# How would be a Lunisolar Calendar with 2 Moons?

The world I'm building it's a Super-Earth named Tempus, and it has 2 moons in an orbital resonance. One of the moons, named Tidra Moon, is closest to the planet and basically has the same influence on the Tempus that our moon has on earth, specially the tide influence (that's where the name Tidra come from). The other moon, named Enera Moon, is further away (the size of Enera would be the same or smaller than Tidra) and has and energetic influence on living beings (mostly magic).

With that, I was trying to elaborate the Lunisolar Calendar of Tempus Planet, although, I've been struggling with when every lunar phase of each moon would happen...

I want the years to be longer than on Earth, around 500 days seems appropriate, for the moons cycles I was thinking on 20:40 (Tidra:Enera) at first, with months following the Cycle of Tidra, therefore, the months would have 20 days, but that would result in 25 month a year, which seems too much for me...

I was also considering 30:40, 30:60 or 40:60 for the moon cycles, but I really wanted to visualize the frequency of each moon phase and the calendars to decide... 40 days, because would be approximately 12 months, with some leap years (but I think it would have a lot of leap years, correct me if I'm wrong) and the 30 days would be approximately 16 months which is ok, guess, also with leap years, but less in my analysis...

I've been trying to simulate the first years of the calendar until the 'pattern' of the cycles repeated...

Still I'm struggling with how to actually create the calendar.. I would truly appreciate any help regarding this :)

Of course, I'm only dealing with approximations, not exact numbers, as it should be when dealing with any other calendar and orbit.

Thanks in advance! Have a great week!

• Orbital resonance links the duration of the periods of revolution of the two satellites. The sinodic periods, which is what is important for a calendar, would not be in the same nice tidy relationship. As to how to construct your calendar, Excel is your friend. Anyway, the chance of getting the sinodic period of a natural satellite to be an integer number of mean solar days is basically zero, and the same for the duration of a year. It will always be some integer number of days plus a fraction with many digits. All calendars are approximations. Commented May 4 at 21:47
• Unless, of course, you are talking designed solar systems, maybe Kardashev 1+. Commented May 4 at 23:19
• @JahJahs i am unsure at what getting at as it seems you already have figured out your own calendar. Secondly there is basically no definitive answer to how to make a calendar but for all intends and purposes just make a month how long you want. The n divide it through the day of your years and you have the number of months. The rest are lap days, just add them whenever they feel convenient in our world it's 1/4 day extra so we have an extra day every 4 years. Really that is all i think if you make it more clear what you want i can give you an definitive answer. Commented May 8 at 14:41
• @Fallenspacerock Thats not really how lunisolar calendars work. Our leap years come from our solar calendar, with a leap day every 4 years because the solar year isn't an exact integer ratio of the number of days in it. Lunisolar calendars are about using lunar phases to set month lengths and then adding leap months whenever the lunar year falls too far out of line with the solar year. Same basic idea but you are making each new or full moon the start of a month, then figuring out when you need to add or subtract a month based on how much longer or shorter the lunar year is than the solar year Commented May 9 at 18:10
• @Escapeddentalpatient While the merit of a lunar calendar is opinion based and debatable, the history of how and why they've evolved is rooted in facts. As are the limitations of orbital mechanics which make certain month lengths physically impossible as the OP has described them. So, despite lunar calendars being a bit more controversial than the average person may expect, there is plenty of meat here for non-opinion based answers. Commented May 10 at 14:28

Lunisolar calendars on earth all exist to facilitate the same thing, allowing you to use the moon as a timekeeping tool while keeping the months in consistent seasons of the solar year. If you are a person in ancient greece, you want to make sure that Hekatambion always happens at the start of the summer, Poseideon is always in the middle of winter, and so on, so that you know how the weather is going to change, when to harvest, when to plant, etc. based on which lunar month it is. On earth, you need to slot an extra month in there every few years to keep things lined up because the lunar year drags behind the solar year by about 11 days, and this is what things like the metonic cycle are used for. You get a little more than a month behind every three years, so you need to add a month every 2-3 years, with whether it is 2 or 3 varying on a 19 year cycle.

