:draconic month 195:eclipse season 182: 179: 152:lunar distance 148:Earth's shadow 65:(not to scale) 54: 51: 47:eclipse series 43:eclipse cycles 22: 9: 6: 4: 3: 2: 10264: 10253: 10250: 10248: 10245: 10243: 10240: 10239: 10237: 10216: 10214: 10206: 10205: 10202: 10196: 10195:Solar eclipse 10193: 10191: 10188: 10186: 10183: 10181: 10178: 10176: 10175:Eclipse cycle 10173: 10171: 10168: 10167: 10165: 10161: 10151: 10148: 10146: 10140: 10138: 10135: 10133: 10130: 10128: 10125: 10123: 10120: 10118: 10115: 10114: 10112: 10110: 10106: 10100: 10097: 10095: 10092: 10090: 10087: 10085: 10082: 10080: 10077: 10075: 10072: 10070: 10067: 10065: 10062: 10060: 10057: 10055: 10052: 10050: 10047: 10045: 10042: 10040: 10037: 10035: 10032: 10030: 10027: 10025: 10022: 10020: 10017: 10015: 10012: 10010: 10007: 10005: 10002: 10000: 9997: 9995: 9992: 9990: 9987: 9985: 9982: 9980: 9974: 9972: 9969: 9967: 9964: 9962: 9959: 9957: 9954: 9952: 9949: 9947: 9944: 9942: 9939: 9937: 9934: 9932: 9929: 9927: 9924: 9922: 9919: 9917: 9914: 9912: 9909: 9907: 9904: 9902: 9899: 9897: 9894: 9892: 9889: 9887: 9884: 9882: 9879: 9877: 9874: 9872: 9869: 9867: 9864: 9862: 9859: 9857: 9854: 9852: 9849: 9847: 9844: 9842: 9839: 9837: 9834: 9832: 9829: 9827: 9824: 9822: 9819: 9817: 9814: 9812: 9809: 9807: 9804: 9802: 9799: 9797: 9794: 9792: 9789: 9787: 9784: 9782: 9779: 9777: 9774: 9772: 9769: 9767: 9764: 9762: 9759: 9757: 9754: 9752: 9749: 9747: 9744: 9742: 9739: 9737: 9734: 9732: 9729: 9727: 9724: 9722: 9719: 9717: 9714: 9712: 9709: 9707: 9704: 9702: 9699: 9697: 9694: 9692: 9689: 9687: 9684: 9682: 9679: 9677: 9674: 9672: 9669: 9667: 9664: 9662: 9659: 9657: 9654: 9653: 9651: 9647: 9644: 9638: 9633: 9627: 9624: 9622: 9619: 9617: 9614: 9612: 9609: 9607: 9604: 9602: 9599: 9597: 9594: 9592: 9589: 9587: 9584: 9582: 9579: 9577: 9574: 9572: 9569: 9567: 9564: 9562: 9559: 9557: 9554: 9552: 9549: 9547: 9544: 9542: 9539: 9537: 9534: 9532: 9529: 9527: 9524: 9522: 9519: 9517: 9514: 9512: 9509: 9507: 9504: 9502: 9499: 9497: 9494: 9492: 9489: 9487: 9484: 9482: 9479: 9477: 9474: 9472: 9469: 9467: 9464: 9462: 9459: 9457: 9454: 9452: 9449: 9447: 9444: 9442: 9439: 9437: 9434: 9432: 9429: 9427: 9421: 9419: 9416: 9414: 9411: 9409: 9406: 9404: 9401: 9399: 9396: 9394: 9391: 9389: 9386: 9384: 9381: 9379: 9376: 9374: 9371: 9369: 9366: 9364: 9361: 9359: 9356: 9354: 9351: 9349: 9346: 9344: 9341: 9339: 9336: 9334: 9331: 9329: 9326: 9324: 9321: 9319: 9316: 9314: 9311: 9309: 9306: 9304: 9301: 9299: 9296: 9294: 9291: 9289: 9286: 9284: 9281: 9279: 9276: 9274: 9271: 9269: 9266: 9264: 9261: 9259: 9256: 9254: 9251: 9249: 9246: 9244: 9241: 9239: 9236: 9234: 9231: 9229: 9226: 9224: 9221: 9219: 9216: 9214: 9211: 9209: 9206: 9204: 9201: 9199: 9196: 9194: 9191: 9189: 9186: 9184: 9181: 9179: 9176: 9174: 9171: 9169: 9166: 9164: 9161: 9159: 9156: 9154: 9151: 9149: 9146: 9144: 9141: 9139: 9136: 9134: 9131: 9129: 9126: 9124: 9121: 9119: 9116: 9114: 9111: 9109: 9106: 9104: 9101: 9099: 9096: 9094: 9091: 9089: 9086: 9084: 9081: 9079: 9076: 9075: 9073: 9067: 9062: 9056: 9053: 9051: 9048: 9046: 9043: 9041: 9038: 9036: 9033: 9031: 9028: 9026: 9023: 9021: 9018: 9016: 9013: 9011: 9008: 9006: 9003: 9001: 8998: 8996: 8993: 8991: 8988: 8986: 8983: 8981: 8978: 8976: 8973: 8971: 8965: 8963: 8960: 8958: 8955: 8953: 8950: 8948: 8945: 8943: 8940: 8938: 8935: 8933: 8930: 8928: 8925: 8923: 8920: 8918: 8915: 8913: 8910: 8908: 8905: 8903: 8900: 8898: 8895: 8893: 8890: 8888: 8885: 8883: 8880: 8878: 8875: 8873: 8870: 8868: 8865: 8863: 8860: 8858: 8855: 8853: 8850: 8848: 8845: 8843: 8840: 8838: 8835: 8833: 8830: 8828: 8825: 8823: 8820: 8818: 8815: 8813: 8810: 8808: 8805: 8803: 8800: 8798: 8795: 8793: 8790: 8788: 8785: 8783: 8780: 8778: 8775: 8773: 8770: 8768: 8765: 8763: 8760: 8758: 8755: 8753: 8750: 8748: 8745: 8743: 8740: 8739: 8737: 8731: 8726: 8720: 8717: 8715: 8712: 8710: 8707: 8705: 8702: 8700: 8697: 8695: 8692: 8690: 8687: 8685: 8682: 8680: 8677: 8675: 8672: 8670: 8667: 8665: 8662: 8660: 8657: 8655: 8652: 8650: 8647: 8645: 8642: 8640: 8637: 8635: 8632: 8630: 8627: 8625: 8622: 8620: 8617: 8615: 8612: 8610: 8607: 8605: 8602: 8600: 8597: 8595: 8592: 8590: 8587: 8585: 8582: 8580: 8577: 8575: 8572: 8570: 8567: 8565: 8562: 8560: 8557: 8555: 8552: 8550: 8547: 8545: 8542: 8540: 8537: 8535: 8532: 8530: 8527: 8525: 8522: 8520: 8517: 8515: 8512: 8510: 8507: 8505: 8502: 8500: 8497: 8495: 8492: 8490: 8487: 8485: 8482: 8480: 8477: 8475: 8472: 8470: 8467: 8465: 8462: 8460: 8457: 8455: 8452: 8450: 8447: 8445: 8442: 8440: 8437: 8435: 8432: 8430: 8427: 8425: 8422: 8420: 8417: 8415: 8412: 8410: 8407: 8405: 8402: 8401: 8399: 8397: 8390: 8382: 8379: 8378: 8376: 8372: 8369: 8367: 8364: 8363: 8361: 8360: 8358: 8352: 8346: 8343: 8341: 8338: 8336: 8333: 8331: 8328: 8327: 8325: 8323: 8319: 8315: 8308: 8303: 8301: 8296: 8294: 8289: 8288: 8285: 8273: 8265: 8263: 8253: 8251: 8241: 8240: 8237: 8231: 8228: 8226: 8223: 8221: 8218: 8216: 8215:Lunar eclipse 8213: 8211: 8208: 8206: 8203: 8201: 8198: 8196: 8195:Eclipse cycle 8193: 8189: 8186: 8184: 8181: 8180: 8179: 8176: 8174: 8173:Allais effect 8171: 8170: 8168: 8164: 8158: 8155: 8153: 8150: 8148: 8145: 8143: 