# Top 10 Eclipse Cycles and Periods

Eclipse cycles and periods have been known by people since ancient times. To this day, we can calculate eclipses with these cycles and periods. They follow predictable patterns with only minimal errors.Cycles are always recurrent. In contrast, periods may be individual.

*1*

**Saros**

This cycle is the one most people know about when it comes to eclipses. It consists of 223 synodic months and approximates 239 draconic months and 242 anomalistic months, thus approximating 18 tropical years + 11 days + 8 hours.

This regularity leads to similar eclipses, though the 8-hour shift after 11 days contributes to such series being temporary. From 3000 B.C. to 5000 A.D., there are between 69 and 89 members in a Saros series.

*2*

**Inex**

When a Saros series ends, the next such series starts an Inex later. One Inex equals 358 synodic months, which subtracts roughly 20 days from 29 tropical years.

For all intents and purposes, eclipses an Inex apart occur toward the same geographic longitude but at the opposite node of our Moon's orbit (hence the opposite latitude). Every third Inex achieves nearly an integer number of anomalistic months, making the circumstances similar, leading to a cycle named a triad.

*3*

**Sar**

Half of the Saros, therefore, 223 lunar fortnights or 111 1/2 synodic months, are calculated. It equals approximately 9 tropical years + 5 1/2 days + 4 hours, leading to opposing eclipses of similar character at the same node of the Moon's orbit.

*4*

**Square Year**

This is the eighth convergent in the continued fractions development of the ratio between the eclipse year and the synodic month. It equals 4,519 synodic months, approximating 365 tropical years + 4 1/2 months. It adds a Saros over 12 Inex, giving it an astronomical life expectancy. In Epoch 2000, there's a total of 14,911 members in a square year series.

*5*

**Metonic Cycle**

The period spans over 19 tropical years during which moon phases and eclipses occur around the same day of the year. The offset from 19 tropical years averages 2 hours, 4 minutes, and 58 seconds, making it the most accurate of cycles less than a century for synchronization with the Gregorian, Julian, and other common calendars.

It adds 7 synodic months over 19 lunar years. It combines 110 hollow months with 125 full months, giving it a fairly short life expectancy of up to 5 members in an eclipse series (taking up the Callippic period).

*6*

**Tritos**

This period is defined by roughly 1 month being subtracted from 11 tropical years. It involves 135 synodic months and approximates 12 synodic periods of Jupiter, meaning eclipses in opposition with Jupiter achieve another opposition in a Tritos.

Interestingly, a Tritos is 144.68134573055698 anomalistic months, which is near the fraction of 2/3. Every third Tritos equals 434.04403719167095 anomalistic months, which is nearly an integer number, allowing eclipses to have similar properties.

*7*

**Lunar Year**

This period consists of 12 synodic months, therefore over 11 days shorter than a tropical Earth year. It equals 10 Inex - 16 Saros, therefore it does not have a very long life expectancy for such a series.

*8*

**Tzolkinex**

Known by the Mayans, a tzolk'in (260 days) is multiplied nearly tenfold, leading to eclipses 88 synodic months apart. It approximates 7 tropical years + 1 month + 13 days. It equals 2 Saros - 1 Inex, resulting in eclipses occurring one Saros series earlier. Every third cycle comes close to an integer number of anomalistic months and therefore has similar properties.

*9*

**Short Callippic Cycle**

Subtracting a synodic month from the Callippic period results in a lasting cycle of 939 synodic months, which is 2 Inex + 1 Saros, giving it nearly an integer number of draconic months but poor anomalistic returns. This leads to similar eclipses at varying distances from Earth a month before the 76-year anniversary.

*10*

**Callippic Period**

The period spans around 76 tropical years during which a day is subtracted from the calendars after 4 Metonic cycles. It equals 940 synodic months (441 hollow + 499 full), so the offset averages roughly 5 hours and 54 minutes in our calendars.

It defines the total life expectancy of a Metonic eclipse series, which is why eclipses regularly happen 1 synodic month below this, forming the short Callippic cycle.

*11*

**Hectolunex**

This period spans 100 synodic months, during which eclipses occur over a month later after 8 tropical years. It equals 9 Inex - 14 Saros and is fairly close to an integer number of anomalistic months, but poor in draconic returns.

This is why eclipses show different characters even at a similar distance from Earth. Interestingly, since it is the antidote to a Tritos, if you combine this with that, you will get the Metonic cycle.