It's not a foregone conclusion that you have to use every celestial body you have to make calendars. In the case of earthly lunisolar calendars, we have one celestial body with a consistent, trackable phase period that is convenient for making months out of if you don't have fancy modern clocks, the moon, and another whose relative position decides how your crops will grow and whether you will freeze to death, the sun, so we try to line them up so we can chop the year up into manageable months that still tell us when to plant and when to hunker down.

If you have two moons and a sun, a lot of people will probably just decide to use the one that is the easiest to line up with the solar year and may ignore the other one for practical purposes. You don't need to account for both moons in your calendar just because you have two moons. The Egyptians set their calendar by where Sirius was in the sky but, despite being able to see Sirius, no one else really thought to keep time with it. Our modern calendar doesn't care about the moon or stars at all. It just tracks the sun and divides the months up semi-arbitrarily to get roughly equal lengths that are consistent year to year. Most civilizations would probably use the easiest moon to fit into the year, probably the one whose offset from the solar year is a ratio of it's phase period that is easiest to work with. The moon is basically a giant sun dial in these systems, and you can choose to look at the sun dial that is easier to read rather than always having to pay attention to both of them, though some cultures will inevitably do that or choose to focus on the more cumbersome moon for various reasons such as culture, religion, or geography.

Our moon has a 29.5 day phase period and an 11 day offset from the solar year, but if we had a second one whose phases cycled every 40 days and whose year was 5 days behind the solar year, most lunisolar calendars would probably track that one instead because you can just drop in an intercalary month every 8 years instead of having to muck around with something like a metonic cycle. And if we had a second moon that you needed a 37 year cycle to keep lined up with the seasons, then most societies probably keep using the one with the 19 year cycle. Some civilizations may decide to use the other moon. Others may use the primary moon for their primary calendar while having another calendar based on the secondary moon to track festivals related to that moon's deity or something. Hell, maybe the secondary moon's calendar is just lunar, rather than lunisolar, and doesn't use intercalation because it's not used for purposes where seasons matter. Still others may go extra crazy and develop super complicated calendars based on the motions of both moons.

If you are going with a lunisolar calendar and not some sort of crazy lunilunisolar calendar that has no earth equivalent, it probably wouldn't actually work that much different from similar calendars found here. Decide on a lunar year, a lunar month, and a solar year, and then figure out when you need to slot in extra months to keep the seasons from drifting. The big difference would probably just be that there would be more variation in calendars because different people may follow a different moon for different reasons, and that this planet's version of crazypants astronomers like the Egyptians or the Mayans may have even more calendars tracking more things than their earthly equivalents.

If you are looking for logic on how to set cycles like those, you can look at the metonic cycle for inspiration. The length of a solar year is 365.24 days. The length of a lunar month is 29.53 days. If you just kept trying multiples of years divided by 29.53 until you got something close to a whole number, you could come up with the approximate length of your cycle. In this case it's (19 X 365.24)/29.53 = 235.0003, so there are 235 lunar months in 19 solar years, or at least close enough to that that it will keep your seasons in place. Then it's just doing the fenagling to figure out where to stick your long years in that cycle. In this case, there are 12-13 new or full moons in a given solar year. 19 X 12 = 228, so we need 7 13 month years somewhere. They need to be 2-3 years apart because we are falling a little more than a month behind every 3 years, so you try sticking 7 extra months in a 19 year cycle 2-3 years apart until you get a cycle that looks good and repeats. This same sort of formula could be used with different numbers stuck in, but there is going to be some trial an error no matter what. There is no formula, even for a particular calendar type, that will let you plug in numbers and spit out a calendar.

If I were to write this out in a semi-algorithmic way, it would be:

1. Select a solar year length, a lunar month length, and figure out how many months occur in a solar year.
2. See what the offset is between the number of days in the solar year and the number of days in the lunar year and see how many years it will take before you are a month behind.
3. Check (numYears X daysInYear)/daysInMonth for every value of numYears until you get a whole number (or really really close to a whole number). Now you have the number of months and years in your cycle.
4. Check numYears * monthsInYear to see how many months would be in your cycle with no long years. Whatever the difference is between that number and the result of the previous step is how many long years you need.
5. Try plugging in long years spaced according to the offset found in step 2 until you get a set of long and short years that has the right numbers of each, keeps its spacing, and repeats.

