Search the Community

Recently, I wanted to create a fantasy world setting with two moons. And, of course, because I’m a complete mathochist, I decided to have a theoretically possible solar system in which to create this. This lead down the rabbit hole, and I got to have a long worldbuilding session (actually several) to create this world, with some pretty amazing results. So, I figure, why not go over this whole process on these forums? I’ll go into it in detail, explaining as much as I can, but I’ll leave markings if you don’t want to go through all the hard work. IMPORTANT NOTE: Whenever I mention something like ‘full moon’ or ‘equinox’, I’m not refer to the day, I’m referring to the precise position which occurs in an instant. Keep this in mind. WARNING! GEOMETRY AHEAD! SKIP TO WHERE THERE’S MORE CAPITAL LETTERS TO AVOID! Earth has one moon, but, like all orbiting bodies it follows very specific rules, known as Keplerian geometry. There are a few rules to Keplerian geometry, but (for now) we’re just interested in the one which states that all orbiting bodies orbit in an ellipse with two foci. All planets must have the star they’re orbiting around as a focus point, consequently, all moons have the planet they’re orbiting as a focus point. That’s good. All Kelplerian orbits have 5 points known as Lagrangian points. These are fixed points in which objects can be placed to have stable orbits. In relation to the Earth and its Moon, they are as follows: L1 is between the Moon and Earth. L2 is on the far side of the Moon, lining up with the Earth (though not with the Sun, because the Moon orbits the Earth). L3 is the far side of the Moon’s orbit. L4 and L5 are 60 degrees off in the orbit, ahead and behind respectively. (Yes, L4 and L5 are slightly more complicated than that, but that isn’t needed now). I do know (some of) the physics behind it, but that’s a bit off-topic right now. So, it seems that, to have two Moons, we just have to put a Moon on the L3 point, right? Wrong. Because L1, L2, L3 are all unstable points. Can’t put stuff of any decent size mass there. I mean, theoretically, you might be able to put very small mass objects in L3, (like, say, an artificial satellite) but we’d have to resort to magic rock to have a Moon-sized object. So that’s out. We can put a Moon in the L4/5 spot, but I’d rather avoid that because I like the thematic idea of opposite Moons. So, suppose we avoid Lagrangian points, and just have two Moons in the same orbit, opposite each other. Does that work? Yes. And no. The L3 points aren’t enough to keep it in balance, so, (as best as I can figure, and I’m not an astrophysicists) it would need to be perfect placed to avoid them accelerating towards each other due to gravitational forces. A solution, sure, but it’s inelegant and isn’t likely to ever occur naturally. Instead, I decided to follow the binary approach, as in, ‘binary star system’. Binary stars orbit each other (oddly enough) sharing one focus point, while having the other one opposite each other. And, since the Earth is a focus point, we can have two moons orbiting it similar to a binary star system’s. Solved! END OF GEOMETRY SECTION! Long story short, we can two moons orbiting a planet opposite each other. We’re going to assume that the orbital period is exactly 28 days (synodic orbit), because it makes my life easier. (You’ll notice I’m about to make a lot of these assumptions) Now, I could go through the complete lunar calendar with respective positions, but seems like work which doesn’t involve math or writing, so instead, I’ll just list a quick set of rules to follow. 1. There will always be a total of a full moon, if you add the two moons together. 2. Draw the two moons in orbit around the planet. Draw a line between them so it looks like a ‘divide’ symbol. The respective moons can only be seen by people from their side of the planet, both can be seen while on the line itself. The moons can only be seen at night, though. 3. The moon which can only be seen in the beginning of the night is the waxing moon. The moon which is seen after midnight is waning. 