Someone do the maths on this.

[physicscarp]

If you're going for realism, I'm surprised no one mentioned that Kepler's Third law doesn't allow the stated system to exist anyways.

The ratio of the squares of the periods of any two satellites (moons) is equal to the ratio of the cubes of their average distances from the central body (planet).

So, given the numbers in the OP, we'd have

(1 month)^2 (77,000 miles)^3
------------ = -----------------
(3 months)^2 (257,000 miles)^3

.1 =/= .027

These moons can't be orbiting the same body, unless there are severe perturbations from one another and/or perturbations from the sun.

 

[orsal]

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.

I think you mean 960 days, the least common multiple of 30 and 64. And STARP, it's the least common multiple you want. If you choose one orbital period to be an exact multiple of the other, then the LCM is just the longer period. On the other hand, if you make the lengths "out of sync", you can have both individual periods fairly short but have conjunction much less common. For example, if the periods are 30 and 31 days respectively, they'll both be full at the same time only once in 930 days.

 

[Nadaka]

I think you mean 960 days, the least common multiple of 30 and 64. And STARP, it's the least common multiple you want. If you choose one orbital period to be an exact multiple of the other, then the LCM is just the longer period. On the other hand, if you make the lengths "out of sync", you can have both individual periods fairly short but have conjunction much less common. For example, if the periods are 30 and 31 days respectively, they'll both be full at the same time only once in 930 days.

dho! yep

 

[Thunderfoot]

Of course, there is another phenomena that must be considered for even more dramatic effect. If Luna A is at 0 degrees (relative to planetary axis of rotation) and Luna B is at an elevation of 5 degrees (relative to A)The orbits cannot both be circular in nature (or elliptical for you purists) along the same track. For celestial reference look at the planets, though they all share similar paths at different distaces, they all share a common rotational axis in relation to the sun. (Which is one reason Pluto was expelled, it has a different orbit).

Your orbital axises would have to be different meaning the moons would cross paths (in relation to each other) at least twice causing an Umbral Eclipse twice during the rotational cycle. Otherwise your planet must have two gravitational centers. For evidence of this, look at the multiple paths of Saturn's and Jupiter's moons, they have "atom-like(orbital model)" paths around their respective planets which from the surface would cause the moons to "disappear" for a time as they duck behind their stellar cousins. Of course if the moons have different sizes in terrestial viewing (ie one is visually larger from the planet's surface) the point is kind of moot, though the resulting Lunar eclipses could be really interesting and possibly cause for some sort of "superstitious" mumbo-jumbo that will give your cosmos some credence. Also the solar eclipses should be stunning.

 

[Nadaka]

not quite. I would assume that the moons have sufficiently different inclination of orbits to not eclipse every time they are in conjunction.

for most of the year the direction where the moons are in conjunction will not be in the direction of the intersection of their orbital planes. even then, it would depend on the length of the year. If the length of the year is exactly a multiple of month (as the original suggested lunar orbits were) it is possible that the moons would never align for an eclipse, or it is possible that they would align for an eclipse twice a year when they are in conjunction.

This would actually make an interesting astronomical foundation for a fantasy calender. you could have each season begin or end with the new or full moon conjunction, and twice a year (with a 12 month year) you could have a solstice or equinox lunar eclipse.

In a real system, both orbits would be a little bit eliptical and inclined to some degree, and while the paths would cross, they may not both be at the crossing point at the same time. This would also vary with the precession of the orbits.