Note: Usually the intercal month falls at the same time every leap year but it doesn't have to. The romano-british Coligny Calendar, for example, alternates between intercalating at the start and middle of the year, so you can play around as long as your spacing falls within the wobble given by your offset.

Another note: As pointed out by @Nosajimiki in the comments, it's not entirely true that our calendar doesn't care about the stars, as the constellations are used as a reference point for tracking the sun's motion. I meant more that it's not sidereal in the sense of the egyptian calendar where you are tracking a star instead of the sun or dependent on moon phases like a lunisolar calendar. Solar calendars can be substantially more arbitrary than ours. The Greek State Calendar (distinct from the lunisolar planting and festival calendar), for example, just divided the year into ten 36 day months, with the extra 5 days being scattered differently in different places and times in their history, so that calendar really had nothing to do with the stars in a way that isn't really true for ours. Months are totally arbitrary and just meant to split up time.

@Nosakijimi also makes a good point in their own answer about lunisolar calendars needing knowledge of the solar year to come into existance, and so many cultures that use them also have a solar calendar. The fact that most cultures throughout history have used multiple calendars for different purposes is something I don't think I've ever seen reflected in fiction, so it would be kind of cool to see a diverse set of calendar systems all used side by side like various ritual, planting, and state calendars have been throughout history.

Solar calendars have the benefit of being much more precise, but they need specialists to produce since you have to precisely track the motion of the sun relative to the stars in the background while both things are spinning around you due to the rotation of the earth. Lunar calendars are easier to read. You just look at the phase of the moon to see what day it is and count the moons to see what month it is, but also less precise, both because of the day level resolution of the moon phases and the fact that your months are jumping back and forth due to lunar year offset and intercalation. Because of this, a lot of cultures will use lunisolar calendars for the masses while using precise solar calendars for people who can afford to have a calendar on their wall or lunisolar calendars for festivals and solar calendars for planning or lunisolar calendars in rural areas but solar calendars in the city and so on. Even in cultures that have dispensed with using the moon to keep time, it may still rear its head from time to time for historical reasons. Easter, for example, is timed based on a lunisolar framework even though we don't keep time that way any more because it's super old and the date was set back when we did. Thinking about which calendars might be used for which things, given the particularities of economic systems, class, culture, population distribution, and other such things in your specific fictional society, could make an interesting worldbuilding challenge that I don't think I've ever seen an author take the time to do before.

• "Our modern calendar doesn't care about the moon or stars at all" <- Actually, UTC which most countries now use is based on the Sidereal Year which is calculated from the position of the stars in the sky. Commented May 10 at 14:17
• That was probably a bad way to put it. I had just been talking about the egyptian sidereal calendar, which is an actual sidereal calendar that uses a star as its baseline for setting the start of the year rather than the sun or moon. Solar calendars that track the motion of the sun along the ecliptic, using constellations as reference points, isn't really the same thing. The point there was that some cultures looked at the moon, some looked at the sun, some even looked at stars, but you don't have to look at every celestial body you have to know when to plant grain. Commented May 10 at 14:26

## Tidra should not have longer months than Luna for orbital mechanical reasons

There is a relationship between how long a moon takes to orbit a planet, and how big and far away it is. For example, Luna is a very large moon compared to Earth. Most moons are not much bigger 1/100th the diameter of the planet they orbit; so, for Luna to be 1/4th of Earth's diameter makes it an extreme outlier. Infact, it is proportionally the biggest moon in the solar system by a pretty large margin; so, if Tidra takes up the same area in the night sky, it is most likely a smaller moon that is closer to Tempus than Luna is to Earth. Since closer moons orbit faster, and Tempus is a Super Earth meaning it has more gravity, your orbital period for Tidra should probably be shorter than Luna's not longer. 1-20 days would be far more likely than 30+. To make your months any more than about 30 days, you would need to actually have a binary planet, not a planet/moon system. That said, since you've not decided on the size of Enera in the night sky, other than it being smaller, that moon has a lot more wiggle room for what you want to do with it.