8140: 8138: 8135: 8133: 8130: 8128: 8125: 8124: 8122: 8118: 8112: 8109: 8107: 8104: 8102: 8099: 8097: 8094: 8092: 8089: 8087: 8084: 8082: 8079: 8077: 8074: 8072: 8069: 8067: 8064: 8062: 8059: 8057: 8054: 8052: 8049: 8047: 8044: 8042: 8039: 8037: 8034: 8032: 8029: 8027: 8024: 8022: 8019: 8017: 8014: 8012: 8009: 8007: 8004: 8002: 7999: 7997: 7994: 7992: 7989: 7987: 7984: 7982: 7979: 7977: 7974: 7972: 7969: 7967: 7964: 7962: 7959: 7957: 7954: 7952: 7949: 7947: 7944: 7942: 7939: 7937: 7934: 7932: 7929: 7927: 7924: 7922: 7919: 7917: 7914: 7912: 7909: 7907: 7904: 7902: 7899: 7897: 7894: 7892: 7889: 7887: 7884: 7882: 7879: 7877: 7874: 7872: 7869: 7867: 7864: 7862: 7859: 7857: 7854: 7852: 7849: 7847: 7844: 7842: 7839: 7837: 7834: 7832: 7829: 7827: 7824: 7822: 7816: 7814: 7811: 7809: 7806: 7804: 7801: 7799: 7796: 7794: 7791: 7789: 7786: 7784: 7781: 7779: 7776: 7774: 7771: 7769: 7766: 7764: 7761: 7759: 7756: 7754: 7751: 7749: 7746: 7744: 7741: 7739: 7736: 7734: 7731: 7729: 7726: 7724: 7721: 7719: 7716: 7714: 7711: 7709: 7706: 7704: 7701: 7699: 7696: 7694: 7691: 7689: 7686: 7684: 7681: 7679: 7676: 7674: 7671: 7669: 7666: 7664: 7661: 7659: 7656: 7654: 7651: 7649: 7646: 7644: 7641: 7639: 7636: 7634: 7631: 7629: 7626: 7624: 7621: 7619: 7616: 7614: 7611: 7609: 7606: 7604: 7601: 7599: 7596: 7594: 7591: 7589: 7586: 7584: 7581: 7579: 7576: 7574: 7571: 7569: 7566: 7564: 7561: 7559: 7556: 7554: 7551: 7549: 7546: 7544: 7541: 7539: 7536: 7534: 7531: 7529: 7526: 7524: 7521: 7519: 7516: 7514: 7511: 7509: 7506: 7504: 7501: 7499: 7496: 7494: 7491: 7489: 7486: 7484: 7481: 7479: 7476: 7474: 7471: 7469: 7466: 7464: 7461: 7459: 7456: 7454: 7451: 7449: 7446: 7444: 7441: 7439: 7436: 7434: 7431: 7429: 7426: 7424: 7421: 7419: 7416: 7414: 7411: 7409: 7406: 7404: 7401: 7399: 7396: 7394: 7391: 7389: 7386: 7384: 7381: 7379: 7376: 7374: 7371: 7369: 7366: 7364: 7361: 7359: 7356: 7354: 7351: 7349: 7346: 7344: 7341: 7339: 7336: 7335: 7333: 7323: 7318: 7312: 7309: 7307: 7304: 7302: 7299: 7297: 7294: 7292: 7289: 7287: 7284: 7282: 7279: 7277: 7274: 7272: 7269: 7267: 7264: 7262: 7259: 7257: 7254: 7252: 7249: 7247: 7244: 7242: 7239: 7237: 7234: 7232: 7229: 7227: 7224: 7222: 7219: 7217: 7214: 7212: 7209: 7207: 7204: 7202: 7199: 7197: 7194: 7192: 7189: 7187: 7184: 7182: 7179: 7177: 7174: 7172: 7169: 7167: 7164: 7162: 7159: 7157: 7154: 7152: 7149: 7147: 7144: 7142: 7139: 7137: 7134: 7132: 7129: 7127: 7124: 7122: 7119: 7117: 7114: 7112: 7109: 7107: 7104: 7102: 7099: 7097: 7094: 7092: 7089: 7087: 7084: 7082: 7079: 7077: 7074: 7072: 7069: 7067: 7064: 7062: 7059: 7057: 7054: 7052: 7049: 7047: 7044: 7042: 7039: 7037: 7031: 7029: 7026: 7024: 7021: 7019: 7016: 7014: 7011: 7009: 7006: 7004: 7001: 6999: 6996: 6994: 6991: 6989: 6986: 6984: 6981: 6979: 6976: 6974: 6971: 6969: 6966: 6964: 6961: 6959: 6956: 6954: 6951: 6949: 6946: 6944: 6941: 6939: 6936: 6934: 6931: 6929: 6926: 6924: 6921: 6919: 6916: 6914: 6911: 6909: 6906: 6904: 6901: 6899: 6896: 6894: 6891: 6889: 6886: 6884: 6881: 6879: 6876: 6874: 6871: 6869: 6866: 6864: 6861: 6859: 6856: 6854: 6851: 6849: 6846: 6844: 6841: 6839: 6836: 6834: 6831: 6829: 6826: 6824: 6821: 6819: 6816: 6814: 6811: 6809: 6806: 6804: 6801: 6799: 6796: 6794: 6791: 6789: 6786: 6784: 6781: 6779: 6776: 6774: 6771: 6769: 6766: 6764: 6761: 6759: 6756: 6754: 6751: 6749: 6746: 6744: 6741: 6739: 6736: 6734: 6731: 6729: 6726: 6724: 6721: 6719: 6716: 6714: 6711: 6709: 6706: 6704: 6701: 6699: 6696: 6694: 6691: 6689: 6686: 6684: 6681: 6679: 6676: 6674: 6671: 6669: 6666: 6664: 6661: 6659: 6656: 6654: 6651: 6649: 6646: 6644: 6641: 6639: 6636: 6634: 6631: 6629: 6626: 6624: 6621: 6619: 6616: 6614: 6611: 6609: 6606: 6604: 6601: 6599: 6596: 6594: 6591: 6589: 6586: 6584: 6581: 6579: 6576: 6574: 6571: 6569: 6566: 6564: 6561: 6559: 6556: 6555: 6553: 6543: 6538: 6532: 6529: 6527: 6524: 6522: 6519: 6517: 6514: 6512: 6509: 6507: 6504: 6502: 6499: 6497: 6494: 6492: 6489: 6487: 6484: 6482: 6479: 6477: 6474: 6472: 6469: 6467: 6464: 6462: 6459: 6457: 6454: 6452: 6449: 6447: 6444: 6442: 6439: 6437: 6434: 6432: 6429: 6427: 6424: 6422: 6419: 6417: 6414: 6412: 6409: 6407: 6404: 6402: 6399: 6397: 6394: 6392: 6389: 6387: 6384: 6382: 6379: 6377: 6374: 6372: 6369: 6367: 6364: 6362: 6359: 6357: 6354: 6352: 6349: 6347: 6344: 6342: 6339: 6337: 6334: 6332: 6329: 6327: 6324: 6322: 6319: 6317: 6314: 6312: 6309: 6307: 6304: 6302: 6299: 6297: 6294: 6292: 6289: 6287: 6284: 6282: 6279: 6277: 6274: 6272: 6269: 6267: 6264: 6262: 6259: 6257: 6254: 6252: 6249: 6247: 6241: 6239: 6236: 6234: 6231: 6229: 6226: 6224: 6221: 6219: 6216: 6214: 6211: 6209: 6206: 6204: 6201: 6199: 6196: 6194: 6191: 6189: 6186: 6184: 6181: 6179: 6176: 6174: 6171: 6169: 6166: 6164: 6161: 6159: 6156: 6154: 6151: 6149: 6146: 6144: 6141: 6139: 6136: 6134: 6131: 6129: 6126: 6124: 6121: 6119: 6116: 6114: 6111: 6109: 6106: 6104: 6101: 6099: 6096: 6094: 6091: 6089: 6086: 6084: 6081: 6079: 6076: 6074: 6071: 6069: 6066: 6064: 6061: 6059: 6056: 6054: 6051: 6049: 6046: 6044: 6041: 6039: 6036: 6034: 6031: 6029: 6026: 6024: 6021: 6019: 6016: 6014: 6011: 6009: 6006: 6004: 6001: 5999: 5996: 5994: 5991: 5989: 5986: 5984: 5981: 5979: 5976: 5974: 