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.
The Top Ten
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, meaning 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) therefore 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.

The Contenders
11 Hectolunex

100 synodic months in 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, which's why eclipses show different character even at a similar distance from Earth.
Interestingly, since it's the antidote to a tritos, if you combine this with that, you'll get the Metonic cycle.

12 Octaëteris

Not really a cycle, but an individual period.
It equals 99 synodic months so that generally in 8 tropical years, the moon phases occur around 1 1/2 days later, and 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's 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 character 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

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

21 eclipse seasons and halfway between a short and full decaëteris.
It equals 10 Inex - 15 1/2 Saros, which's 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 Lunar Semester
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