# Calendar with seven magical moons

My magic system is dependent on the moons; whichever moons are in the sky dictates what magic you can use, so the moons and their places in the sky are very important.

The problem is, there are seven moons. 1 moon orbits twice every day, another once every day, 2 at once every 6 days, 1 at once every 26 days, 1 at once every 18 days, and 1 at once every 3 days.

How can I create a simple calendar so that I can keep track of where the moons are when (moon phases don't matter)?

• What do you mean by simple? The easiest way, in my opinion would be to just list how many days since the designated starting position has passed. Something like iuo 1, selune and tryrean 3, prima 13, matra 2. – cHARLES cHESS Feb 2 at 23:23
• Are you asking how you, the author, can keep track of the many lunar positions, or are you asking how people in your fictional world might devise calendars to keep track of their many moons? – Sal Feb 2 at 23:54
• Are those resonant orbits? – rek Feb 3 at 0:10
• Why would the calendar be based on all of the moons? Just base your month on the longest orbit such that every month has 26 days. Let the other moons enjoy their stroll across the sky without any special attention from your characters. – Henry Taylor Feb 3 at 0:14
• @Sal, I'm asking how I, the auther, can keep track of lunar positions. – Just an enby Feb 3 at 0:25

You're describing a 1:2:6:12:12:36:52 "Laplace resonance" There are lovely systems with orbital resonances in real life.

The calendar you need must be based on the least common multiple of these numbers. So we factorize each one: -;2;2x3;2x2x3;2x2x3;2x2x3x3;2x2x13. Now we string together enough factors that each one has enough pieces to work with, which is to say 2x2x3x3x13. So our LCM is 36x13 (we could have seen everything but 52 will evenly divide 36). That means the calendar is 468 periods long, where the period is half a day. So it's a 234 day calendar. Makes sense to split it into 13 months of 234/13 = 8 days, no wait, make that 8 months of 13 days. Each month starts with the 26-day moon getting to one end or the other of its orbit. The daily and twice-daily moons don't need a calendar.

The 3, 6, and 18 day moons don't fit the calendar neatly, so so need either a week or a "fortnight" of 18 days, call it an "eightnight" (the apostrophe for 'teen' in there isn't written, I dunno why). Okay, so the eightnight is longer than a month, that's a trouble. Maybe have a thirtnight and an eightnight and not say which is the week and which is the month, or give them different names; you could almost use an Earthly precedent.

When to start it depends on conjunctions - what's the most interesting? With a 3, 6, and 18 day cycle, the three moons could line up at once, or the 6 and 18 might line up and every time the 3 is skewed to the side. Similarly with any of the others. But once you have a most interesting day, the thirtnight and eightnight counts start from that, with the whole thing repeating in 234 days.

• Around Saturn, Tethys, Telesto and Calypso all have the same orbital period. So do Dione, Helene, and Polydeuces, because in each triplet, the latter two occupy the L4 and L5 Lagrange points of the former's orbit. – notovny Feb 3 at 1:27
• D'oh, I should have remembered this. The L4 and L5 points aren't relevant because the moon would stay fixed in the sky and have an orbital period equal to the year. But Saturn has Janus and Epimetheus which do have the same overall orbit and period by periodically swapping position. (They are sort of in orbit around each other, but do so within a giant horseshoe around the planet) There would be strange, subtle variations in relative placement that I think are beyond the level a calendar would match. Good point! – Mike Serfas Feb 3 at 1:41
• Telesto and Calypso are in the L4 and L5 points of Tethys' orbit, so they all have a 1.887 day orbit around Saturn, and aren't fixed in the Saturnian sky. Similar with Helene, Polydeuces, and Dione (2.74 days.) Objects in the Saturn orbit L4 and L5 orbits wouldn't be fixed in the Saturnian sky either, but those objects wouldn't be moons of Saturn. – notovny Feb 3 at 10:34
• Well, I could have thought about that one a moment ... yes, one moon could be in the L4/5 point of another moon. And yes, by "fixed" I was thinking relative to the planet-star axis, not the sky. Still, I at least prefer the Epimetheus example, and looking it up Ethan Siegel seems to cast aspersions on long term Trojan stability. – Mike Serfas Feb 3 at 12:00

Here is a Excel table for the slow moons. I have made an executive decision to change the 26 day moon to a 27 day moon because otherwise it would take forever for them to all get back together.

I have divided your planet into 27 zones. You can think of them like time zones. Divide the 27 zones by days to orbit the earth to figure out how many zones each moon jumps forward each day. 27 day obviously is 1 zone each day. 18 day jumps 1.5 zones. 6 day jumps 4.5 zones. 3 day jumps 9 zones. It takes 55 days for the slow moons to all be in the same zone again.

Of course the 3 day moon does not teleport from zone 1 to zone 10. It crosses over zones 1 thru 10 in the course of the day.

If you don't have excel you can make a paper table and just do the additions by hand.

### 26 day months. 6 day weeks.

Get rid of Sunday, and make your months 26 days long.

• 2 times a day.
• (Eg Peaks at 4am and 4pm)
• one once per day,
• (eg every night at 8pm)
• two have weekly orbits.
• Eg one peaks Tuesday 11pm
• the other Saturday 3am
• one monthly
• (eg peaks on the 4th of the month at 1am)
• one 3 weekly
• (peaks at 2pm every 3rd tuesday)
• one peaks twice a week
• (2am mondays and thursdays)