5971: 5969: 5966: 5964: 5961: 5959: 5956: 5954: 5951: 5949: 5946: 5944: 5941: 5939: 5936: 5934: 5931: 5929: 5926: 5924: 5921: 5919: 5916: 5914: 5911: 5909: 5906: 5904: 5901: 5899: 5896: 5894: 5891: 5889: 5886: 5884: 5881: 5879: 5876: 5874: 5871: 5869: 5866: 5864: 5861: 5859: 5856: 5854: 5851: 5849: 5846: 5844: 5841: 5839: 5836: 5834: 5831: 5829: 5826: 5824: 5821: 5819: 5816: 5814: 5811: 5809: 5806: 5804: 5801: 5799: 5796: 5794: 5791: 5789: 5786: 5784: 5781: 5779: 5776: 5774: 5771: 5769: 5766: 5764: 5761: 5759: 5756: 5754: 5751: 5749: 5746: 5744: 5741: 5739: 5736: 5734: 5731: 5729: 5726: 5724: 5721: 5719: 5716: 5714: 5711: 5709: 5706: 5704: 5701: 5699: 5696: 5694: 5691: 5689: 5686: 5684: 5681: 5679: 5676: 5674: 5671: 5669: 5666: 5664: 5661: 5659: 5656: 5654: 5651: 5649: 5646: 5644: 5641: 5639: 5636: 5634: 5631: 5629: 5626: 5624: 5621: 5619: 5616: 5614: 5611: 5609: 5606: 5604: 5601: 5599: 5596: 5594: 5591: 5589: 5586: 5584: 5581: 5579: 5576: 5574: 5571: 5569: 5566: 5564: 5561: 5559: 5556: 5555: 5553: 5543: 5538: 5527: 5524: 5521: 5518: 5515: 5512: 5509: 5506: 5505: 5503: 5499: 5493: 5492:United States 5490: 5488: 5485: 5483: 5480: 5478: 5475: 5473: 5470: 5468: 5465: 5463: 5460: 5458: 5457:British Isles 5455: 5453: 5450: 5449: 5447: 5443: 5437: 5434: 5432: 5429: 5427: 5424: 5422: 5419: 5417: 5414: 5412: 5409: 5407: 5404: 5402: 5399: 5397: 5394: 5392: 5389: 5387: 5384: 5382: 5379: 5377: 5374: 5372: 5369: 5367: 5364: 5362: 5359: 5357: 5354: 5352: 5349: 5347: 5344: 5342: 5339: 5337: 5334: 5332: 5329: 5327: 5324: 5322: 5319: 5317: 5314: 5312: 5309: 5307: 5304: 5302: 5299: 5297: 5294: 5292: 5289: 5287: 5284: 5282: 5279: 5277: 5274: 5272: 5269: 5267: 5264: 5262: 5259: 5257: 5254: 5252: 5249: 5247: 5244: 5242: 5239: 5237: 5234: 5232: 5229: 5227: 5224: 5222: 5219: 5217: 5214: 5212: 5209: 5207: 5204: 5202: 5199: 5197: 5194: 5192: 5189: 5187: 5184: 5182: 5179: 5177: 5174: 5172: 5169: 5168: 5166: 5163: 5159: 5155: 5149: 5146: 5142: 5139: 5137: 5134: 5132: 5129: 5127: 5124: 5122: 5119: 5117: 5114: 5112: 5109: 5108: 5106: 5104: 5101: 5099: 5096: 5095: 5093: 5089: 5086: 5084: 5080: 5072: 5069: 5068: 5067: 5064: 5062: 5059: 5057: 5054: 5052: 5049: 5048: 5046: 5042: 5038: 5031: 5026: 5024: 5019: 5017: 5012: 5011: 5008: 5002: 4999: 4997: 4994: 4991: 4988: 4985: 4982: 4981: 4973: 4972:0-943396-81-6 4969: 4965: 4964:Lunar Tetrads 4961: 4959: 4958:0-943396-51-4 4955: 4951: 4947: 4945: 4944:0-943396-35-2 4941: 4937: 4934: 4931: 4928: 4925: 4922: 4919: 4918: 4911: 4907: 4903: 4897: 4893: 4886: 4879: 4873: 4865: 4861: 4857: 4850: 4843: 4835: 4831: 4827: 4820: 4813: 4811: 4809: 4800: 4799: 4789: 4784: 4780: 4776: 4772: 4768: 4761: 4754: 4747: 4743: 4738: 4731: 4725: 4718: 4713: 4706: 4701: 4694: 4689: 4682: 4677: 4667: 4662: 4658: 4654: 4650: 4646: 4639: 4632: 4630: 4628: 4626: 4616: 4614: 4605: 4599: 4591: 4587: 4580: 4578: 4567: 4558: 4549: 4540: 4533: 4529: 4524: 4517: 4513: 4508: 4500: 4494: 4490: 4483: 4477: 4472: 4464: 4457: 4455: 4453: 4451: 4449: 4447: 4445: 4443: 4441: 4439: 4437: 4435: 4433: 4431: 4429: 4427: 4425: 4423: 4421: 4419: 4417: 4415: 4413: 4411: 4409: 4407: 4405: 4403: 4401: 4399: 4397: 4395: 4393: 4391: 4389: 4387: 4385: 4378: 4373: 4371: 4369: 4359: 4355: 4345: 4342: 4341: 4335: 4331: 4329: 4325: 4321: 4315: 4308: 4307: 4306: 4300: 4299: 4298: 4291: 4288: 4285: 4284: 4283: 4274: 4255: 4252: 4246: million 4241: 4237: 4233: 4230: 4227: 4223: 4219: 4215: 4210: 4198: 4194: 4191: 4182: 4178: 4174: 4165: 4164: 4163: 4160: 4157: 4153: 4149: 4129: 4126: 4120: 4116: 4112: 4109: 4106: 4102: 4098: 4094: 4089: 4077: 4073: 4070: 4061: 4057: 4053: 4044: 4043: 4042: 4033: 4029: 4025: 4016: 4008: 4004: 4000: 3998: 3993: 3987: 3978: 3974: 3971: 3967: 3958: 3955: 3952: 3949: 3948: 3947: 3938: 3930: 3926: 3922: 3920: 3916: 3912: 3908: 3900: 3896: 3889: 3888: 3887: 3883: 3875: 3867: 3863: 3860: 3856: 3851: 3844: 3843: 3842: 3840: 3836: 3832: 3822: 3813: 3800: 3797: 3796: 3792: 3789: 3788: 3783: 3781:Accuratissima 3780: 3779: 3774: 3771: 3770: 3765: 3762: 3761: 3756: 3753: 3752: 3747: 3744: 3743: 3739: 3735: 3732: 3731: 3727: 3724: 3723: 3719: 3716: 3715: 3711: 3708: 3707: 3706: 3703: 3695: 3692: 3691: 3686: 3682: 3677: 3673: 3669: 3665: 3661: 3657: 3654: 3653: 3648: 3641: 3638: 3637: 3633: 3629: 3625: 3622: 3621: 3617: 3613: 3609: 3606: 3605: 3601: 3597: 3592: 3589: 3588: 3584: 3581: 3580: 3575: 3572: 3571: 3566: 3563: 3562: 3557: 3553: 3551: 3548: 3547: 3542: 3539: 3538: 3533: 3530: 3529: 3524: 3521: 3520: 3516: 3512: 3509: 3508: 3503: 3500: 3499: 3494: 3490: 3487: 3486: 3482: 3477: 3474: 3473: 3469: 3465: 3463:Mercury cycle 3462: 3461: 3457: 3454: 3453: 3449: 3445: 3441: 3437: 3433: 3429: 3424: 3421: 3420: 3416: 3398: 3396: 3393: 3392: 3387: 3383: 3380: 3379: 3375: 3372:, located at 3371: 3367: 3364: 3363: 3359: 3354: 3351: 3350: 3346: 3322: 3317: 3315: 3312: 3311: 3307: 3304: 3303: 3298: 3295: 3294: 3275: 3272: 3271:Metonic cycle 3269: 3268: 3263: 3259: 3251: 3247: 3245: 3242: 3241: 3237: 3234: 3233: 3228: 3223: 3220: 3219: 3214: 3211: 3210: 3206: 3201: 3199: 3196: 3195: 3180: 3178: 3175: 3174: 3169: 3166: 3165: 3160: 3157: 3156: 3152: 3149: 