Is This Lunar Arrangement Astrophysics-Compatible?

[The Glyphstone]

For my current world-building project, I've finally settled on some details about the world's surroundings, and I'm curious if astrophysics will permit the setup I've envisioned - plenty of 'shut up its magic' options available if the answer is a flat 'no', though.

As concisely as possible, the planet has five moons, or what look to be five moons, but only two of the five are visible in the night sky at any one time. The lunar cycle has one moon - Moon A - visible for a period of 25 days, then for the next 25 days it gradually wanes as Moon B waxes, until only B is visible for 25 days, repeat for C-D-E-A-etc.

Can a situation like this be approximated using real stuff in space? The only crucial thing is what it looks like from the surface, so the actual nature of the 'moons' doesnt mandate they be orbiting the planet directly for instance. I dunno.

[Grey_Wolf_c]

For my current world-building project, I've finally settled on some details about the world's surroundings, and I'm curious if astrophysics will permit the setup I've envisioned - plenty of 'shut up its magic' options available if the answer is a flat 'no', though.

As concisely as possible, the planet has five moons, or what look to be five moons, but only two of the five are visible in the night sky at any one time. The lunar cycle has one moon - Moon A - visible for a period of 25 days, then for the next 25 days it gradually wanes as Moon B waxes, until only B is visible for 25 days, repeat for C-D-E-A-etc.

Can a situation like this be approximated using real stuff in space? The only crucial thing is what it looks like from the surface, so the actual nature of the 'moons' doesnt mandate they be orbiting the planet directly for instance. I dunno.

IIRC (and I probably don't), orbital periods are directly related to the radius of the orbit. So for every Moon to have the exact same periods, they'd all need to be in the same orbit, possibly in the Lagrange points. I think those allow up to 6 stable points around the orbit, so, maybe? Although I think that 3 would be visible at some points?

It'd take magic to get all the moons to those positions, I suspect, but they should be stable enough for a few human lifespans.

Grey Wolf

[Lord Torath]

Aren't the Legrange points "stationary" with respect to the sun and the planet? In which case, the moons would not go through phases at all.

Grey Wolf is correct that the orbital period (and thus the length of the moon phases) is determined by the orbital radius (and the mass of the body being orbited, but in this case they're all orbiting the same body). So if you want all these moons to have the same duration of phases, they're going to need to share the same orbit. If each body has a 50-day "lunar" cycle, they'll each be about 10-days (72^o) apart in their orbits. So at any time, you'll have 4-5 moons visible to the planet (depending on whether or not a moon is currently "new", and thus the near side is completely in shadow), but only three will be visible at a time to someone standing on the surface of the planet. Unless they're at one of the poles.* Then they'll be able to see all of them (again, assuming none of them are "new").

I think it could be stable until something else interferes.

Edit: Playing around with layouts, it looks like you'll have 2-3 moons visible at night. The other moons will be in the daytime sky. If one moon is full, the two to either side will just be visible near the horizons. Really, whenever you have one moon directly overhead, the two to either side will be visible, yes, even during the day. When you've got a moon directly "underfoot", you'll only have two moons visible above you.

* Okay, it's not really the poles, but it's the point where the axis of the moons' orbit passes through the surface of the planet. If the moons orbit along the equatorial plane, then those points are the poles of the planet.

[jayem]

You can of course see our moon for most of it's orbit. So in the pentogram case you'd see two very cresent moons at miday (one rising then sinking), as afternoon draws on a near half moons would become peaking sinking at midnight. At which point the full moon will be visible along with the rising other near half moon, and then as the full moon sinks the first cresent rises.

Spoiler: For a nearer single moon visible case

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Ignoring the stability issues, you are looking at 5 copies of an orbit where each moon is sunside of the planet for 100 days and spaceside of the planet for 25.

This means that you want roughly the area sunside to be four times the area the other side (Kepplers 2nd Law). By eye, I'd guess that you'd want the maximum distance to be about twice the minimum distance. This will still have a bit of overlap, the further you take it away the longer the new moon phase is.

You want it's period to be about 5 times the length of the moon. So it's average distance needs to be about three times the size of our moon (Keppler 3)

So far so good. Except during the eccentricity is (I believe) in the Suns frame of reference. So if you get this effect in Winter then in Summer you will see 4 nearly full stationary small moons and one new moon invisible.
This might be something you can ignore if you are good at bluffing.

_________
The lagrangian points with respect to (earth+moon) are in the suns orbit. The lagrangian points of the moon round the earth are in the moons orbit.
The stability isn't such an issue if the moons are relatively small (such that their interactions could be neglected).

Larger you would need to place in Langrangian orbits to be stable. This would allow a stable double moon situation. Either a semi-stable (but easily understood) moon and anti-moon, or moons in each others L4 and L5 position.
If you had 6 moons you could have them in pseudo-lagrangian points. Moons 3 and 5 are not in lagrangian points with respect to Moon 1, and so will not be stable*, but some of this might be offset by their relationship to Moons 2&4 or moons 4&6. If you have enough "A wizard does it" points...

