# If a planet has 3 moons, is it possible to have triple Full/New Moons at once?

In the story I created, the Kingdom of Oneirou has 3 Moons--Artemis, Rahu, and Zorya--all of which have their own independent lunar cycles.

However, it's officially stated as early as Chapter 2 or 3 that, once a year [each], all 3 Moons' phases are synchronized to Full Moon and New Moon. Let's say, for the sake of argument, that all 3 (while operating on their own separate lunar cycles) still follow the same 30~ days to complete one full cycle.

If we pretend that Oneirou still has the same 365 days = 1 Year like Earth, is this possible? If both events are not possible within a 365 day period, then how long would their year have to be extended to account for this?

• It is not only possible, it is logically necessary. Any three numbers have a least common multiple; as a consequence, there must be occasions when all three moons are new of full at the same time. Whether those occassions occur once per year or once per decade or once per century depends on the orbital parameters; it's your world, you pick the parameters. – AlexP Apr 26 at 14:50
• @AlexP: That's not true, as pointed out by L.Dutch below, using the real-life example of the inner three Galilean moons of Jupiter. All you can prove is that the moons will eventually (approximately) return to any configuration they've been in before. There's no guarantee that all three lining up on the same side of the planet is part of the accessible state space of the system. (Also, your mathematical claim isn't quite correct, either: for example, what's the least common multiple of the numbers $7$, $\sqrt2$ and $\pi$?) – Ilmari Karonen Apr 26 at 15:13
• @IlmariKaronen: 5859, within ±0.1. – AlexP Apr 26 at 15:59
• Here is a picture of three of Jupiter's moons casting shadows on the planet (which makes them new moons) at the same time. So it is quite obviously possible. – AlexP Apr 26 at 16:07
• @AlexP: As I already pointed out below, the moons casting shadows on Jupiter in that picture are Io, Europa and Callisto. The moons locked in a mutual resonance are Io, Europa and Ganymede. There are no pictures of these inner three moons simultaneously eclipsing Jupiter, and due to the resonance there never will be. – Ilmari Karonen Apr 26 at 16:45

You can get orbital resonances like those exhibited by Ganymede, Europa and Io around Jupiter.

an orbital resonance occurs when orbiting bodies exert a regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers.

However, that doesn't match what you are asking.

all 3 Moons' phases are synchronized to Full Moon and New Moon

when a conjunction happens, it's either Full Moon or New Moon or whatever phase it is, but it cannot be more than one in the same cycle. Moreover, for the Ganymede/Europa/Io system there is never a triple conjunction.

all 3 (while operating on their own separate lunar cycles) still follow the same 30~ days to complete one full cycle

if they have the same orbital period, they orbit at the same distance. So, either they are the same body, or they are going to become one very soon. As you see from the resonance, the periods are different.

To have more bodies sharing the same orbit, there must be one significantly more massive than the others, and the smaller one have to be in the lagrangian points of the large one. But then they won't have a simultaneous phase.

• Could you have 3 moons equidistant around a planet, in the same orbit? I doubt it would fix anything, but it naively seems reasonable... – Matthew Apr 26 at 11:54
• @Matthew you can have two in a horseshoe orbit, but then you have no conjunctions - instead they just drift slowly to about pi/3 apart, then begin drifting away from each other again. If two moons have the same orbit and they get in conjunction, they become a single body. – John Dvorak Apr 26 at 12:40
• No idea if you can get six moons orbiting in each other's L3 and L4 points, but you can have one large moon shepherding two small moons in its two stable Lagrangian points. Not what the asker wanted, but still a cool system. – John Dvorak Apr 26 at 12:43
• @AlexP: The Laplace resonance between Io, Europa and Ganymede is exact, at least on average, because it's stabilized by gravitational interactions between the moons. If they start to drift out of the resonance, they get pulled back in. As for the article you linked to, the third moon in that photo is Callisto, which isn't part of the resonance, not Ganymede, which is. – Ilmari Karonen Apr 26 at 15:29
• The time between New Moons on Earth isn't Moon's orbital period because the Earth is also going around the sun, so there is a small shift. If the sidereal periods of three moons have an integer ratio, that isn't true in the orbit relative to the sun (synodic periods) anymore. – JiK Apr 26 at 15:58

This might fit your description: a 1:3:5 resonance.

Near moon: new on day  3 9 **15** 21 27, full on day 6 12 18 24 **30**.

Middle moon: new on day 5 **15** 25, full on day 10 20 **30**.

Far moon: new on day **15**, full on day **30**.


So: not all planets are having all their special phases on the same day, but there are days they're all having the same special phase.

I'm just a lowly software developer and don't know if a 1:3:5 resonance would be stable.

It's a question of interpretation whether a cycle need have one time around, or could be allowed more. For instance the full "Otto Cycle" in an internal combustion engine is actually two revolutions. Various climate cycles and orbital cycles, precessions of the earth's axis etc. are discussed in terms of many years.

Your mention of the 30 days period is under the rubric of "for the sake of argument" so I'm thinking it may not be central to your question.