*12*

**Octaëteris**

This is not really a cycle but an individual period. It equals 99 synodic months, so generally, in 8 tropical years, the moon phases occur around 1 1/2 days later. Occasionally, eclipses will occur too.

It equals 47 Saros - 29 Inex and marks the start of a new Hectolunex series after the last such series ends.

*13*

**Hibbardina**

Although sometimes described as a cycle, it is really a period separating similar eclipses with opposite gamma values.

Adding 1 synodic month gives eclipses the same chances of happening. Adding 1 lunar fortnight over it creates a sar (half-saros). It equals 31 Saros - 19 Inex and equals 111 synodic months, which subtracts around 9 days off of 9 tropical years.

It is near an integer number of anomalistic months but poor in draconic returns, giving eclipses very different characters despite the Moon being nearly the same distance from Earth.

*14*

**Long Hibbardina**

Like the Hibbardina, it's a period separating similar eclipses of opposite gamma values and has the same chances of occurring.

Subtracting a lunar fortnight creates a Sar. It equals 19 Inex - 30 Saros, equaling 112 synodic months, adding around 20 days over 9 tropical years.

Like the Hibbardina, it's near an integer number of anomalistic months but poor in draconic returns, giving it different eclipses at nearly the same distance.

*15*

**Short Decaëteris**

This is another period of similar eclipses with opposite gamma values. It equals 15 Saros - 9 Inex, which is 123 synodic months, subtracting around 20 days off of 10 tropical years.

It is also equivalent to 3 heptons, each occurring near an integer number of weeks, meaning eclipses a short decaëteris apart will take place near the same day of the week.

*16*

**Decaëteris**

Like the short Decaëteris, it is a period separating similar eclipses with opposite gamma values.

It equals 29 Inex - 46 Saros, which is 124 synodic months, adding around 9 days over 10 tropical years.

*17*

**Icosihenon**

This period spans 21 eclipse seasons and is halfway between a short and full decaëteris. It equals 10 Inex - 15 1/2 Saros, which is 123 1/2 synodic months, creating opposing eclipses around 10 tropical years - 5 1/2 days apart.

For this reason, it has a much better life expectancy than a short or full decaëteris.

*18*

**Aubrey Cycle**

Named after the calculation of using the Aubrey Holes at Stonehenge.

With 56 Aubrey holes, each being nearly a year apart, a full cycle takes nearly 56 years, subtracting around 3 1/2 days off, with opposing eclipses. It equals 1 Inex + 1 1/2 Saros, which is 692 1/2 synodic months.

It also approximates 176 1/2 synodic periods of Mercury, meaning Mercury comes toward the opposite position in the sky during each cycle.

*19*

**Exeligmos**

A triple Saros in which eclipses in the same Saros series are visible from roughly the same terrestrial longitude.

Because of the approximately 8-hour shift over 11 days after 18 tropical years in a Saros cycle, it takes 3 such cycles to achieve this since Earth's rotation period is taken into account.

*20*

**Octon**

Eight eclipse seasons in which 47 synodic months are calculated. It equals 2 Inex - 3 Saros, therefore 1/5 of the Metonic cycle.

Although it is fairly close to a whole number of draconic returns, it is poor in anomalistic returns. Therefore, the Moon's distance varies greatly with each eclipse despite returning to the same node.

*21*

**Hepton**

Seven eclipse seasons in which 41 synodic months are calculated. It equals 5 Saros - 3 Inex and comes very close to a whole number of weeks and fairly close to a whole number of anomalistic months.

This means eclipses occur roughly 6 hours earlier on the weekday schedules at nearly the same distance from Earth despite achieving the opposite nodal position.

Meaning every fourth Hepton is roughly one day earlier in the week.

*22*

**Hexon**

*23*

**Hipparchic Cycle**

As an eclipse cycle, Hipparchus defined it as 25 Inex - 21 Saros, or 4,267 synodic months, subtracting approximately 1 3/8 days from 345 tropical years.

By comparing his own observations with Babylonian records from 345 years earlier, he could verify the accuracy of the various periods that the Chaldeans used.

Ptolemy pointed out that dividing it by 17 still gives a whole number of synodic months (251) and anomalistic months (269). However, it isn't an eclipse interval since it's nowhere near a whole or half integer number of draconic months.

Despite its name, it is a period separating similar eclipses with opposite gamma values.

*24*

**Basic Period**

*25*

**Thix**

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