10-18-2017, 01:01 AM | #1 |
Join Date: Mar 2013
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[Space] Triple Full Moons
Hey All,
I'm (finally) about to get my Fantasy game off the ground and one of my players is playing a werewolf. Trouble is, my Fantasy world has 3 moons (technically moonlets), and I've decided (as to not make the game too disruptive) to only force a transformation on a simultaneous triple full moon. This shouldn't happen too infrequently as each moon goes through a full cycle every 2 - 6 hours (depending on the moon), but every calculation I come up with seems way to frequent to be right. I've found online calculations for planets with 2 moons, but none with 3, and I don't know how it's further complicating things. Any and all Mathematics (Applied) (IQ/H) or Astronomy (IQ/H) assistance would be greatly appreciated. Here are the figures I'm currently working with:
I understand that the Suns (or their combined center of mass) and all three moons must be approximately aligned to all show full, but for the life of me can't figure out how to calculate it. Ya'll are awesome. 'Preciate ya! Jinumon |
10-18-2017, 03:22 AM | #2 |
Join Date: Dec 2006
Location: Meifumado
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Re: [Space] Triple Full Moons
A full moon is when you have the Sun, Moon and Earth in linear conjunction. If you have 2 suns, then each moon will be in conjunction at 2 points in its orbit. You'll have to decide if moons are "full" when they're in conjunction with one or other of the suns or at the midpoint between these, which would be the brightest, assuming equal intensity of the suns.
However, when Lerrom is at the point in its orbit where it's perpendicular to the axis between the 2 suns, they'll be about 15 degrees apart in the sky. This will happen twice in their 64 day orbit, plus an offset due to the planet's movement around its orbit, so a bit more than every 32 days. As the moons are orbiting the planet 4 to 12 times a day, just go for the solar cycle as being the werewolf's cycle, about every 40 days or so. When the suns rotate their perpendicular away from the planet, their relative brightness will drop, until the lowest point when the planet and 2 suns are in conjunction.
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10-18-2017, 03:36 AM | #3 | |
Join Date: Jun 2006
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Re: [Space] Triple Full Moons
Quote:
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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10-18-2017, 04:36 AM | #4 |
Join Date: Dec 2006
Location: Meifumado
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Re: [Space] Triple Full Moons
Speaking of which, moons often fall into harmonic orbits of simple integral ratios. You could set them to a 2:5:8 resonance or something, meaning it'd be easy to calculate how often they're all full.
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10-18-2017, 06:54 AM | #5 | |
Join Date: Jun 2017
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Re: [Space] Triple Full Moons
Quote:
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. |
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10-18-2017, 11:52 AM | #6 |
Join Date: Aug 2004
Location: Shoreline, WA (north of Seattle)
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Re: [Space] Triple Full Moons
Personally, I'd duck the question and have only one moon matter for... reasons. (Maybe each sort of lycanthrope is the result of the mating of one sun god and one moon god, so they're only forced to change when the gods "mate" again.)
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10-18-2017, 01:31 PM | #7 | |
Join Date: Mar 2013
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Re: [Space] Triple Full Moons
Quote:
As a follow-up question, assuming his transformation lasts from the triple full moon and for the remainder of the night, what would the frequency classification be for a Disadvantageous Alternate Form? A regular full moon is Rare (from GURPS Horror). Jinumon |
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10-18-2017, 02:52 PM | #8 | |
Join Date: Jun 2006
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Re: [Space] Triple Full Moons
Quote:
On the other hand, I'm not sure the phases are *visible*. Assuming Lerrom is earth-like, all these moons appear to be inside the Roche limit, so they're necessarily tiny. None of them are likely to show a visible disk, they're just points of light that vary in brightness.
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10-18-2017, 03:06 PM | #9 | |
Join Date: Jun 2005
Location: Lawrence, KS
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Re: [Space] Triple Full Moons
Quote:
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10-18-2017, 03:34 PM | #10 | |
Join Date: Jun 2006
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Re: [Space] Triple Full Moons
Quote:
Of course if the effect lasts until the end of the night once it happens, instead of never more than 3.9 minutes - the time it takes for Moon A to move through 1/30th of its phase cycle, that's even more complication. Something closer to 1/4 of the time than the 1/27000th you'd get for just the period of phase match.
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astronomy, mathematics, moon, moons, space |
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