*The anti-moon situation is not stable in that any movement will make it fail. This is already failed.

[Jay R]

Aren't the Legrange points "stationary" with respect to the sun and the planet? In which case, the moons would not go through phases at all.

First of all, we are only talking about the 4th and 5th Lagrange points: L4 and L5. L1, L2, and L3 are very different.

The earth-sun Lagrange points are stationary with respect to the sun and earth. They are 60 degrees in front of and behind the earth in its orbit around the sun, and would always show a gibbous (large-than-half-lit) phase from the earth.

But the earth-moon L4 and L5 are 60 degrees in front of and behind the moon in its orbit around the earth. They would have phases just as the moon does -- one of them 5 almost 5 days ahead of the moon, and the other 5 days behind the moon.

These are only stable equilibria if the small moon is less than 1/25 the mass of the moon. [And even then, the sun's gravity makes it very complicated.] If I were using a Lagrangian moon in my world I would ignore that fact, either because magic affects it, or because the laws of physics are different.

[In one game I ran, Lagrangian points were not possible, because it was a Ptolemaic universe with the Earth at the center of the universe, and the planets (which included the sun and moon, in circular orbits with epicycles.]

[The Glyphstone]

I can definitely work with the five moons spread equidistantly, giving 3 visible on the night-side at a time and 2 on the dayside. 5 and 3 are already written in as meta-cosmically significant numbers for the setting, so including the sun would have 3 celestial bodies visible on each side of the planet. The stability can be fudged without issue, with all the multiples of five involved.

[factotum]

Is five moons equidistant from each other on the same orbit (a) ever likely to occur (assuming it wasn't built that way by some ancient aliens) and (b) actually stable, though? I know three bodies in the same orbit is a stable configuration, I think five is one example of a Klemperer rosette, which is known to be a non-stable system--any perturbation of the perfect symmetry of the orbiting bodies makes it non-symmetric and everything goes to heck.

[Eldan]

No, several bodies in the same orbit are not long-term stable. Because orbits are not perfect by themselves. Even if they were perfectly circular, there would still be tidal forces from the stars, and that would be enough to make the orbits non-circular over time, which means that the moons are faster at some points of their orbits than in others, which means that eventually, they would knock each other out of orbit.

[Rydiro]

As concisely as possible, the planet has five moons, or what look to be five moons, but only two of the five are visible in the night sky at any one time. The lunar cycle has one moon - Moon A - visible for a period of 25 days, then for the next 25 days it gradually wanes as Moon B waxes, until only B is visible for 25 days, repeat for C-D-E-A-etc.

Im going to comment on the logic of Your Constellation. You'd have five moons in a Pentagon. Going with your 50 days cycle that would be:
A B_ C_ D_ E_ A
0 10 20 30 40 50
In this case A is at new moon. Full moon at 25. Half moon at 12.5 and 37.5. Thats why I'd suggest a 100 day cycle. With 100 days you'd have a nice 5 day lunar week, a 20 day lunar month, and a 100 day lunar year. Just double your numbers above. From this constellation,your weeks would be:
Week 1, day 0 - week of A in new moon (month of A)
Week 2, day 5 - week of B in half moon waxing
Week 3, day 10- week of C in full moon
Week 4, day 15-week of D in half moon waning
Week 5,day 20 -week of E in new moon, (month of E)
etc.

Other than that, I'd say lunar belief/magic nudges the moons back to their place.

[Jay R]

No, several bodies in the same orbit are not long-term stable. Because orbits are not perfect by themselves. Even if they were perfectly circular, there would still be tidal forces from the stars, and that would be enough to make the orbits non-circular over time, which means that the moons are faster at some points of their orbits than in others, which means that eventually, they would knock each other out of orbit.

That is correct in our universe. In a Ptolemaic universe, the base orbits are perfect circles (modified by circular epicycles), and the bodies circling Earth aren't affected by each other's gravity. In fact, Ptolemy didn't even assume Earth's gravity was involved. Newton's law of universal gravitation was still 15 centuries away. So there's no compelling reason why they might not be stable.

And in a universe with arcane and divine magic, there are any number of ways that they might be stable:

• the decisions of gods
• a long-ago epic spell of a great wizard
• influence from other planes
• forces we have never seen (four moons might be composed of the four primary elements, and be unable to exist except at 90 degrees from each other)
• magic fields having long-range effects about which we know nothing
• etc.

In any event, we know that gravity is not universal (levitation and flight spells), that energy is not conserved (fireballs and magic missiles), and that electricity is not electrons attracted to the most positive available charge (lightning can be aimed).