3148: 3143: 3140: 3139: 3135: 3131: 3130:Arctic Circle 3127: 3124: 3123: 3118: 3116: 3115:Synodic month 3113: 3112: 3108: 3104: 3101: 3097: 3093: 3089: 3084: 3080: 3077: 3076: 3065: 3062: 3059: 3056: 3053: 3050: 3047: 3044: 3041: 3039: 3035: 3031: 3028: 3027: 3023: 3020: 3017: 3014: 3011: 3008: 3005: 3002: 2999: 2997: 2993: 2989: 2986: 2985: 2981: 2978: 2975: 2972: 2969: 2966: 2963: 2960: 2957: 2955: 2951: 2947: 2944: 2943: 2939: 2936: 2933: 2930: 2927: 2924: 2921: 2918: 2915: 2913: 2909: 2905: 2903:accuratissima 2902: 2901: 2897: 2894: 2891: 2888: 2885: 2882: 2879: 2876: 2873: 2871: 2867: 2863: 2860: 2859: 2855: 2852: 2849: 2846: 2843: 2840: 2837: 2834: 2831: 2829: 2825: 2821: 2818: 2817: 2813: 2810: 2807: 2804: 2801: 2798: 2795: 2792: 2789: 2787: 2783: 2779: 2776: 2775: 2771: 2768: 2765: 2762: 2759: 2756: 2753: 2750: 2747: 2745: 2741: 2737: 2734: 2733: 2729: 2726: 2723: 2720: 2717: 2714: 2711: 2708: 2705: 2703: 2699: 2695: 2692: 2691: 2687: 2684: 2681: 2678: 2675: 2672: 2669: 2666: 2663: 2661: 2657: 2653: 2650: 2649: 2645: 2642: 2639: 2636: 2633: 2630: 2627: 2624: 2621: 2619: 2615: 2611: 2608: 2607: 2603: 2600: 2597: 2594: 2591: 2588: 2585: 2582: 2579: 2577: 2573: 2570: 2569: 2565: 2562: 2559: 2556: 2553: 2550: 2547: 2544: 2541: 2539: 2535: 2531: 2528: 2527: 2523: 2520: 2517: 2514: 2511: 2508: 2505: 2502: 2499: 2497: 2493: 2489: 2486: 2485: 2481: 2478: 2475: 2472: 2469: 2466: 2463: 2460: 2457: 2455: 2451: 2447: 2444: 2443: 2439: 2436: 2433: 2430: 2427: 2424: 2421: 2418: 2415: 2413: 2409: 2405: 2402: 2401: 2397: 2394: 2391: 2388: 2385: 2382: 2379: 2376: 2373: 2371: 2367: 2364: 2363: 2359: 2356: 2353: 2350: 2347: 2344: 2341: 2338: 2335: 2333: 2329: 2325: 2322: 2321: 2317: 2314: 2311: 2308: 2305: 2302: 2299: 2296: 2293: 2291: 2287: 2283: 2280: 2279: 2275: 2272: 2269: 2266: 2263: 2260: 2257: 2254: 2251: 2249: 2245: 2241: 2238: 2237: 2233: 2230: 2227: 2224: 2221: 2218: 2215: 2212: 2209: 2207: 2203: 2199: 2196: 2195: 2191: 2188: 2185: 2182: 2179: 2176: 2173: 2170: 2167: 2165: 2161: 2157: 2154: 2153: 2149: 2146: 2143: 2140: 2137: 2134: 2131: 2128: 2125: 2123: 2119: 2115: 2113: 2110: 2109: 2105: 2102: 2099: 2096: 2093: 2090: 2087: 2084: 2081: 2079: 2075: 2071: 2068: 2067: 2063: 2060: 2057: 2054: 2051: 2048: 2045: 2042: 2039: 2037: 2033: 2029: 2026: 2025: 2021: 2018: 2015: 2012: 2009: 2006: 2003: 2000: 1997: 1995: 1991: 1987: 1984: 1983: 1979: 1976: 1973: 1970: 1967: 1964: 1961: 1958: 1955: 1953: 1949: 1945: 1942: 1941: 1937: 1934: 1931: 1928: 1925: 1922: 1919: 1916: 1913: 1911: 1907: 1903: 1900: 1899: 1895: 1892: 1889: 1886: 1883: 1880: 1877: 1874: 1871: 1869: 1865: 1862: 1861: 1857: 1854: 1851: 1848: 1845: 1842: 1839: 1836: 1833: 1831: 1827: 1823: 1820: 1819: 1815: 1812: 1809: 1806: 1803: 1800: 1797: 1794: 1791: 1789: 1785: 1781: 1779:Mercury cycle 1778: 1777: 1773: 1770: 1767: 1764: 1761: 1758: 1755: 1752: 1749: 1747: 1743: 1739: 1736: 1735: 1731: 1728: 1725: 1722: 1719: 1716: 1713: 1710: 1707: 1705: 1701: 1698: 1697: 1693: 1690: 1687: 1684: 1681: 1678: 1675: 1672: 1669: 1667: 1663: 1659: 1657: 1654: 1653: 1649: 1646: 1643: 1640: 1637: 1634: 1631: 1628: 1625: 1623: 1619: 1616: 1613: 1612: 1608: 1605: 1602: 1599: 1596: 1593: 1590: 1587: 1584: 1582: 1569: 1566: 1563: 1562: 1558: 1555: 1552: 1549: 1546: 1543: 1540: 1537: 1534: 1532: 1528: 1526: 1523: 1522: 1518: 1515: 1512: 1509: 1506: 1503: 1500: 1497: 1494: 1492: 1489: 1486: 1482: 1479: 1478: 1474: 1471: 1468: 1465: 1462: 1459: 1456: 1453: 1450: 1448: 1444: 1440: 1437: 1436: 1432: 1429: 1426: 1423: 1420: 1417: 1414: 1411: 1408: 1406: 1402: 1398: 1395: 1394: 1390: 1387: 1384: 1381: 1378: 1375: 1372: 1369: 1366: 1364: 1360: 1356: 1354: 1353:Metonic cycle 1351: 1350: 1346: 1343: 1340: 1337: 1334: 1331: 1328: 1325: 1322: 1320: 1317: 1314: 1310: 1307: 1306: 1302: 1299: 1296: 1293: 1290: 1287: 1284: 1281: 1278: 1276: 1272: 1269: 1267: 1264: 1263: 1259: 1256: 1253: 1250: 1247: 1244: 1241: 1238: 1235: 1233: 1221: 1219: 1216: 1215: 1211: 1208: 1205: 1202: 1199: 1196: 1193: 1190: 1187: 1185: 1181: 1177: 1174: 1173: 1169: 1166: 1163: 1160: 1157: 1154: 1151: 1148: 1145: 1143: 1139: 1135: 1133: 1130: 1129: 1125: 1122: 1119: 1116: 1113: 1110: 1107: 1104: 1101: 1099: 1095: 1091: 1089: 1086: 1085: 1081: 1078: 1075: 1072: 1069: 1066: 1063: 1060: 1057: 1055: 1051: 1047: 1044: 1043: 1039: 1036: 1033: 1030: 1027: 1024: 1021: 1018: 1015: 1013: 1009: 1005: 1002: 1001: 997: 994: 991: 988: 985: 982: 979: 976: 973: 971: 967: 963: 960: 959: 955: 952: 949: 946: 943: 940: 937: 934: 931: 929: 925: 921: 918: 917: 913: 910: 907: 904: 901: 898: 895: 892: 889: 887: 883: 879: 876: 875: 871: 868: 865: 862: 859: 856: 853: 850: 847: 845: 841: 837: 835: 834:synodic month 832: 831: 827: 824: 821: 818: 815: 812: 809: 806: 803: 801: 784: 780: 777: 776: 772: 767: 762: 757: 752: 747: 742: 737: 734: 731: 728: 727: 724: 722: 718: 713: 709: 707: 697: 692: 688: 684: 680: 674: 669: 665: 661: 657: 652: 651:synodic month 647: 644: 640: 638: 633: 631: 627: 623: 619: 615: 611: 606: 579: 560: 547: 533: 532: 531: 529: 520: 517: 514: 511: 510: 509: 507: 503: 499: 495: 485: 483: 479: 475: 471: 467: 461: 457: 455: 451: 444: 434: 