4. Once every two weeks is full moon, swapping moons. Once every other series of two weeks is perfect half-moons, swapping waning and waxing Are we done? Hah! As I said, I’m a mathochist, and, what’s more, I’m a Julian-loving mathochist at that. I haven’t even started. Because now that we’ve gotten the moon out of the way, let’s talk about the planet. MORE GEOMETRY! IT’S FUN, I PROMISE! Kepler’s Law of Orbital Motion states that planets have a constant area speed. In other words, time it takes to cover a portion of the orbit such that it has area n between the start point, end point, and the sun (as a triangle, of sorts) is the same time it takes to cover any other points with the same area. Or, bluntly, area = time. (Not entirely right, but right enough for this discussion.) Equinoxes and solstices are caused by the tilt in the Earth’s spin which is completely independent from the elliptical orbit. Equinoxes are when the tilt is in a tangent to the Earth’s orbit to the Sun, solstices are when it is either pointing towards the Sun or away from it. Equinoxes have equal 12 hour day/night, solstices have longest day or longest night (summer, winter respectively). This is important because of the equinoxes and the solstices. Since these occur at 90 degrees from each other, we can adjust the time between solstices and equinoxes by moving the free focus point around and mucking around with length and width of the ellipse. (If you want to draw a diagram, draw a plus. The center of the plus is the sun. Draw an ellipse, with one focus being the center of the plus. Where the lines of the plus and the ellipse lines meet are the solstices and equinoxes.) Time adjustment to is possible, but it is complicated, so let’s move on. I’m just going to assume all the finite little adjustments I’m about to mention is possible because I think it is and because even I have my limits when it comes to this stuff. Calendar math is just a hobby. AND WE’RE ALL DONE WITH GEOMETRY! COME BACK, PLEASE! Now, this section requires some math. You can’t skip it, because this is necessary for orbital calculations. Promise. (Well, okay, you can skip to the last three paragraphs, but come on! It’s calendar math. Why would you want to skip it?) (No seriously. Don’t skip if you want to learn how to do this yourself.) So, let’s say we make the year 364 days, exactly 6 hours. (cough can’t imagine why I’d do that cough) That means (aside from needing a leap year precisely every four years, but see the note on that later) the solstice would move six hours, and we’d have a total of 13 28-day months. What does this mean? Well, let’s assume the winter solstice occur at precisely 1200 hours the first year. At Year+1, it will occur at precisely 1800 hours. At Year+2, it will occur at 2400, Year+3 0600, Year+4 back to 1200 and the cycle repeats. Same for the others. Now it’s easy to see why time adjustment between the equinoxes and solstices are necessary. There are 13 lunar months. If there is an equal amount of time between solstices + equinoxes, only one solstice/equinox can fall out during a full moon. If, say, the distance between them is 5-3-2-3 months (this is possible), they can all occur during a full moon, they just have variable time lengths between them. (In fact, the Earth’s distance between equinoxes is slightly off.) All’s well that ends well? Ha! Because, remember, the equinox progresses 6 hours per year (assuming the year cycle we established. Remember, you can whip up any numbers to your own liking) So, after a perfect solstice / full moon overlap, in 4 years, the full moon will have moved 1 day forward. In 28 years the full moon will have moved 1 week forward, and the winter equinox will now occur during perfect half-moons. In 56 years, we’ll be back at full moon, but with the other moon (remember, this planet has two moons) and in 112 years, it’ll be back where it started. All-in-all, I now have a 112-year lunar cycle calendar to use for my fantasy world. But wait! I was using the winter solstice in conjunction with the full moon as an example but we still have the summer solstice, vernal equinox, and autumnal equinox to use within our 112-year cycle. Can we have a system which only allows one full moon per year to coincide with one of the four? Yes, the easiest way to do this is to add a six-hour gap in the cycles, giving us 5-3-2-3, except each one also has six hours in addition to the months, but giving either the 5 or 2 an extra 12 hours after subtracting a day. (The math works, trust me on this. There may be other ways, but this is my way.) SUMMARY: So, every four years, the winter solstice, vernal equinox, summer solstice, autumnal equinox all swap between full moons, but these series of four years only occur every 28 years, but every cycle of 28 swaps between one of four options, (Full moon A, equal moons waning A, waxing B; Full moon B; equal moons waxing A, waning B; in that order unless I made a mistake) giving us a full cycle of 112 years total. Now, how does this cycle work when we have a specific 13-month calendar? Evil laugh. I thought you’d never ask. Since every four years adds a day, the calendar is moved one month every 112 years, if we don’t add leap days (which I don’t intend to). Which means, when a winter solstice occurs during a full moon during a specific month, that will not happen again for 1456 years. See? Math and world-building is fun. And, for those who remember me, I'm back. Nice to be here again.