Quote:
Originally Posted by malloyd
Actually it's worse than that. The suns don't need to be aligned, and in fact the less aligned they are the longer the "full" moons last - if they are at maximum separation there is a 14 degree slice of sky the moons can be in in which they will be fully lit viewed from the planet.
With only one sun I suppose you need to calculate the solar (rather than sidereal) periods of the moons, and find the integer solutions to
p1 x - p2 y = 0
p2 y - p3 z = 0
p3 z - p1 x = 0
These kinds of problems are called Diophantine equations, and are not simple to solve.
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I don't think it is quite as bad as this. It doesn't make sense to make it a Diophantine equation because the period of the moons are so short. The period of one of the moons is only about 2 hours. With those sorts of periods each full moon is only going to last a few minutes, depending on what is considered "full."
Also, because the period of the moons is much shorter than the orbital period, the difference between the solar and sidereal periods should be negligible.
Looking at it numerically, depending on what you mean by a full moon, it looks like to me you will have a full moon about every 33.2 hours, and each full moon lasts about 20 minutes.
For details....
This ignores the difference between the solar and sidereal periods because they should be small. Also, it ignores any effect of two suns because from the point of view of the planet the two suns remain fairly close together. To first approximation, the motion of the suns shouldn't effect the frequency of the full moon too much. The perpendicular component of each moon's displacement is given by x= A cos(2 pi t/T +phi). We could solve for where those all intersect, but that will get messy because you have to define how close they need to get to count as an intersection. Simpler, just look at the function x=cos(2 pi t/T_1) + cos(2 pi t/T_2) + cos(2 pi t/T_3). When this function approaches 3, then all three moons are aligned behind the planet. We will ignore the phases because they hold the information of when the next full moon will occur and we are only interested in the frequency of full moons.
When we graph that function, the result is a messy squiggle (technical term) but it gets close to 3 (i.e. all three moon are aligned) about once every 33 hours. Sometimes the alignment is close enough so that you'll get a second or even third full moon with only a few (about 4) hours difference.