431: 427: 423: 419: 415: 414:synodic month 407: 404: 400: 396: 393: 389: 385: 382: 381: 380: 371: 369: 365: 361: 358:, and to the 357: 353: 349: 348:synodic month 341: 338: 334: 330: 327: 323: 319: 316: 315: 314: 305: 302: 298: 294: 290: 284: 274: 271: 266: 262: 260: 259:sidereal year 246: 228: 224: 210: 209:synodic month 206: 201: 198: 196: 187: 178: 176: 172: 171:orbital nodes 168: 163: 161: 155: 153: 149: 145: 141: 136: 134: 130: 129:Earth's orbit 126: 121: 119: 115: 111: 107: 106:lunar eclipse 103: 99: 95: 94:solar eclipse 91: 87: 83: 79: 75: 71: 64: 63:solar eclipse 59: 50: 48: 44: 40: 33: 28: 19: 10174: 10170:Danjon scale 8396:saros series 8194: 8183:Solar viewer 8120:Other bodies 7728:31 Jul. 2000 7331:next partial 6551:next annular 5158:Saros series 5056:Shadow bands 4963: 4949: 4895: 4885: 4872: 4855: 4842: 4825: 4797: 4770: 4766: 4753: 4737: 4724: 4712: 4700: 4688: 4676: 4648: 4644: 4598:cite journal 4589: 4566: 4557: 4548: 4539: 4523: 4507: 4488: 4482: 4471: 4358: 4332: 4324:Dynamic time 4316: 4312: 4304: 4295: 4280: 4271: 4161: 4145: 4039: 4026: 4022: 4001: 3988: 3984: 3962: 3944: 3935: 3923: 3904: 3893: 3884: 3880: 3859:Saros series 3852: 3848: 3831:saros series 3828: 3790:Mackay cycle 3701: 3700: 3681:eccentricity 3675: 3628:Julian years 3623:Basic period 3531:Utting cycle 3483:(see below). 3386:Julian years 3370:Aubrey holes 3365:Aubrey cycle 3321:Julian years 3042:1,209,011.84 3037: 3033: 3000:1,076,773.86 2995: 2991: 2953: 2949: 2945:Mackay cycle 2911: 2907: 2869: 2865: 2827: 2823: 2785: 2781: 2743: 2739: 2701: 2697: 2659: 2655: 2617: 2613: 2575: 2537: 2533: 2495: 2491: 2453: 2449: 2411: 2407: 2369: 2365:Basic period 2331: 2327: 2289: 2285: 2247: 2243: 2205: 2201: 2163: 2159: 2121: 2117: 2077: 2073: 2035: 2031: 2027:Utting cycle 1993: 1989: 1951: 1947: 1909: 1905: 1867: 1829: 1825: 1787: 1783: 1745: 1741: 1703: 1665: 1661: 1621: 1617: 1580: 1567: 1564:Aubrey cycle 1530: 1490: 1484: 1446: 1442: 1404: 1400: 1362: 1358: 1318: 1312: 1274: 1270: 1231: 1183: 1179: 1141: 1137: 1097: 1093: 1053: 1049: 1011: 1007: 969: 965: 927: 923: 885: 881: 843: 839: 799: 782: 720: 719:) and inex ( 716: 714: 710: 705: 703: 695: 672: 645: 641: 634: 607: 604: 524: 505: 491: 476:, Moon, and 470:Moon's orbit 462: 458: 446: 411: 377: 345: 311: 288: 286: 267: 263: 202: 199: 192: 164: 156: 150:at the mean 143: 137: 125:Moon's orbit 122: 118:lunar phases 68: 46: 42: 37: 10150:2070 Apr 25 10145:2053 Aug 29 10137:2006 Mar 14 10132:1999 Jan 31 10127:1988 Mar 03 10122:1981 Jan 20 10117:1963 Jan 09 10094:2060 Nov 08 10089:2053 Mar 04 10084:2052 Apr 14 10079:2049 Nov 09 10074:2049 Jun 15 10069:2049 May 17 10064:2048 Dec 20 10059:2045 Aug 27 10054:2045 Mar 03 10049:2042 Oct 28 10044:2042 Apr 05 10039:2038 Dec 11 10034:2038 Jul 16 10029:2038 Jun 17 10024:2038 Jan 21 10019:2035 Feb 22 10014:2034 Apr 03 10009:2031 Oct 30 10004:2031 Jun 05 9999:2031 May 07 9994:2030 Dec 09 9989:2027 Aug 17 9984:2027 Jul 18 9979:2027 Feb 20 9971:2024 Mar 25 9966:2023 May 05 9961:2020 Nov 30 9956:2020 Jul 05 9951:2020 Jun 05 9946:2020 Jan 10 9941:2017 Feb 11 9936:2016 Sep 16 9931:2016 Aug 18 9926:2016 Mar 23 9921:2013 Oct 18 9916:2013 May 25 9911:2012 Nov 28 9906:2009 Aug 06 9901:2009 Jul 07 9896:2009 Feb 09 9891:2005 Apr 24 9886:2002 Nov 20 9881:2002 Jun 24 9876:2002 May 26 9871:2001 Dec 30 9866:1998 Sep 06 9861:1998 Aug 08 9856:1998 Mar 13 9851:1995 Oct 08 9846:1994 Nov 18 9841:1991 Jul 26 9836:1991 Jun 27 9831:1991 Jan 30 9826:1987 Oct 07 9821:1987 Apr 14 9816:1984 Nov 08 9811:1984 Jun 13 9806:1984 May 15 9801:1983 Dec 20 9796:1980 Aug 26 9791:1980 Jul 27 9786:1980 Mar 01 9781:1977 Sep 27 9776:1976 Nov 06 9771:1973 Jul 15 9766:1973 Jun 15 9761:1973 Jan 18 9756:1969 Sep 25 9751:1969 Aug 27 9746:1969 Apr 02 9741:1966 Oct 29 9736:1966 May 04 9731:1965 Dec 08 9726:1962 Aug 15 9721:1962 Jul 17 9716:1962 Feb 19 9711:1959 Sep 17 9706:1958 Oct 27 9701:1958 Apr 04 9696:1955 Jun 05 9691:1955 Jan 08 9686:1951 Sep 15 9681:1951 Aug 17 9676:1951 Mar 23 9671:1951 Feb 21 9666:16 Oct 1940 9661:22 Apr 1940 9656:23 Mar 1940 8362:Modern era 7723:1 Jul. 2000 5472:Philippines 5107:Modern era 5103:Middle Ages 3763:Megalosaros 3758:Gregorian). 3607:Hipparchian 3564:Square year 2819:Megalosaros 2323:Hipparchian 2155:Square year 763:Anomalistic 748:Anomalistic 528:beat period 466:inclination 277:Periodicity 181:Recurrences 140:inclination 90:conjunction 18:Saros Cycle 10236:Categories 10099:2107 May 7 8345:By century 5501:Historical 5445:Visibility 4773:(3): 905. 4744:. Data in 4350:References 4156:super-moon 4019:(344.979). 3754:Heliotrope 3749:character. 