Top 10 Eclipse Cycles and Periods
Eclipse cycles and periods have been known by people since ancient times. Even today, we can calculate eclipses using these cycles and periods. They follow predictable patterns with only minimal errors.
Cycles always repeat. In contrast, periods may be individual.
-
Saros
This cycle is the one most people know about when it comes to eclipses. It consists of 223 synodic months and approximates 239 anomalistic months and 242 draconic months, thus approximating 18 tropical years plus 10-11 days and 8 hours.
This regularity leads to similar eclipses, though the 8-hour shift 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.
-
Inex
When a Saros series ends, the next such series starts an Inex later. One Inex equals 358 synodic months, which subtracts around 19 and a half 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 and leading to a cycle named a triad.
-
Sar
Half of the Saros cycle, or 223 lunar fortnights or 111 1/2 synodic months, is calculated. It equals approximately 9 tropical years, 5 days, and 16 hours, leading to opposing eclipses of a similar character at the same node of the Moon's orbit.
-
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 and 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.
-
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).
-
Tritos
This period is defined by roughly one month being subtracted from 11 tropical years. It involves 135 synodic months and approximates 10 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 close to the fraction 2/3. Every third Tritos equals 434.04403719167095 anomalistic months, which is nearly an integer, allowing eclipses to have similar properties.
-
Lunar Year
This period consists of 12 synodic months, therefore around 10 to 11 days shorter than a tropical Earth year.
It equals 10 Inex minus 16 Saros, therefore it does not have a very long life expectancy for such a series.
-
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, and 12 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.
-
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.
-
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.
-
?
Short Dodecaëteris
It's equal to 4 triëterides minus a synodic month, or a Tritos plus a lunar year. Therefore, 147 synodic months, or approximately 12 years minus 6 weeks, are calculated, ending toward the opposite node of the Moon's orbit and 11 Saros series later, as it equals 11 Inex minus 17 Saros.
-
?
Lambert II Cycle
It is equal to 9 Inex plus 1 Saros, or 3,445 synodic months, which is approximately 278 tropical years, 6 months, and 15 days. It ends toward the opposite node of the Moon's orbit and 9 Saros series later. It is nearly a half-integer number of draconic months and nearly a whole number of anomalistic months, meaning the circumstances of the eclipses are similar.
-
Half Metonic Cycle
Half of the Metonic cycle leads to eclipses alternating from solar to lunar, or lunar to solar, over 235 lunar fortnights or 117 1/2 synodic months, occurring at the opposite node.
It equals 5 Inex minus 7 1/2 Saros, or approximately 9 tropical years and 6 months.
-
Horologia
110 Inex plus 7 Saros, or 40,941 synodic months, ending on the same node of the Moon's orbit and 110 Saros series later.
It is roughly a whole number of weeks, draconic and anomalistic months, leading to similar eclipses toward the same day of the week.
It is useful for calculating the timing of solar and lunar eclipses in general.
-
Tetracontahex
-
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.
-
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.
-
Hibbardina
Although sometimes described as a cycle, it is really a period separating similar eclipses with opposite gamma values.
Adding one synodic month gives eclipses the same chances of happening. Adding one lunar fortnight over it creates a sar (half-Saros). It equals 31 Saros minus 19 Inex and equals 111 synodic months, which subtracts around 9 days from 9 tropical years.
-
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 minus 30 Saros, equaling 112 synodic months, adding around 19 and a half days over 9 tropical years.
-
Short Decaëteris
This is another period of similar eclipses with opposite gamma values. It equals 15 Saros minus 9 Inex, which is 123 synodic months, subtracting around 19 and a half days from 10 tropical years.
It is also equivalent to 3 Heptons, each occurring near a whole number of weeks, meaning eclipses a Short Decaëteris apart will take place near the same day of the week.
-
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.
-
Icosihenon
This period spans 21 eclipse seasons and is halfway between a short and full Decaëteris. It equals 10 Inex minus 15 and a half Saros, which is 123 and a half synodic months or 247 lunar fortnights, creating opposing eclipses around 10 tropical years minus 5 and a quarter days apart.
For this reason, it has a much better life expectancy than a short or full Decaëteris.
-
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 and a half days off, with opposing eclipses. It equals 1 Inex plus 1 and a half Saros, which is 692 and a half synodic months or 1,385 lunar fortnights.
It also approximates 176 and a half synodic periods of Mercury, meaning Mercury comes toward the opposite position in the sky during each cycle.
-
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 10 or 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.
-
Octon
Eight eclipse seasons in which 47 synodic months are calculated. It equals 2 Inex minus 3 Saros, which is one-fifth of the Metonic cycle.
Although it is fairly close to a whole number of draconic returns, it is poor in anomalistic returns. Because of this, the Moon's distance varies greatly with each eclipse, even though it returns to the same node.
However, every third octon is close to an integer number of anomalistic months, which gives it similar properties.
-
Hepton
Seven eclipse seasons in which 41 synodic months are calculated. It equals 5 Saros minus 3 Inex and comes close to a whole number of weeks and anomalistic months.
This means eclipses occur irregularly, on average, roughly 6 hours earlier on the weekday schedules. They happen at nearly the same distance from Earth, despite occurring at the opposite nodal position.
It is also over synodic periods of Jupiter. As a result, eclipses in opposition with Jupiter will be near such opposition in a Hepton.
-
Hexon
A Hexon is six eclipse seasons in which 35 synodic months are calculated.
It is nearly a whole number of months, occurring around two months short of three tropical years at the same node.
It equals 13 Saros minus 8 Inex cycles. It has the same timing results as two Tritos cycles, so the antidote is a dihectalunex (two hectalunex). Adding the Metonic cycle to this creates a double Tritos.