Yes, you can handwave away all the real-world physics that makes these impossible, but having done so, you can also handwave away the real-world physics that says the orbits aren't stable.

If I were building a world and wanted multiple moons, I would include them, and include the following in my introduction to the campaign:

The world has multiple moons. Your characters grew up knowing this and do not question the physics of it, any more than they wonder why lightning bolts don't always travel to the nearest positive charge. They have no knowledge of real-world physics. [Neither does anybody else in the world. This world's equivalent to Newton must wait for the works of this world's equivalent to Kepler, who will need the decades of measurements from this world's equivalent of Brahe and the work of this world's equivalent of Copernicus, etc. The players will not be able to invent modern physics, or railroads, or machine guns, or anything else that will take centuries of work past the medieval age.]

Here is a similar introduction from a game I ran years ago:

Spoiler: Introduction to D&D campaign

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A warning about meta-knowledge. In a game in which stone gargoyles can fly and people can cast magic spells, modern rules of physics and chemistry simply don’t apply. There aren’t 92 natural elements, lightning is not caused by an imbalance of electrical potential, and stars are not gigantic gaseous bodies undergoing nuclear fusion. Cute stunts involving clever use of the laws of thermodynamics simply won’t work. Note that cute stunts involving the gross effects thereof very likely will work. Roll a stone down a mountain, and you could cause an avalanche. But in a world with teleportation, levitation, and fireball spells, Newton’s three laws of motion do not apply, and energy and momentum are not conserved. Accordingly, modern scientific meta-knowledge will do you more harm than good. On the other hand, knowledge of Aristotle, Ptolemy, medieval alchemy, or medieval and classical legends might be useful occasionally.

I urge DMs and players to approach the game with a sense of wonder instead of trying to pick it apart.

[Lord Torath]

That is correct in our universe. In a Ptolemaic universe, the base orbits are perfect circles (modified by circular epicycles), and the bodies circling Earth aren't affected by each other's gravity. In fact, Ptolemy didn't even assume Earth's gravity was involved. Newton's law of universal gravitation was still 15 centuries away. So there's no compelling reason why they might not be stable. <snip>

With this in mind, you could go with jayem's highly-elliptical orbit that has one moon around the earth, and the other 4 moons sun-ward. And the ellipse just always maintains its orientation relative to the sun, so you have one moon in the gibbous/full phase, and the other 4 in the crescent/new phase. (I love Spelljammer Physics!)

That said, if you stick with the 5-moons 72^o apart on a circular orbit, you've got 10 days between full moons, which could also make an natural week, with a 50-day "month". I think, with all due respect to Rydiro, that there would be less emphasis on the half- and new phases of the moons when it comes to the calendar and week length. Moon A being half-full is less important than Moon B being completely full, especially when Moon B will be full before Moon A leaves the gibbous stage. If I were the one making a calendar for this planet, that's how I'd handle the weeks/months.

[Eldan]

That is correct in our universe. In a Ptolemaic universe, the base orbits are perfect circles (modified by circular epicycles), and the bodies circling Earth aren't affected by each other's gravity. In fact, Ptolemy didn't even assume Earth's gravity was involved. Newton's law of universal gravitation was still 15 centuries away. So there's no compelling reason why they might not be stable.

Well, yeah. Obviously. My own universe is a perfectly square flat plane with an ocean eternally gushing over the side, where the stars are lanterns hung into the branches of the world tree by the mother goddess so travellers don't get lost at sea. But I was answering this as a physics question.

[Grey_Wolf_c]

Well, yeah. Obviously. My own universe is a perfectly square flat plane with an ocean eternally gushing over the side, where the stars are lanterns hung into the branches of the world tree by the mother goddess so travellers don't get lost at sea. But I was answering this as a physics question.

Question: was the ocean sustained by Discworld rules, or was there a spot where water just gushed out out of nowhere?

Grey Wolf

[Eldan]

Question: was the ocean sustained by Discworld rules, or was there a spot where water just gushed out out of nowhere?

Grey Wolf

Some of it is scooped up by the storm god and deposited back as rain, but a lot also comes out of deep sea trenches.

[Fat Rooster]

I think it is doable, but the setup would be extremely unstable. Handwavium is fine for that though. The trick would be having all of them on highly elliptical orbits that are large enough that they are perturbed by the star's gravity so that the apogee is always towards the sun*. When they are high in their orbit they are hidden by the lack of illumination of the side you can see, greater distance, and glare from the sun. They take it in turns to loop round behind the planet, and because the orbit's are so eccentric they can spend very little of their time actually visible at night.

*The masses of the star and planet and the planet's orbit would have to be quite specific for it to work. Messing with the gravitational constant might make it easier though.

It essentially relies on using the L1 point to continually adjust the orbits so that it works out. With perfect setup it would need no energy to maintain, even if there were other perturbations to worry about. It would be like bouncing a basketball on a marble in terms of how precise it would need to be though.