My suggestion for Tidra is to actually make it approximate a work week instead of a month, and to make Enera's month's something more reasonably divisible if you want to make some sort of Lunisolar calendar... that said, neither should be exactly divisible by a solar year.

## That said, most civilizations throughout history used Zodiac Months not Lunar Months.

The other big problem with your calendar is that you've made things evenly divisible. There should not a be an exact relationship between the orbital period of a moon, the rotation of planet, and the planet's orbital period around the sun. And for any semi-advanced civilizations, there should not be a relationship between months and lunar cycles except by coincidence. Here on Earth, a solar year is actually closer to 13 lunar months than 12, even though we say our 12 month system is based on the moon. This is because our 12 month system was never actually not based on the moon at all.

On Earth, we've divided our night sky into a number of constellations that just so happen to be close to lunar cycles. So, if you have a 500 day year you should not be basing the length of "months" on the moons at all, but instead on how many constellations can be seen with the naked eye. If your people can see more stars in the night sky due to either better night vision, or more actual stars, then your planet may have more months due to more recognizable constellations; if your people see less stars, then fewer months. This is why our own months are not all the same length, and don't actually line up with lunar cycles very well, because they originally corresponded to the alignment of the 12 Roman Zodiac constellations as seen from Rome, which are not all the same size. Because of this, it is very much possible to have a 25.63 lunar month year, but to only count 10-15 zodiac months. It is perfectly fine for these numbers to not be at all close, and in your setting, I would not expect them to be.

## But what about actual lunar calendars?

When civilizations do use lunar cycles as a means of measuring time, we've usually used them for sprints of time. Agricultural societies might say "we need to harvest in 2 moons" the same way a modern person might say, "the Taylor Swift concert is in 3 weeks." It's a nice and useful way to measure a chunk of days, but not something we base our annual calendars off of. As far as I can tell, every lunar calendar since the dawn of agriculture has actually been a Lunisolar calendar meaning that the moon cycle was in some way corrected for by measuring the solar year using the positioning of the stars or the shadow of the sun or the society kept parallel lunar and solar calendar systems the same way we keep years and weeks in a desynced parallel.

In short, if your people are exclusively using actual moon phases to track the passage of years instead of stars, zodiacs, or shadow length, they are probably still a hunter gatherer society. The only times people really use stand alone moon phase calendars in the past few thousand years is in almanacs to predict the rise and fall of the tide. Even most lunar holidays/ceremonies which take place at a certain phase of the moon are determined by a solar calendar, not by just counting lunar cycles. So the length of a lunar cycle is irrelevant for predicting a harvest moon. Likewise, the phases of your moons should be mostly irrelevant for annual time keeping.

• Zodiac months are for solar calendars. Commented May 9 at 22:20
• The modern gregorian calendar is solar so this is the most intuitive way for most modern people to imagine a calendar but lunisolar calendars have been in use throughout human history, and present something of an advantage for largely illiterate agricultural societies because you can tell what time of month it is by looking at the phase of the moon and the time of year by counting full or new moons, which is a lot easier for a subsistence farmer than tracking the motion of the sun along the ecliptic. Commented May 9 at 22:29
• @Jeremiah Not exactly because lunar calendars desync from planting cycles way too quickly to be reliable from year to year for planting. A solar year is about 12 2/3 lunar months; so, if a farmer starts to use a lunar calendar when he is 20, then by the time he is 30, he'll be off by an entire season making them useless for agricultural societies. Instead, what we often think of as lunar calendars are actually Lunisolar calendars that just measure sprints of time in months the same way we may talk about upcoming events in a measurement of weeks, Commented May 10 at 13:42
• @Jeremiah Agreed, I actually updated my answer to reflect this more clearly before you even commented. Commented May 10 at 15:04
• The point in your update about side by side solar and lunar calendars and lunisolar calendars being used for sprints of time is one that I kind of wish I would see more in fiction. If you looked at ancient greece, for instance, they had a 365 day state calendar so political wonks could set up meetings for precise days, but a greek peasant wouldn't know exactly what day it was. It would just be the middle tenth of Thargelion. I don't think I've seen these sorts of class differences in timekeeping in a fantasy book. It's always the 14th of the Month of the Hydra, and everyone just knows that. Commented May 10 at 15:21