Moons cycle

[Crow_Nightfeath]

So my brother and I are building a world with two moons, they orbit at different rates one orbits like earth's moon going through a cycle roughly every 29 days, the other one is on a 91 day cycle. The planet, called Bob (cause we can't agree on any other names, and it's a Titan A.E. reference), goes around the sun at a 365 day cycle. (We wanted to keep everything pretty close to earth's because it's simpler math.)

So the question I have is how does a double full moon work, or would it end up being an eclipse or what?

[Yora]

A 29 day cycle and a 91 day cycle mean that one moon is much farther away than the other, which is good to make the orbits somewhat plausible. The moon with the longer period should look significantly smaller in the sky, so it should easily fit behind the nearer moon, making eclipses possible.

However, eclipses would probably be very short. I wouldn't think more than a couple of minutes. And if the orbits around the planet are exactly on the same plane, one would happen probably every 32 days or so. (If you really need it I could calculate the exact interval for you.) Technically speaking, full moon is just a single moment every month where sun, earth, and moon are perfectly lined up, but the movement of sunlight over the moon is so slow that the moon looks full from the Earth for a whole night or two. At a 91 day cycle, this would probably be more like 5 days or so.
Since you can have full moons for a whole night and the eclipse would only last for minutes, having both in the sky is not a problem. It might even be possible that for people near the poles the eclipse isn't even a full one if the orbits aren't perfectly flat.

That being said, while two full moons are possible, it would be quite a rare event. The perfect alignment would happen only once every 29*91 days, which is 2639 days, so about every 7 Earth years. But the smaller outer moon should be looking close to full one month before and after that. If the orbits of the moons are not flat (which I think is quite likely for a rocky planet) a full moon eclipse would be even considerably rarer than that.

[Crow_Nightfeath]

Oh cool thanks, yeah I'm not great at astronomy. And I couldn't find anything about it through Google.

[Crow_Nightfeath]

Except I know it would happen more often then that using D&D rules for full moon, in D&D a full moon with the normal moon lasts 3 nights, and we wanted the other one to last about a week, which is pretty close to the 5 days you were saying. So there is a lot more chances of them happening at the same time.

[Yora]

That's true. I think saying a double full moon happens for at least one night every two or three years would be very plausible.

[Crow_Nightfeath]

Yeah though from several tests I've found it happens every 1-3 years. I've yet to find a 3 year gap, but I'm not counting the possibility out.

[the_david]

How badly do you want your lunar cycles to be 29 days and 91 days? And how badly do you want your years to have 365 days?
You see, months are derived from our lunar cycle. (Well, not anymore but there used to be a time when a month had 29 days.) If the same goes for your setting than your year would have 12.6 months per year. (Or 4.01, depending on which moon you prefer.) You might want to either adjust the number of days per year, or the number of days per month.

Here are a couple suggestions:
- 364 days in a year, 13 months of 28 days each. A week would have 7 days and a month would have 4 weeks. This would also mean that new moon and full moon would always be a monday/moonday/whatever. Unless you really want 3 days of full moon, than you've got to think of something else. It would also mean that both moons could be full once a year. (Or never. That's also a possibility.)
- 360 days in a year, 12 months of 30 days each. Weeks don't line up as pretty, but if you'd change the other lunar cycle to 90 days you could have both moons full once ever 3 months. If you actually want to use a calender in game than you're better off with something as close to ours as possible as it would be easier to compare with our year. A calender having 12 months helps a lot.
- The 3 days of full moon thing isn't a hard rule. It works in most settings, but for some settings you might want to change things up a little bit. Consider that the slower moon could be full for a longer period than the faster moon. This might mean that lycanthropes only become active for 1 night under the faster moon, and 3 (or more) nights under the other moon. Or they only change under the faster moon while the slower moon has some other effect.

[Crow_Nightfeath]

I've actually already got the year broken into various months, 13 of them, each named after one of the 13 major gods, with varying days based off a tier system of how powerful the god is compared to the others.

[jqavins]

- 360 days in a year, 12 months of 30 days each. Weeks don't line up as pretty...

If weeks are seven days. Weeks of ten days (as one friend of mine made his world) or five or six days line up just fine.