• A 1:3:5 resonance can be stable, but I'm pretty sure that one that also has a triple conjunction is unstable. – Mark Apr 26 at 22:20
• This seems like the most feasible way to produce the convergences that the question mentioned. However, (and I may be mistaken), wouldn't the convergences drift with respect to the solar year? For example, a quarter-year after a triple full moon, the next time the moons are at the same phase will be triple half-moons, because the sun's position relative to those moons has shifted by 90 degrees. – Gilad M Apr 26 at 23:49
• cool point Gilad! If it's critical to be triple new and triple full the entire year around, then what if the orbits weren't 6, 10, and 30 days exactly, but 6 and 10 days minus (or plus?) one day a year? Granted that wouldn't persist over many millions of years, due to resonance, but it not inherently unstable in terms of satellites being flung out of the system or crashing into the planet. Instead, the orbits just very very very slowly adjust into a resonance. (Earth's moon will eventually be geosynchronous but needs another billion or two years, a similar effect, but the orbit's safe now) – Swiss Frank Apr 27 at 13:19
• OTOH, if there is only a triple new-moon once a year, that too would be a cool reason for a massive religious cult outpouring of some sort. (A triple full isn't going to be quite as easy to make out: a 97% lit moon can easily be mistaken for 100%, while 0% and 3% are utterly different.) Think about that: only one day a year ALL the moons disappear... – Swiss Frank Apr 27 at 13:20

You say they all have the same 30 day cycle, but separate cycles? They must then have separate phases, like a 3-phase electric generator.

https://en.wikipedia.org/wiki/Three-phase#/media/File:3_phase_AC_waveform.svg

Half the moon is lit at any given time.

In a new moon, the lit half is facing fully away from the planet (or close enough the sliver is pretty minimal). For this to happen monthly, this requires the moon's orbit be nearly coplanar with the planet-sun orbit.

If the moon is entirely coplanar, you'll get a solar eclipse every month. So the orbit may be slightly off coplanar like Earth's moon; that will make new moons common, but solar eclipses rare. *But they aren't really new moons then, since there is a thin wedge of lunar surface exposed to the sun and visible to the planet; they're more like 95% new moons. You'd need to declare a threshold of "good enough".

In a full moon, the lit half of the moon is facing "nearly fully" toward the planet, so the sun, planet and moon are in a row, in that sequence. But not quite that way; after all, that would be an lunar eclipse!

Again, the orbit may be slightly off coplanar, and it would need to be if you don't want a lunar eclipse every month. But again, *they aren't really full moons then; they're more like 95% full moons. Again a "good enough" is required.

"All full moons" mean all the moons are on the far side of the planet from the star, in the "good enough" zone.

"All new moons" would mean all the moons are between the planet and the star, again in the "good enough" zone.

We can't say definitively what's possible on your world because you have to define what you call "good enough". But possible? Sure. If you declare 10% of a moon's arc to be "new moon", then unless some other mechanic occurs controlling the moons' motion, you'll have triple new moons 0.1% of the time and triple full moons 0.1% of the time.

As stated by others, about the same period implies about the same distance, which makes the system with synchronized moons' phases unstable. This leaves you no good choices, but you may be able to sidestep it somehow, for example, by explaining why the equality of inertial and gravitational mass does not hold for the moons.

Without this equality, their distances can be different and the unstability gone. Following this idea may be pretty hard, unless you're into hard sci-fi.

You can't have the same period. If it's the same period, then whatever the visual angle between them is initially is the angle forever.

You probably can't have a small difference in periods. They tend to be unstable.

A 1:2:4 resonance and a 1:3:5 resonance may work. But having the same phase, means that planet, moon 1, moon 2, moon 3 will have to be close to a straight line. To be also either new or full you have to have the sun in that line too.

Lets assume that being within 10 degrees counts as 'being in phase' (The difference between phases of the moon changes 12 degrees a day)

Let's use the 1:2:4 resonance, and we'll make the periods 1 week, 2 weeks and 4 weeks. So the outer moon has about the same period as Luna. If the resonance was perfect, they would all line up once a month. Whether it was a new or full moon depends on the relation between the orbital period of Outer compared to the year. If the relationship is not a resonance, then on the average 1/36 (360 degrees / 10 degrees) of the lineups will also be either new or full.

However the lineups will not be distributed well. They may be an average of every 3 years, but you might get 3-6 in close succession with half a year between them, then go 10-20 years between them.

There would be a pattern to it. The 10 degree limit means that lineups would take whatever time it takes the fastest moon to move 10 degrees. So 1/36 of a week. A few hours. If the year were 10 months long then the lineup from one month to another would move 36 degrees across the sky.

Remember that only half the lineups will be visible. The other half will be on the back side of the planet from any one point.

It's unlikely that the resonance will be perfect, so you may get long periods where there are no lineups.

As an aside, search this site for "Can a planet have multiple large moons" I asked that question some years ago both here, on physics.SE and a couple of physics forums. The upshot is, "No, it's unstable." and one moon either gets ejected, hits the planet or another moon.

If any of the moons rotate on there axis, the numbers of full moons could increase. The sizes of each moon can change the amounts of full moons.

• Welcome to the site Charles Archer, when you have a few minutes, please take the tour and read up in our help center about how we work: How to Answer. At the moment your answer is very short and quite unclear. Can you edit it to explain what you mean by suggesting that the number could increase because of rotation? Also it's not clear what you mean by the sizes of the moons changing the ammounts of the moons. Answers here are expected to be clear and authoritative, so editing yours to fit would be much appreciated. – Confounded by beige fish. Apr 26 at 18:43