3616:Hipparchus 3573:Gregoriana 3556:Hipparchus 3374:Stonehenge 3212:Hibbardina 3150:Lunar year 3125:Pentalunex 3024:alternate 2982:alternate 2940:alternate 2916:672,441.04 2874:665,855.72 2832:659,270.40 2790:652,685.07 2777:heliotrope 2748:646,099.75 2730:alternate 2706:614,383.90 2688:alternate 2664:607,798.58 2646:alternate 2622:601,213.26 2580:549,741.44 2542:332,750.68 2524:alternate 2500:214,037.71 2458:206,241.63 2416:203,465.76 2374:190,295.11 2336:161,177.95 2294:142,809.92 2252:142,455.56 2210:135,870.24 2197:Gregoriana 2168:133,448.73 2150:alternate 2126:126,007.02 2106:alternate 2082:122,876.78 2040:112,304.83 1998:109,528.95 1980:alternate 1956:101,732.88 1938:alternate 1858:alternate 1732:alternate 1650:alternate 1609:alternate 1519:alternate 1433:alternate 1303:alternate 1212:alternate 1175:Hibbardina 1170:alternate 1082:alternate 961:lunar year 956:alternate 914:alternate 877:pentalunex 828:alternate 281:See also: 102:opposition 8111:Oct. 2098 8106:Sep. 2098 8101:Apr. 2098 8096:Dec. 2094 8091:Jul. 2094 8086:Jun. 2094 8071:Oct. 2087 8066:Jun. 2087 8046:Aug. 2083 8041:Jul. 2083 8036:Feb. 2083 8031:Nov. 2076 8026:Jul. 2076 8021:Jun. 2076 8006:Oct. 2069 7996:Apr. 2069 7986:Dec. 2065 7981:Aug. 2065 7976:Jul. 2065 7971:Feb. 2065 7966:Sep. 2062 7961:Mar. 2062 7956:Nov. 2058 7951:Jun. 2058 7936:Sep. 2054 7931:Aug. 2054 7926:Mar. 2054 7921:Oct. 2051 7916:Apr. 2051 7906:Dec. 2047 7901:Jul. 2047 7896:Jun. 2047 7891:Jan. 2047 7886:Nov. 2040 7871:Aug. 2036 7866:Jul. 2036 7861:Feb. 2036 7846:Dec. 2029 7841:Jul. 2029 7836:Jun. 2029 7831:Jan. 2029 7826:Sep. 2025 7821:Mar. 2025 7813:Oct. 2022 7808:Apr. 2022 7803:Jan. 2019 7798:Aug. 2018 7793:Jul. 2018 7788:Feb. 2018 7783:Sep. 2015 7778:Oct. 2014 7773:Nov. 2011 7768:Jul. 2011 7763:Jun. 2011 7758:Jan. 2011 7753:Sep. 2007 7748:Mar. 2007 7743:Oct. 2004 7738:Apr. 2004 7733:Dec. 2000 7718:Feb. 2000 7713:Sep. 1997 7708:Oct. 1996 7703:Apr. 1996 7698:Nov. 1993 7688:Dec. 1992 7683:Aug. 1989 7678:Mar. 1989 7673:Apr. 1986 7663:Dec. 1982 7658:Jul. 1982 7653:Jun. 1982 7648:Jan. 1982 7643:Oct. 1978 7638:Apr. 1978 7633:Nov. 1975 7623:Dec. 1974 7618:Aug. 1971 7613:Jul. 1971 7608:Feb. 1971 7603:Mar. 1968 7593:Dec. 1964 7588:Jul. 1964 7583:Jun. 1964 7578:Jan. 1964 7573:Sep. 1960 7568:Mar. 1960 7563:Dec. 1956 7558:Aug. 1953 7553:Jul. 1953 7548:Feb. 1953 7543:Oct. 1949 7538:Apr. 1949 7533:Nov. 1946 7528:Jun. 1946 7518:Jan. 1946 7513:Sep. 1942 7508:Aug. 1942 7503:Mar. 1942 7498:Nov. 1938 7493:Jul. 1935 7488:Jun. 1935 7483:Feb. 1935 7478:Jan. 1935 7473:Oct. 1931 7468:Sep. 1931 7463:Apr. 1931 7458:Nov. 1928 7453:Jun. 1928 7448:Dec. 1927 7443:Aug. 1924 7438:Jul. 1924 7433:Mar. 1924 7428:Nov. 1920 7418:Jul. 1917 7413:Jun. 1917 7408:Jan. 1917 7403:Dec. 1916 7398:Sep. 1913 7393:Aug. 1913 7388:Apr. 1913 7383:Nov. 1910 7378:Dec. 1909 7373:Aug. 1906 7368:Jul. 1906 7363:Feb. 1906 7358:Oct. 1902 7348:Apr. 1902 7343:Nov. 1873 7338:Jan. 1639 7281:Aug. 2092 7276:Feb. 2092 7261:Dec. 2085 7256:Jun. 2085 7216:Jul. 2074 7211:Jan. 2074 7156:Jul. 2056 7151:Jan. 2056 7091:Jul. 2038 7086:Jan. 2038 6863:Dec. 1973 6858:Jan. 1973 6843:Sep. 1969 6838:Mar. 1969 6788:Dec. 1954 6783:Jan. 1954 6773:Sep. 1951 6768:Mar. 1951 6743:Jul. 1944 6698:Aug. 1933 6693:Feb. 1933 6628:Aug. 1915 6623:Feb. 1915 6366:Dec. 2057 6361:Jan. 2057 5943:Jan. 1944 5893:Oct. 1930 5888:Apr. 1930 5823:Oct. 1912 5818:Apr. 1912 5798:Dec. 1908 5793:Jan. 1908 5743:Dec. 1889 5738:Jan. 1889 5510:(1312 BC) 5452:Australia 5098:Antiquity 4793:See also 4728:Based on 4192:− 3798:Horologia 3772:Immobilis 3709:Cartouche 3582:Hexdodeka 3577:calendar. 3352:Exeligmos 3325:⁠28 3262:Histogram 3230:penumbra. 3205:tzolk'ins 3198:Tzolkinex 3078:Fortnight 3051:43877.031 3048:44429.003 3029:Horologia 3009:39077.897 3006:39569.496 2987:Selenid 2 2967:31310.116 2964:31703.996 2958:862736.15 2925:24403.993 2922:24710.994 2883:24165.001 2880:24468.996 2861:immobilis 2841:23926.009 2838:24226.997 2799:23687.016 2796:23984.998 2757:23448.024 2754:23743.000 2715:22297.004 2712:22577.499 2693:Selenid 1 2673:22058.012 2670:22335.501 2631:21819.019 2628:22093.502 2589:19951.022 2586:20202.006 2571:cartouche 2551:12076.070 2548:12227.987 2425:7,384.107 2239:hexdodeka 1914:71,227.78 1872:63,431.70 1834:51,471.82 1792:40,899.87 1750:35,702.48 1708:31,715.85 1670:27,758.75 1626:23,742.59 1585:20,449.93 1535:19,755.96 1525:exeligmos 1495:10,571.95 1132:tzolkinex 778:fortnight 679:tzolkinex 656:tzolkinex 618:full moon 580:− 561:× 498:ephemeris 270:lunations 98:full moon 10242:Eclipses 10213:Category 9626:2170 May 9621:2123 Jun 9616:2094 Jun 9611:2090 Sep 9606:2087 May 9601:2084 Jan 9596:2083 Jul 9591:2076 Jun 9586:2072 Aug 9581:2069 May 9576:2065 Jul 9571:2058 Jun 9566:2055 Feb 9561:2054 Aug 9556:2054 Feb 9551:2051 Oct 9546:2051 Apr 9541:2050 Oct 9536:2050 May 9531:2048 Jan 9526:2047 Jul 9521:2047 Jan 9516:2044 Sep 9511:2044 Mar 9506:2043 Sep 9501:2043 Mar 9496:2040 Nov 9491:2040 May 9486:2037 Jan 9481:2036 Aug 9476:2036 Feb 9471:2033 Oct 9466:2033 Apr 9461:2032 Oct 9456:2032 Apr 9451:2029 Dec 9446:2029 Jun 9441:2028 Dec 9436:2026 Mar 9431:2025 Sep 9426:2025 Mar 9418:2022 Nov 9413:2022 May 9408:2021 May 9403:2019 Jan 9398:2018 Jul 9393:2018 Jan 9388:2015 Sep 9383:2015 Apr 9378:2014 Oct 9373:2014 Apr 9368:2011 Dec 9363:2011 Jun 9358:2010 Dec 9353:2008 Feb 9348:2007 Aug 9343:2007 Mar 9338:2004 Oct 9333:2004 May 9328:2003 Nov 9323:2003 May 9318:2001 Jan 9313:2000 Jul 9308:2000 Jan 9303:1997 Sep 9298:1996 Sep 9293:1996 Apr 9288:1993 Nov 9283:1993 Jun 9278:1992 Dec 9273:1990 Feb 9268:1989 Aug 9263:1989 Feb 9258:1986 Oct 9253:1986 Apr 9248:1985 Oct 9243:1985 May 9238:1982 Dec 9233:1982 Jul 9228:1982 Jan 9223:1979 Sep 9218:1978 