As for three day full moons, the plausibility of that depends one just how close to full is close enough. In the real world, if the exact moment of a full moon is at exactly midnight on some day, then most people glancing at the mood on the night before or the night after are liable to call it full; the full moon lasts for three days to the casual observer, but not to one who looks carefully. On the other hand, half way around the world, the exact moment happens at noon; the moon would look full the nights before and after, so the full moon is two nights to the casual observer, but gets skipped if you look carefully enough.

As for eclipses, they would probably be quite rare. Think about lunar and solar eclipses here on Earth. A full moon happens when the moon and sun are on opposite sides of Earth; if Earth's orbital plane (called the ecliptic) around the sun were the same as the moon's orbital plane around the Earth then every full moon would be a lunar eclipse. And likewise, every new moon would be a solar eclipse.

These eclipses happen only when a full or new moon occurs at the same moment that the moon is crossing the Earth's ecliptic. Lunar eclipses are more frequent because the Earth casts a larger shadow than the moon does.

In the fantasy world, inter-lunar eclipses (when the faster moon passes in front of the slower one) would, likewise, happen only when the two cross the same longitude at just the moment when one is crossing the other's ecliptic. The do't have to be full, new, or any other particular phase, but they will have the same phase. Dark eclipses, when they both pass through the planet's shadow at the same time, would be even rarer, naturally, since they require that both moons are full and both cross the planet's ecliptic simultaneously. Yora noted that her (I think?) numbers assume the two moons have the same ecliptic plane and that eclipses would be less common if they don't, and they most likely wouldn't; I wish to amplify that. Pretty much no two objects in the solar system have the same ecliptic. Everything's orbital inclination is pretty much random, so the two moon's sharing one would be astonishing unless a god decided to force it. My gut feel is that eclipses would happen only once every few decades or more, and dark eclipses would be only every few centuries.

You might be able to find data for moons of Jupiter or Saturn. Pick two good sized ones and see if you can find how often one eclipses the other, and how often they are simultaneously eclipsed by their planet. It should happen in your fantasy world more frequently of your moon's periods are shorter than those of the Jovian or Saturnian moons (and less frequently the Jovian and Saturnian moons are faster) and also less often in proportion to the ratio of your planet's size (the same as Earth, I presume?) to Jupiter's or Saturn's.

EDIT: I figured out an easier way to estimate it.

Our moon is eclipsed by the Earth, partially or totally, about one and a half time per year on average. If we had a second one with the same frequency of eclipses then they would be eclipsed on the same night about once every 158 years. I also suspect that the one orbiting slower would have proportionally fewer eclipses of its own, so the co-eclipse period should about 158 years times 91/29, which is 495 years.

[Yora]

7 day weeks make sense at a 28 day month. If your lunar month is 30 days, then 5, 6, or 10 days per week make much more sense.

I use a 16 day month, which is so short I don't use weeks at all. If I have any effects with durations of weeks, I use 8 days for each interval.

[jqavins]

My friend has 30 day months, divided into 3 ten day weeks. He also has two moons; one has a 30 day period, and the other I don't remember. You'd expect it would be 10 days, but I think it's five. But then why not 6 weeks of five days in each month?

Also, he has a 364 day year, with one day each quarter that is not counted as part of any month or week. Naturally, these are holidays and party days. But how do they work with the moon cycles? I've actually never thought to ask him until now, and I don't know if he's ever thought it through. (The longer moon could easily have a 30⅓ day period and the other 10¹/₉ days, so the extra days are like lunar leap days to set the months and weeks back in sync. But I don't know if "how it could be" is how he's decided it is.) No such perfect ratios of the moon₁, moon₂, and planet orbits should be possible without outside intervention, but this world has pretty active gods, so that's OK.

[lightningcat]

Are there astrological generators that can handle multiple moons that you guys are using, or is this old pen and paper math?
Asking because I have a (mostly dead) campaign with 4 moons.

[jqavins]

Are there astrological generators that can handle multiple moons that you guys are using, or is this old pen and paper math?
Asking because I have a (mostly dead) campaign with 4 moons.

Speaking for myself, but I'd guess it's the same for Yora, it is simple least common multiples with some ratiometric scaling. Back of the envelope stuff. Probably there are better astronomical calculators out there that would do it, if one wants to search for them. As for astrological generators, I guess those are likely out there too, but beware astrological woohoo crowding out the science.

[lightningcat]

I meant astronomical, but I should have been sleeping instead of playing on the internet. But for some reason, you people are just too entertaining.