Someone do the maths on this.

[AE020704]

That's all well and good, but you rather miraculously failed to answer the OP's question. 10/10 for proving the point that it's a needlessly complex bit of fluff for any campaign world, though.


Wizards cast spells, Elves are real, the two moons are both full every three months.

Which of these is your suspension of disbelief having trouble with?

 

[orsal]

Your question does not contain enough information for a proper response to be formulated.

Correct, so far...

The phases of the moon depend on where from the planet you are viewing them from, so we'd need a specific vantage point. After that we would also need the orbital axis of each moon.

Incorrect, as others have noted. What we *do* need to know, but are not given, is how the phases match up.

Beta is full once every three months. Either Alpha is full at the same time, or not. Since Alpha's period is exactly one-third of Beta's (I'm assuming that the figures given are precise), if they are in sync at one time they will be in sync again three months later, and if not, then they won't ever be in sync.

So either every full Beta coincides with a full Alpha, or none do. The answer, therefore, is either every three months, or never, depending on information we are not given.

 

[helium3]

Ignore this post, I didn't fully read the OP.

 

[Nadaka]

AE020704: As I said in my first post, the answer is either once every 3 month or never, depending on data not given. The second post was to correct a minormiscalculation on Pbartenders part.

ORSAL: I would point out that the moons would be in conjunction twice in 3 months, rather than just once.

helium3: in his original post. "Luna Alpha, the larger of the two, orbits the planet in the traditional time of one month. Luna Beta, however, is smaller, slower and further away, and it orbits the planet in three months."

we have to assume that he meant literally, exactly 1 and 3 months. We also have to assume synodic months, otherwise we would need additional information about the planets orbit. We also have to assume the moons orbit in aproximately in the same plane as the orbit of the parent planet, a moon with an axis pointing towards the sun woud remain forever at half moon (until its orbit decayed to something stable). We also have to assume the orbits are very near circular or in tidally locked elliptical orbits, otherwise precession would also be a factor. I have not even begun to scratch the surface of orbital mechanics here.

 

[orsal]

ORSAL: I would point out that the moons would be in conjunction twice in 3 months, rather than just once.

That is correct -- so, if they share full moons, they also share new moons. But it wasn't the question asked, so I didn't answer it.

 

[Pbartender]

your math is off.

You are right, but I wasn't exactly using math... I simply forgot the little bit of extra time Alpha takes to catch up with Beta. It threw off my visualization of the situation.

To look at in a much, much simpler way that won't make poor, tired, befuddled STARP's head explode...

Alpha makes one half revolution in the time it takes Beta to make one sixth of a revolution. Now, just plot it out...

Alpha 0, Beta 0 -- CONJUNCTION, FULL!
Alpha 1/2, Beta 1/6
Alpha 1, Beta 1/3 (2/6)
Alpha 1 1/2, Beta 1/2 (3/6) -- CONJUNCTION, NEW!
Alpha 2, Beta 2/3 (4/6)
Alpha 2 1/2, Beta 5/6
Alpha 3, Beta 1 (6/6) -- CONJUNCTION, FULL!

So, yes, the two moons share two phases -- every one and one half months -- and those two phases will be opposing phases... Assuming that one conjunction is always full, the other is always new.

 

[Umbran]

a moon with an axis pointing towards the sun woud remain forever at half moon (until its orbit decayed to something stable).

Careful there - there are two axes to consider - one of rotation, and one of revolution around the planet.

In real orbital mechanics, to first approximation angular momentum is conserved. Which means that either of these axis is fixed with respect to the distant stars. Neither of the moon's axes can always point at the local sun - that would mean the direction the axis points would change over the year, and that means changing the body's angular momentum.

There are second order effects - like precession of an axis. And technically the sum total of a planet's angular momentum must be preserved, so if you have a mechanism for it you can change one axis of spin if you also change another at the same time. But to do so requires some rather peculiar arrangements....

 

[Nadaka]

For the life of me, I don't recall where I saw it, but I believe there is a "saddle" or "pringle" shaped orbit that is more generally acts the way I am talking about. It was on a website about odd orbits from Lissajous orbits at L1 legrange points to some rather wierd systems of bodies orbiting in a circle, with no mass at the center.

But that is stuff way, way beyond me.

 

[STARP_Social_Officer]

Thanks everyone for either your simplistic, or in some cases, incredibly complex answers. Also thanks to Pbartender for his concern for my poor head.

I totally agree, of course, with the idea of suspension of disbelief, and dramatic appropriateness. Absolutely it's not worth getting bogged down in scientific minutiae. However, I wanted my world to at least be reasonably realistic in terms of its cosmology - I'm satisfied with the three months unless someone can get me a better answer. My players do notice this stuff, and they do ask questions. If I tell them both moons are full every three months, you can rest assured they will find a way to make this an issue. Leaving the anal qualities of my players aside for the moment, I was actaully hoping it would be rarer than three months, but I'll survive. Thankyou, and it's goodnight from me, and it's goodnight from him.

 

[Nadaka]

to make it less often, you just need to change the period of 1 moon a little. Then the peroids won't match up so well.

For instance... if alpha has a period of 30 days and beta has a period of 64 days...
it should create a larger cycle that takes 1024 days before the full moons occure at exactly the same time.