Top 10 Celestial Cycles

Galactic Year

The period it takes for the barycenter in our Solar System (which our star orbits) to orbit the barycenter of our Milky Way galaxy.
It approximates 225,000,000 Earth years.

Earth Year

The period it takes for Earth to orbit the barycenter in our solar system.
It equals 365.256363004 days in a sidereal year and 365.242190402 days in a tropical year.
It equals 365.2425 days in the Gregorian calendar and 365 and one-quarter days in the Julian calendar.
In our common calendars, it's defined as 365 days, while a leap year is 366 days.

Lunar Year

It is defined as a year on the Moon, equal to 12 synodic months or around 354 days, 8 hours, 48 minutes, and 34 seconds.
It's also the first Metonic interval and is useful for calculating eclipses, though there are up to five members in a lunar year series, as a lunar year equals 10 Inex minus 16 Saros.

Martian Year

It's defined as 779.94 days, which is 880.85% longer than a sidereal Earth year.
It's the period Mars takes to orbit the barycenter in our Solar System.

Venusian Year

It's defined as 224.701 sidereal days (which is shorter than our year), making it shorter than a Venusian day. It's 583.92 synodic days (which is 92% longer than a Venusian day).
That's 61.5198% of a sidereal Earth year.

Mercurian Year

The period it takes for Mercury to orbit the barycenter in our Solar System.
It equals 87.9691 sidereal days or 24.0846% of an Earth year. Therefore, it's 115.88 synodic days.
It's also half of a Mercurian day.

Jovian Year

The period it takes for Jupiter to orbit our Solar System's barycenter.
It equals 4,332.59 sidereal days and 398.88 synodic days.

Saturnian Year

The period it takes for Saturn to orbit our Solar System's barycenter.
It equals 10,755.7 sidereal days and 378.09 synodic days.

Uranian Year

The period it takes for Uranus to orbit our Solar System's barycenter.
It equals 30,688.5 sidereal days and 42,718 Uranian solar days, as well as 369.66 synodic days.

Neptunian Year

The period it takes for Neptune to orbit our Solar System's barycenter.
It equals 60,195 sidereal days and 89,666 Neptunian days, as well as 367.49 synodic days.

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Trion

It's defined as an eclipse cycle equal to 3 eclipse seasons, alternating between solar and lunar.
It equals 35 lunar fortnights, which is half of a hexon.
It equals 6 1/2 Saros minus 4 Inex cycles.

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Tetron

It's defined as an eclipse cycle equal to 4 eclipse seasons, alternating between solar and lunar.
It equals 47 lunar fortnights, which is half of an octon and one-tenth of the Metonic cycle.
It equals 1 Inex minus 1 1/2 Saros cycles.

Lambert II Cycle

It's defined as an eclipse cycle equal to 9 Inex plus 1 Saros cycle, equaling 3,445 synodic months (about 278 tropical years, 6 months, and 15 days), ending near the opposite node and coming close to a half-integer number of draconic months and a whole number of anomalistic months. This allows eclipses to be somewhat similar.

Tetracontahex

It's defined as an eclipse cycle equal to 40 Inex plus 6 Saros cycles, or 15,685 synodic months (about 1,266 tropical years minus 6 days), ending toward the same node and taking place near a whole number of anomalistic months, leading to similar eclipses.

Trihectaëteris

It's defined as a period within 300 tropical years where the Moon phases occur about 13 1/2 days earlier.
It equals 3,708 synodic months, which is 309 lunar years, and is over a whole number of anomalistic months, meaning the Moon's distance in this period is nearly the same.
It was studied in Quranic culture over 1,400 years ago.

Short Callippic Period

It subtracts roughly one month from the Callippic cycle, so that 2 Inex plus 1 Saros, or 939 synodic months, are calculated.
It is close to an integer number of draconic months but poor in anomalistic returns, meaning eclipses a short Callippic period apart have similar characteristics but occur at varying distances from Earth.

Tzolkinex

It's defined as an eclipse cycle that's very close to 10 times the length of the Mayan calendar known as a tzolk'in.
A tzolkinex equals 88 synodic months, or 2,598.691 days, or about 7 tropical years, 1 month, and 12 days.
It equals 2 Saros minus 1 Inex, meaning eclipses a tzolkinex apart jump back by a Saros series.
Three tzolkinex cycles equal 22 lunar years and come close to an integer number of anomalistic months, giving eclipses similar properties.

Tetradia

It's defined as an eclipse cycle that measures the frequency of tetrads (4 total lunar eclipses in 2 lunar years).
It's defined as 22 Inex minus 4 Saros (6,984 synodic months or about 565 tropical years and 7 months) by Meeus II, and 19 Inex minus 2 Saros (7,248 synodic months or about 586 tropical years and 6 days) by Meeus I.
Both take place around the same dates on the Julian calendar.

Half Exeligmos

It's defined as an eclipse cycle equal to 1.5 Saros cycles, or 669 lunar fortnights, alternating between solar and lunar eclipses toward the same node.

Half Metonic Cycle

It's defined as half of the Metonic cycle, or 235 lunar fortnights, or 55 hollow months plus 62 and a half full months, leading to eclipses alternating between solar and lunar in approximately 9.5 tropical years.

Semanex

It's defined as an eclipse cycle equal to 311 synodic months, or about 25 tropical years, 1 month, and 3 weeks, or 3 Saros minus 1 Inex cycle.
It is approximately a whole number of weeks. This means eclipses take place on the same day of the week, with an offset of just over 14 minutes.
It adds a Tzolkinex over a Saros cycle.

MacDonald Cycle

It's defined as an eclipse cycle briefly mentioned by A.C.D. Crommelin in 1905, Torroja Menéndez in 1941, George van den Bergh in 1951, and MacDonald in 2000. Eclipses of long durations visible from the British Isles between 1 and 3000 A.D. tend to occur in pairs separated by this period.
It equals 3,709 synodic months or about 299 tropical years, 10 months, and 17 days.

Utting Cycle

It's defined as an eclipse cycle of 3,803 synodic months, or about 307 tropical years, 5 months, 23 days, and 8 hours.
It's also known as a Decamonos, as it's 10 Inex cycles plus 1 Saros cycle. First mentioned by James Utting in 1827.

Accuratissima

It's defined as an eclipse cycle that's 1 Saros longer than an Immobilis, equaling 22,771 synodic months or about 1,841 tropical years and 1 month, or 230 octaëterides plus 1 synodic month, ending on the same node.
It is close to a whole number of weeks and near a whole number of anomalistic and draconic months, so similar eclipses occur on the same day of the week.

Gregoriana

It's defined as a period of 4,601 synodic months or approximately 372 Gregorian years, where the Moon phases occur.
It's also an eclipse cycle nicknamed a hexahendecos, as it's 6 Inex cycles plus 11 Saros cycles.

Palaea-Horologia

It's defined as an eclipse cycle equal to 20,359 synodic months, or about 1,646 tropical years, 24 days, and 17.5 hours.
It is nearly an integer number of anomalistic months and shares similar properties.

Horologia

It is defined as an eclipse cycle useful for calculating the timing of solar and lunar eclipses in general.
It equals 40,941 synodic months, or about 3,310 tropical years, 1 month, and 4 weeks, or 110 Inex plus 7 Saros cycles, ending on the same node of the Moon's orbit.
It is roughly a whole number of weeks, draconic months, and anomalistic months, leading to similar eclipses around the same day of the week.