Sep 9213:1978 Mar 9208:1975 Nov 9203:1975 May 9198:1974 Nov 9193:1972 Jan 9188:1971 Aug 9183:1971 Feb 9178:1968 Oct 9173:1968 Apr 9168:1967 Oct 9163:1967 Apr 9158:1964 Dec 9153:1964 Jun 9148:1963 Dec 9143:1960 Sep 9138:1960 Mar 9133:1957 Nov 9128:1957 May 9123:1956 Nov 9118:1954 Jan 9113:1953 Jul 9108:1953 Jan 9103:1950 Sep 9098:1950 Apr 9093:1920 May 9088:1913 Sep 9083:1910 May 9078:1504 Mar 9055:2099 Apr 9050:2075 Jun 9045:2055 Aug 9040:2052 Oct 9035:2048 Jun 9030:2046 Jul 9025:2046 Jan 9020:2041 Nov 9015:2041 May 9010:2039 Nov 9005:2039 Jun 9000:2037 Jul 8995:2035 Aug 8990:2034 Sep 8985:2030 Jun 8980:2028 Jul 8975:2028 Jan 8970:2026 Aug 8962:2024 Sep 8957:2023 Oct 8952:2021 Nov 8947:2019 Jul 8942:2017 Aug 8937:2013 Apr 8932:2012 Jun 8927:2010 Jun 8922:2009 Dec 8917:2008 Aug 8912:2006 Sep 8907:2005 Oct 8902:2001 Jul 8897:1999 Jul 8892:1997 Mar 8887:1995 Apr 8882:1994 May 8877:1992 Jun 8872:1991 Dec 8867:1990 Aug 8862:1988 Aug 8857:1983 Jun 8852:1981 Jul 8847:1979 Mar 8842:1977 Apr 8837:1976 May 8832:1974 Jun 8827:1973 Dec 8822:1972 Jul 8817:1970 Aug 8812:1970 Feb 8807:1965 Jun 8802:1963 Jul 8797:1961 Aug 8792:1961 Mar 8787:1959 Mar 8782:1958 May 8777:1956 May 8772:1955 Nov 8767:1954 Jul 8762:1952 Aug 8757:1952 Feb 8752:1916 Jul 8747:1914 Mar 8742:1903 Apr 8272:Category 8061:May 2087 8001:May 2069 7946:May 2058 7881:May 2040 7693:May 1993 7668:May 1985 7628:May 1975 7598:May 1967 7523:May 1946 7423:May 1920 7353:May 1902 5528:(632 AD) 5522:(585 BC) 5516:(763 BC) 5044:Features 4338:See also 3725:hybridia 3655:Tetradia 3612:Almagest 3358:Almagest 3347:in 1951. 3250:Almagest 3141:Semester 3120:eclipse. 3100:evection 3060:3310.007 3057:3310.094 3054:3488.003 3018:2947.968 3015:2948.046 3012:3106.496 2976:2361.981 2973:2362.043 2970:2488.996 2934:1840.995 2931:1841.043 2928:1939.994 2892:1822.966 2889:1823.014 2886:1920.996 2850:1804.936 2847:1804.984 2844:1901.997 2808:1786.907 2805:1786.954 2802:1882.998 2766:1768.878 2763:1768.925 2760:1864.000 2724:1682.047 2721:1682.091 2718:1772.499 2682:1664.018 2679:1664.062 2676:1753.501 2651:hybridia 2640:1645.989 2637:1646.032 2634:1734.502 2598:1505.070 2595:1505.110 2592:1586.006 2509:7767.781 2506:7865.499 2467:7484.849 2464:7579.008 2422:7476.999 2383:6906.123 2380:6993.002 2345:5849.413 2342:5922.999 2303:5182.807 2300:5248.007 2261:5169.947 2258:5234.985 2219:4930.955 2216:4992.986 2177:4843.074 2174:4904.000 2135:4573.002 2132:4630.531 2091:4459.401 2088:4515.500 2049:4075.727 2046:4127.000 2007:3974.986 2004:4024.991 1965:3692.054 1962:3738.500 1923:2584.973 1920:2617.492 1881:2302.041 1878:2331.001 1843:1867.997 1840:1891.496 1801:1484.323 1798:1502.996 1759:1295.702 1756:1312.002 1717:1151.021 1714:1165.500 1679:1007.411 1676:1020.084 1451:9,361.20 1409:9,184.01 1367:6,939.69 1323:6,585.32 1279:3,986.63 1236:3,292.66 1188:3,277.90 1146:2,598.69 1102:1,387.94 1058:1,210.75 1016:1,033.57 919:semester 743:Draconic 626:ecliptic 614:new moon 133:ecliptic 86:new moon 76:and the 70:Eclipses 39:Eclipses 10163:Related 9649:Partial 8377:Future 8166:Related 8142:Neptune 8137:Jupiter 5487:Ukraine 4860:Bibcode 4830:Bibcode 4775:Bibcode 4653:Bibcode 3907:tetrads 3776:closer. 3745:Proxima 3733:Selenid 3639:Chalepe 3540:Selebit 3496:triads. 3475:Tritrix 3468:Mercury 3408:⁄ 3340:⁠ 3296:Semanex 3285:⁄ 3192:active. 3186:⁄ 2735:Proxima 2560:910.998 2557:911.022 2554:959.987 2518:585.988 2515:586.003 2512:617.499 2476:564.644 2473:564.659 2470:595.008 2434:557.044 2431:557.059 2428:586.999 2403:Chalepe 2392:520.986 2389:521.000 2386:549.002 2354:441.270 2351:441.281 2348:464.999 2312:390.982 2309:390.992 2306:412.007 2270:390.012 2267:390.022 2264:410.985 2228:371.983 2225:371.992 2222:391.986 2186:365.353 2183:365.363 2180:385.000 2144:344.979 2141:344.988 2138:363.531 2100:336.409 2097:336.418 2094:354.500 2069:selebit 2058:307.466 2055:307.474 2052:324.000 2016:299.866 2013:299.874 2010:315.991 1974:278.522 1971:278.529 1968:293.500 1932:195.006 1929:195.011 1926:205.492 1890:173.662 1887:173.667 1884:183.001 1852:140.918 1849:140.922 1846:148.496 1821:tritrix 1810:111.975 1807:111.978 1804:117.996 1762:103.002 1635:861.658 1632:872.497 1594:742.162 1591:751.498 1575:⁄ 1544:716.976 1541:725.996 1504:383.674 1501:388.500 1460:339.733 1457:344.007 1418:333.303 1415:337.496 1396:semanex 1376:251.853 1373:255.021 1332:238.992 1329:241.999 1288:144.681 1285:146.501 1245:119.496 1242:120.999 1226:⁄ 1197:118.960 1194:120.457 794:⁄ 770:seasons 768:Eclipse 753:Eclipse 738:Synodic 732:Formula 468:of the 388:perigee 322:perigee 252:⁄ 238:⁄ 223:precess 216:⁄ 160:perigee 8356:by era 8157:Uranus 8152:Saturn 5482:Turkey 5477:Russia 5467:Israel 5148:Future 5091:By era 4970: 4956: 4942: 4592:: 311. 4495: 3992:syzygy 3660:tetrad 3501:Trihex 3381:Unidos 3300:nodes. 