Creating a lunar cycle with 2 moons

There is a quick & dirty answer:

If we simplify things a bit, take a year if 360 days where Moon A orbits every 30 days, or 12 times a year...

For Moons A & B to have a full moon on the same night 4 times a year, Moon B would be orbiting in sync with Moon A and 3x slower. This also means they’ll be in conjunction (at least, roughly lined up in the sky) 4 times every orbit of Moon B - so Half & New moons, as well.

A simple cycle would go:

A B

New Half Full Full Half New Half Half Full Half New New Half Full Half Half New Half Full Full Half New... etc.

If you want a more ‘realistic’ answer, things can get complicated pretty quickly...

For a year of 365 days, and Moon A orbiting every 28 days, you’ll have 13 (& a bit) orbits a year. If Moon B is still moving exactly 3x slower, you’ll get 4 double-full-moons one year, 5 the next, then 4, then 5 (‘leap’ years aside).

Of course, this is assuming Moon B is 3x slower and synchronised with A, so has perfect conjunctions with A when they’re Full. It could be slightly off, with conjunctions that shift throughout the year.

To get even more complicated, look up tropical, sidereal, and synodic months.

As a side note, Mars’ moon Phobos is about 4x as fast as Deimos.

/r/worldbuilding Thread