# D&D GeneralQuestion for astrophysicists! (Or those with astronomical--lunar--understanding)

#### Mercurius

##### Legend
By way of context, I'm creating an encyclopedic glossary for my novel and doing a lot of world-building in the process--nailing down some details that were left dangling. One such detail is the specifics around the three moons orbiting the planet. I've done tons of online research but haven't been able to come up with a clear understanding, if only due to my own limited understanding of astrophysics. I'll ask a series of related questions with the hopes that someone(s) here can answer them:

One thing I DO understand is that to determine when all three moons are full, I need to find the lowest common multiple of the synodic periods. So if, for example (these aren't the exact numbers), the synodic periods are 10, 37 and 92 days, the LCM is 17020 days. Meaning, all three moons will be full every 17020 days. I also understand that some multiple moon systems sync up, either in the same orbit path, or in a pattern (e.g. 10, 20, 40 days). I'm still playing with different numbers, but do know that they aren't synced. For the sake of this post, let's just say they're 10, 37, and 92, all on different orbital paths and planes.

But what I'm trying to understand is this: How do I determine when the moons will actually cross each other in the sky? And how often will they "perfectly" align? I'm still pretty that this can be done with the synodic period and not the sidereal period, but not entirely sure. Do I need to include inclination or ellipses? And more particularly, how many decimal places in the synodic period would I have to go to get a perfect alignment? Or would such an alignment be virtually impossible in actual physical reality?

Of course the good thing is that this is a fantasy world, so I can do pretty much whatever I want. But it is a world with physical laws, so I do want it to be vaguely realistic.

I've been playing with this assumption, at least as a vague semblance of reality:

Single digit days for alignment of phases: e.g. 10, 37, 92.
One decimal place for moons touching, or converging: e.g. 10.2, 37.1, 92.0.
Two decimal places for near perfect convergence ("lunar eye"): e.g. 10.22, 37.14, 92.03.

So using those numbers, I get the following:
Alignment of phases: 17,020 days, or 47.3 years (assuming 360-day year).
Moons converging: 1,740,732 days, or 4,835.4 years.
Perfect convergence: 174,659,504 days, or 485,165 years.

Again, it doesn't have to be perfectly accurate, just vaguely realistic. Is the above at all plausible?

Any help from the erudite readership would be greatly appreciated!

#### Eltab

##### Lord of the Hidden Layer
It may help if you find and play with a simulator of Jupiter's Galilean moons. Three of the four are in harmonic orbits (2 x the orbit period of the next-inner moon) but the outermost (Ganymede?) is a bit off from the mathematical ratio.

To the best of my knowledge, the moons' orbits will be pulled into the same plane over deep time by mutual gravity and tidal forces. The corollary of this is that if the world is young, the moons could be in slanted orbits relative to each other, which would make 'perfect alignment' a very rare thing.

It may help you do the math (and conserve your sanity) if your year is 360 days long, because that number has so many whole-number factors. Later you can convert to the year-in-days you really want.

#### Umbran

Staff member
But what I'm trying to understand is this: How do I determine when the moons will actually cross each other in the sky? And how often will they "perfectly" align?

So... "alignment" is not an objective thing - it is dependent upon the viewer's position relative to the objects. If Mercury, Venus, and Mars are in alignment from the point of view of Earth, they may not seem to be in a line if you are viewing them from say, Jupiter.

One of your moons has an extremely short period, which suggests it orbits very close to the planet. The closer they are to the viewer, the greater the difference perceived location in the sky will be with small changes of location on the planet surface - what may be "in alignment" from Rome may not be seen as in alignment from New York City, for example.

And more particularly, how many decimal places in the synodic period would I have to go to get a perfect alignment?

That depends on how "perfect" you want things to be.

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#### Plane Sailing

On the one hand, this sounds a little like trying to solve the N-Body problem! n-body problem - Wikipedia

But for practical purposes for your game, this is a just a matter of plot, no? In the Dark Crystal, it was convenient to have the movie set at the point approaching the Great Conjunction (of stars) because plot. So if this is something you want to have as a plot point in your campaign... oh, co-incidence!

#### tetrasodium

##### Legend
Supporter
This might help with formulas

#### Umbran

Staff member
On the one hand, this sounds a little like trying to solve the N-Body problem! n-body problem - Wikipedia

But for practical purposes for your game, this is a just a matter of plot, no? In the Dark Crystal, it was convenient to have the movie set at the point approaching the Great Conjunction (of stars) because plot. So if this is something you want to have as a plot point in your campaign... oh, co-incidence!

Yes. if it is extremely rare, the chances of it happening accidentally during your campaign are negligible. If it happens frequently... it isn't that special.

G

#### Guest 6801328

##### Guest
Yes. if it is extremely rare, the chances of it happening accidentally during your campaign are negligible. If it happens frequently... it isn't that special.

Having characters in the novel argue about how often it occurs could be entertaining.

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