#### Mercurius

##### Legend

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!