10182017, 04:38 PM  #11 
Join Date: Jun 2017

Re: [Space] Triple Full Moons
Putting some numbers in, the moons are so close, I think they could be visible. You're right that they are inside the Roche limit, although for the farther moons they are close to the limit, so they are probably small captured asteroids. If the closest one is the size of Phobos (i.e. about 20 km) and Lerrom is about earthsized, then Moon A will subtend an arc of about 0.18 degrees. For comparison, our moon subtends 0.5 degrees, so Moon A would be a little smaller than half the size of our moon.
The Roche limit also depends on the density of the satellite, so if these moons are captured asteroids with a high iron content, they could be bigger. I'm wondering what tides are like. If the moons are tiny there won't be much tides, I calculate for the case of Phobos being Moon A the tidal acceleration from Moon A would be about 1% of what Earth gets from our moon. However, if the moons are larger and denser, that would go up. 
10182017, 04:55 PM  #12  
Join Date: Jun 2006

Re: [Space] Triple Full Moons
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 MA Lloyd 

10182017, 04:56 PM  #13  
Join Date: Jun 2017

Re: [Space] Triple Full Moons
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10182017, 05:09 PM  #14 
Join Date: Jun 2006

Re: [Space] Triple Full Moons
One side issue maybe worth thinking about is that if it's a fantasy planet, there's no particular reason for the phases of the moon(s) or the tides to be related to their positions at all. They could both perfectly well be driven by magical or divine forces rather than celestial geometry.
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 MA Lloyd 
10182017, 08:23 PM  #15  
Join Date: Mar 2013

Re: [Space] Triple Full Moons
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Jinumon 

10182017, 11:10 PM  #16  
Join Date: Jun 2017

Re: [Space] Triple Full Moons
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The motion of something in a circular orbit is given by x = A sin( 2 pi t/ T + phi) y = A cos( 2 pi t/ T + phi) where x and y are the coordinates, A is the amplitude or radius of the orbit, t is time, T is the period of the orbit, phi is the phase and pi is 3.14159.... For this purpose the phase (phi) can be ignoredthe phase will tell us where in the orbit it starts but that information is not useful to us. It is like if you are asking how long the Earth's year is, you don't need to know if you are starting in winter or summer. Note that the time (t) needs to be in the same units as the period (T). For each individual moon, it will be full when it is directly behind the planet. If we say the y coordinate is the direction of the planet's orbit, and the the x coordinate is the direction perpendicular to the planet's orbit, then the moon will be full when y is at its maximum and x=0. Because we are interested in when the moon is full and not the distance, we can neglect the amplitude and look for when the function cos(2 pi t/T) is a maximum. For one moon, that means we will have one maximum once per period, as we expect. For a bunch of moons, each moon has a separate period. We define a function f= cos(2 pi t/T_1) + cos(2 pi t/T_2) + cos(2 pi t/T_3).* Now T_1 is the period of moon 1, T_2 is the period of moon 2, etc. Each term of this tell us how full each moon is; i.e., when cos(2 pi t/T_3) is one, then moon three is full. By adding all three, we know all three moons are full when the sum is close to 3. (Also if you'd ever care all three moons would be close to new when the sum is close to 3). Now we need to find the time between times when all three are close to full. If the ratios of the periods T_1, T_2, and T_3 are not rational numbers, then the function f is know a quasiperiodic, which you can think of as a step between periodic and chaotic.** A quasiperiodic function will never repeat, but we can look at some overall properties of it. If we plot the function f*** we get a squiggly line that goes between 3 and 3. We can look at when the function is close to 3 and see how long it will be in the area close to 3 and also how long it will be between times close to three****. These times will generally be approximate, in this case it is generally about 35 hours between periods, but sometimes there are two close ones separated by only about 4.5 hours Let me know if that still doesn't make sense or if you have more questions. * I think before I might have named this function x, but I've already used that letter, so it is called f now. Also T_1 should be T subscript 1. ** In this case, technically T_1/T_2 is a rational number because the values for the periods given were given to a finite number of decimal places.(and the same for T_2/T_3 and T_1/T_3) However, I assume that is because for some reason you didn't feel like tying an infinite number of digits. In any case, the function as given will be close to quasiperiodic. *** As far as graphing goes, it will depend of the software you use. I use Octave or Matlab, something like Excel should work too. For this problem I graphed t from 0 to 500 hours so you can see a lot of periods. It you graph for much longer (say to 500,000 hours assuming your program can handle it) you can see some long time scale features too. I would not recommend trying to graph this by hand :) **** When I was eyeballing it I felt "close to three" was about 2.5. You can use whatever threshold of closeness you like 

10192017, 01:11 AM  #17 
Join Date: Mar 2013

Re: [Space] Triple Full Moons
Thank you SO MUCH lich.
I was able to graph the function using some more exact figures and intersected it with a flat line indicating about 99% combined luminosity, resulting in about 1 in every 3 nights. Fun part is that it seems to be largely at random, so I think I'm gonna do it every 1d nights, or on a roll of 5 or 6 on 1d. Should make for a very interesting game. Jinumon PS: I went as far as College Algebra and dabbled with some Trig in High School, but it's been a fair number of years. 
10192017, 02:43 PM  #18  
Join Date: Dec 2006
Location: Meifumado

Re: [Space] Triple Full Moons
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10192017, 06:06 PM  #19 
Join Date: Jun 2017

Re: [Space] Triple Full Moons
You are right, with the moons that close there is a good chance that every full moon is actually a lunar eclipse. I don't know what that means for werewolves. It could be that a werewolf changes not because the moons are full, but because all the moons turn to blood; i.e., when you have a triple lunar eclipse.

10192017, 06:50 PM  #20  
Join Date: Feb 2005
Location: Berkeley, CA

Re: [Space] Triple Full Moons
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We can even account for solar motion. The inner moon undergoes 4488.2 sidereal months per year; it will undergo either 4489.2 or 4487.2 solar months per year, depending on the direction of its orbit (4489.2 would be considered 'standard') and thus its solar month will be 0.08136 or 0.08140 days. Same math applies to the other moons. 

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astronomy, mathematics, moon, moons, space 
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