# How would a Lunar Calendar be set up with 2 moons?

So I have a super-Earth that has 2 moons. Moon 1 is a bit smaller than our moon, and has an orbital period of 19.25 earth days. Moon 2 is larger than our moon and has an orbital period of 147.15 days. A year on the planet itself is about 708.5 days (similar to Mars, actually) if it helps. I was thinking a lunar calendar would be easiest, but I'm not sure entirely on how to set it up. Would it follow the first moon or the second moon? How long would the weeks/months be? I've been entertaining a few ideas, but I'm not sure what would make sense, so I'm hoping you guys could help.

If I've missed anything, or if this isnt the right place for this question, please let me know :)

• Most of the questions you ask seem to be cultural, and generally opinion-based. You are used to weeks-months-years that you have known all your life, and certain cultural conveniences (market day, monthly rent, annual tax returns) are built around them, but there is nothing inherently special about them. Such cultural conveniences can be built around any particular grouping of days - week-equivalents can be 5 or 10 days, month-equivalents can be 20 or 40 or 60 days, year-equivalents can be 250 or 500 or 709 days. – user535733 Feb 7 '18 at 0:50
• A lunar calendar may be the first one to be developed, but it works only in cultures inhabiting an environment without seasons. Arabs, for example. Otherwise, the importance of the solar year is overwhelming. That's why in the end all the other cultures on Earth used various contrived mechanisms to synchronize lunar cycles with the most important solar cycles, and in our own calendar the lunar cycles were lost altogether. – AlexP Feb 7 '18 at 0:54
• Define those moon's masses. It may be that this system is unstable, so realistically you might never have to worry about having two moons. – Renan Feb 7 '18 at 3:10
• Oh trust me, I already did lol. I know the masses, density, radius, eccentricity, and a bunch more info. – Redwolf Feb 7 '18 at 3:23
• By my rough calculations, the two moons would actually line up with each other at approximately at the same interval as our current lunar month. It is highly likely that this would be used. If this was taken as their 'lunar month', this would give them roughly 25 lunar months in their year. This would have to be useful in some way, though. There is no information regarding who or what might live on this super-earth and measuring time, in any way, may have no use to them whatsoever. – Lee Leon Feb 7 '18 at 17:07

The simple answer is to do a calendar for both moons and then choose the lunar year that fits closest with the solar one. For longer ages you can have it as the time between a double eclipse (where both moons line up with the sun).

• The mystically-minded will love looking for the endless nonsensical "relationships" between the various calendars. Poor werewolves will have a rough go of it, though.... – user535733 Feb 7 '18 at 0:45
• I don't understand you.... – skout Feb 7 '18 at 0:48
• I am agreeing with you (and upvoting) – user535733 Feb 7 '18 at 0:53
• I like the two calendars idea proposed by @user535733. Perhaps competing factions would each have a favored calendar, much as some countries like Iran hold to their own ancient calendars. – Willk Feb 7 '18 at 16:10
• Will, he didn't propose it, if he did it was in a very mystic and roundabout way. You proposed it. – skout Feb 8 '18 at 3:34

TwoThree ideas: i) a specific one (orbital resonance) and ii) a more general one (with the calendar itself), and iii) a play around with a possible calendar

An interesting idea to explore is both satellites to be in some kind of orbital resonance, meaning that the periods of both moons are related by a simple arithmetical ratio (1:2, 2:3, 2:5, etc.).

Said ratio is not necessarily exact at every point in time, but in the long term. The periods you suggest could be compatible with a 1:7 or 1:8 resonance, if such a configuration is stable (I don't know).

The phenomenon is pretty common in the solar system and has been observed between exoplanets too.

For example, you could have long and short months. The former could look more like seasons and/or the latter could resemble weeks, it's up to you.

Anyway, with the periods you suggest, your year could be made of five long months and every long month made of seven or eight short ones. The ancients tended to have little problem with months or years having variable lengths, as long they remained stable in the long term and periods were divided in an integer number sub periods (this integer number could vary —usually by one—from one super period to the next). Your five "long months" are slightly (about 27 days) longer than a year, meaning that you'll need a four-long month-year every five regular years or so.

Re: the naming of the months, bear in mind that the word month itself derives from Moon (just as in other languages), so you can get as creative as you wish to name them (actually, I'd advise against calling them months or weeks, except maybe when explaining the concept). Proper names of long months could be aligned to an adapted set of seasons. Short month names could be ok with numerals (something like "the fifth shimi of the borth of Sommerish.)

Update: There's a proposed calendar:

Let's stick to the name borth for the long month and shimi for the short month in the following.

It turns out that the lengths of your year and Moon 2 cycle (borth) make for a nice ancient-looking lunar calendar. Specifically, 27 solar years ($$27\times708.5=19129.5\,$$d) correspond to exactly 130 borths ($$130\times147.15=19129.5\,$$d.)

This allows to build a stable 27-yr cycle of alternating 4- and 5-borth years. Namely one short (4-borth) year every 4 or 5 long (5-borth) years. For example:

• 5 long years ($$5\times5=25$$ borths)
• 1 short year ($$4$$ borths)
• 4 long years ($$4\times5=20$$ borths)
• 1 short year ($$4$$ borths)
• 4 long years ($$4\times5=20$$ borths)
• 1 short year ($$4$$ borths)
• 5 long years ($$5\times5=25$$ borths)
• 1 short year ($$4$$ borths)
• 4 long years ($$4\times5=20$$ borths)
• 1 short year ($$4$$ borths)

This totals exactly $$25+4+20+4+20+4+25+4+20+4=130$$ borths and $$5+1+4+1+4+1+5+1+4+1=27$$ years.

Assuming a circular orbit (equal season length) and arbitrarily choosing the Winter Solstice (just because) as a reference point, the following figure illustrates a possible resulting lunar calendar. Each row is a year, with each borth in a different color. (Dark) red is the 5th borth in the year, and can be seen not to occur in every year (sorry for the size).

The first borth of the year roughly corresponds to winter, the third nearly every year includes the longest day, etc. Hence you can pick names in their language that make reference more or less to seasons.

Your peoples will be celebrating the New Year up to half a borth before or after the actual date, but no more than that (this is what happens with lunar calendars).

Unfortunately, the shimi doesn't fit so nicely with the other two cycles: The shimi-year cycle would take 77 years, and the shimi-borth cycle is even longer, it would take thousands of years for all the three to repeat exactly. My advice here is to look at what we (contemporary folks) do with weeks and months: just choose to what borth a shimi belongs if it overlaps with two of them and call them using ordinal numerals. Just as some call it the first week of August starting on July 28, You'll have the 1st through the 8th shimi of every borth and everyone will get it.

The most important thing to recognize is that there is no one best answer. Different societies will have different calendars, just as they have on Earth. If your planet has a global industrial civilization like ours, then it's reasonable to assume that one calendar has become dominant, but it's not reasonable to assume that the dominant calendar is the most sensible one. There are a lot of accidents in history.

If your setting is pre-industrial then you have a great opportunity for different societies to have different choices about which moon, if any, drives the calendar.