3235:Tritos 3167:Hepton 3083:syzygy 1901:trihex 1768:97.745 1765:97.748 1726:86.831 1723:86.833 1720:91.500 1688:75.997 1685:75.999 1682:80.084 1644:65.002 1641:65.004 1638:68.497 1614:unidos 1603:55.987 1600:55.989 1597:58.998 1553:54.087 1550:54.089 1547:56.996 1513:28.944 1510:28.944 1507:30.500 1469:25.629 1466:25.630 1463:27.007 1427:25.144 1424:25.145 1421:26.496 1385:18.999 1382:19.000 1379:20.021 1341:18.029 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1896:same 1816:same 1774:same 1699:triad 1694:same 1588:692.5 1559:same 1475:same 1391:same 1347:same 1309:saros 1260:same 1254:9.015 1251:9.015 1248:9.499 1239:111.5 1206:8.974 1203:8.974 1200:9.457 1164:7.115 1161:7.115 1158:7.497 1126:same 1120:3.800 1117:3.800 1114:4.004 1088:octon 1076:3.315 1073:3.315 1070:3.493 1040:same 1034:2.830 1031:2.830 1028:2.982 1003:hexon 998:same 992:0.970 989:0.970 986:1.022 950:0.485 947:0.485 944:0.511 941:6.430 938:6.511 911:0.852 908:0.404 905:0.404 902:0.426 899:5.359 896:5.426 872:same 866:0.081 863:0.081 860:0.085 857:1.072 854:1.085 848:29.53 825:0.086 822:0.040 819:0.040 816:0.043 813:0.536 810:0.543 804:14.77 773:Node 765:years 760:years 755:years 729:Cycle 687:saros 664:saros 502:epoch 478:Earth 430:Saros 426:Gamma 368:Gamma 364:saros 301:Earth 138:This 114:Greek 96:. 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5708:1878 5703:1875 5698:1874 5693:1871 5688:1870 5683:1869 5678:1868 5673:1867 5668:1865 5663:1860 5658:1858 5653:1857 5648:1853 5643:1851 5638:1842 5633:1824 5628:1816 5623:1806 5618:1780 5613:1778 5608:1766 5603:1724 5598:1715 5593:1706 5588:1673 5583:1654 5578:1652 5573:1598 5568:1560 5563:1185 5558:1133 5162:list 5141:22nd 5136:21st 5131:20th 5126:19th 5121:18th 5116:17th 5111:16th 4968:ISBN 4954:ISBN 4940:ISBN 4900:The 4604:link 4530:and 4514:and 4493:ISBN 4121:8.85 3835:inex 3833:and 3446:and 3314:Inex 3305:Thix 3063:6976 3021:6213 2994:+ 11 2979:4978 2937:3880 2895:3842 2853:3804 2811:3766 2769:3728 2727:3545 2685:3507 2643:3469 2601:3172 2563:1920 2536:+ 12 2521:1235 2503:7248 2479:1190 2461:6984 2437:1174 2419:6890 2395:1098 2377:6444 2339:5458 2297:4836 2255:4824 2246:+ 12 2213:4601 2204:+ 11 2171:4519 2129:4267 2120:− 21 2085:4161 2043:3803 2001:3709 1959:3445 1917:2412 1875:2148 1837:1743 1795:1385 1753:1209 1711:1074 1664:− 60 1481:inex 1438:thix 1361:− 15 1182:− 19 968:− 16 884:− 33 869:0.17 842:− 61 735:Days 691:inex 668:inex 622:node 506:e.g. 420:and 354:and 287:The 144:mean 78:Moon 8719:163 8714:162 8709:161 8704:160 8699:159 8694:158 8689:157 8684:156 8679:155 8674:154 8669:153 8664:152 8659:151 8654:150 8649:149 8644:148 8639:147 8634:146 8629:145 8624:144 8619:143 8614:142 8609:141 8604:140 8599:139 8594:138 8589:137 8584:136 8579:135 8574:134 8569:133 8564:132 8559:131 8554:130 8549:129 8544:128 8539:127 8534:126 8529:125 8524:124 8519:123 8514:122 8509:121 8504:120 8499:119 8494:118 8489:117 8484:116 8479:115 8474:114 8469:113 8464:112 8459:111 8454:110 8449:109 8444:108 8439:107 8434:106 8429:105 8424:104 8419:103 8414:102 8409:101 8404:100 8394:by 5436:162 5431:161 5426:160 5421:159 5416:158 5411:157 5406:156 5401:155 5396:154 5391:153 5386:152 5381:151 5376:150 5371:149 5366:148 5361:147 5356:146 5351:145 5346:144 5341:143 5336:142 5331:141 5326:140 5321:139 5316:138 5311:137 5306:136 5301:135 5296:134 5291:133 5286:132 5281:131 5276:130 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4596:{{ 4588:. 4576:^ 4383:^ 4367:^ 4320:ΔT 4242:41 3662:. 3630:, 3442:, 3438:, 3434:, 3430:, 3337:18 3331:17 2990:95 2948:76 2906:58 2864:58 2822:58 2780:58 2738:58 2696:55 2654:55 2612:55 2574:52 2532:24 2490:19 2448:22 2406:18 2368:18 2326:14 2284:12 2162:+ 2158:12 2116:25 2076:+ 2072:11 2034:+ 2030:10 1950:+ 1660:40 1570:+ 1516:61 1472:54 1430:53 1403:- 1388:40 1357:10 1344:38 1300:23 1273:− 1257:19 1209:19 1178:31 1167:15 1149:88 1140:− 1105:47 1061:41 1019:35 1006:13 977:12 964:10 880:53 838:38 787:30 785:− 781:19 585:DM 575:SM 566:DM 556:SM 543:EY 416:, 366:. 350:, 254:20 218:13 120:. 49:. 10218:→ 10142:→ 9976:→ 9423:→ 8967:→ 8306:e 8299:t 8292:v 7818:→ 7329:→ 7033:→ 6549:→ 6243:→ 5549:→ 5164:) 5160:( 5029:e 5022:t 5015:v 4898:. 4866:. 4862:: 4836:. 4832:: 4801:. 4791:. 4785:: 4777:: 4771:6 4748:. 4732:. 4719:, 4707:, 4695:, 4683:, 4669:. 4663:: 4655:: 4649:6 4606:) 4501:. 4253:= 4238:/ 4234:1 4231:+ 4224:/ 4220:1 4216:1 4211:= 4199:/ 4195:1 4183:/ 4179:1 4175:1 4127:= 4117:/ 4113:1 4110:+ 4103:/ 4099:1 4095:1 4090:= 4078:/ 4074:1 4071:+ 4062:/ 4058:1 4054:1 3602:. 3410:4 3406:1 3403:+ 3334:/ 3327:+ 3287:4 3283:1 3280:+ 3188:5 3184:1 3109:. 3038:s 3034:i 2996:s 2992:i 2954:s 2950:i 2912:s 2908:i 2870:s 2866:i 2828:s 2824:i 2786:s 2782:i 2744:s 2740:i 2702:s 2698:i 2660:s 2656:i 2618:s 2614:i 2576:i 2538:s 2534:i 2496:s 2492:i 2454:s 2450:i 2412:s 2408:i 2370:i 2332:s 2328:i 2290:s 2286:i 2248:s 2244:i 2242:6 2206:s 2202:i 2200:6 2164:s 2160:i 2122:s 2118:i 2078:s 2074:i 2036:s 2032:i 1994:s 1990:i 1988:6 1952:s 1948:i 1946:9 1910:s 1906:i 1904:3 1868:i 1866:6 1830:s 1826:i 1824:3 1788:s 1784:i 1782:2 1746:s 1742:i 1740:4 1704:i 1702:3 1666:s 1662:i 1622:s 1618:i 1581:s 1577:2 1573:1 1568:i 1531:s 1529:3 1491:i 1487:) 1485:i 1483:( 1447:s 1443:i 1441:4 1405:i 1401:s 1399:3 1363:s 1359:i 1319:s 1315:) 1313:s 1311:( 1275:s 1271:i 1232:s 1228:2 1224:1 1184:i 1180:s 1142:i 1138:s 1136:2 1123:8 1098:s 1094:i 1092:2 1079:7 1054:i 1050:s 1048:5 1037:6 1012:i 1008:s 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Index