Worldbuilding Wednesdays: Orbital Aesthetics

Welcome to Worldbuilding Wednesdays!  Every Wednesday, we spend what is probably far too much time walking through our worldbuilding process.  In this week's post, we introduce a new worldbuilding mechanic:  visualization.

What We Have So Far

Our world is ten times as wide as Earth, with ten times the mass.  That's about 100 times lighter than it should be if it were built the same way Earth was, so we made it 99% hollow.  Given its size and gravitational pull, it wasn't safe to make its rotational period any shorter than 8 days in length, but we also added a new Key Element that, when in doubt, we would make choices that lent themselves to a more Earth-like world.  That meant finding a way to make the day-night cycle closer to one day than 8, which in turn brought into consideration a small, star-like satellite that orbited our world, rather than a distant, massive star that our world orbited.

It's like our world would be wandering through the dark, carrying a lantern!

Close Enough For Celestial Mechanics

Ever since Johannes Kepler used relatively simple math to explain the relatively complicated subject of why planets take as long as they do to go around the sun, we've been able to figure out some pretty complicated things mathematically.  Things such as, "How far away would our Lantern need to be to completely orbit the planet in a single day?" and, "At that distance, how big would it need to be to look about the same size as the sun from the surface of our world?"

And, most importantly, "Wow, that's really close.  It wouldn't get torn apart by gravity at that distance, right?  ...Right?"

Bad news, everyone.

The bad news is that we're unsure who made this picture.

All planets have something called a Roche Limit.  Inside that limit, anything that is normally held together by gravity will have a bad time, because the gravity of the planet it's orbiting is stronger and will pull it apart.  And it turns out that, in order for something to orbit our world in a single day, it would need to be inside the Roche Limit.

Again, we have options.  As mentioned last time, however, we aren't going to keep tweaking physics forever just to get things looking perfect.  After a certain point, we're going to accept that differences will occur and let physics win.  This is one of those times.  Rather than change things again so that the Lantern can survive inside the Roche Limit, we're going to move it outside the Roche Limit and accept that the days of this world will be a different length.

We can mitigate that length a little, though, by a sneaky little trick; we'll say that the Lantern orbits in the opposite direction of the world's rotation.  If we do that, placing the Lantern just outside the Roche Limit gives it an orbital period of 2.3 days and the world a day-night cycle of about 43 hours.  It isn't ideal, but that's about as close as we'll get without altering physics even further.

We're world-building here, not universe-building, so we aren't going to focus much further on how the Lantern works.  What's important for our world is that it does, so we're going to assume that the Lantern gives off enough light to mimic the sun's light on Earth, and that whatever process that causes it to shine isn't going to differ significantly for geologic time scales.  With the other choices made, it will look an awful lot like the normal sun in the normal Earth's sky, with the odd exception that this particular sun would pass in front of, not behind, a moon during eclipses.

Which reminds us...

Fantasy World = 2 Moons

It's time to talk about something that will increasingly come to affect our worldbuilding:  aesthetic choices.  These are choices that we deliberately choose in order to have a sensory impact when it comes time to apply them in whatever project this world is destined for.  They don't necessarily have anything to do with making the physics work, or with making sure that our other decisions don't otherwise pull us too far from the standards of Earth.  Instead, they serve to highlight the fantastic nature of our setting.  These choices show our audience immediately that they're in a different world, in an impactful way that things like "Everything is lighter here" do not.

One of the easiest ways to make an aesthetic change that does not significantly alter the world is to play with the visual background of the entire planet.  Having a sun and a moon is important for keeping things Earth-like, with regular day-night cycles and tides and what-have-you.  Not nearly as important, but aesthetically striking?  A second moon.  Because of the way orbital mechanics work, the second moon will have a much more subdued effect than the first one, but its presence immediately states, "No matter how much this looks like Earth, it isn't."

Where should we put our planet's two moons?  The easy answer is to put them in orbits that resonate with the Lantern's.  As it happens, moons (and orbiting bodies in general) are fans of a 1:2:4 resonance, so placing them in such a fashion that they take (respectively) twice as long and four times as long to orbit around our planet as the Lantern works pretty neatly, as far as the math is concerned.  For similar reasons, we'll say that the moons look to be roughly as big as our moon.  When we were running the math, we decided that they had the same size relationship as the innermost moons of Jupiter, but that isn't strictly necessary and, from the perspective of anyone on the surface, the difference between their apparent sizes and that of our moon from our surface is negligible.

The Hilltop

This last bit is a form of visualization that we'll be revisiting often as we build our world.  You can consider it a bit of a sanity check:  we're working out whether the things that mathematically make sense would also "look right," in the sense that we can translate all of those choices into a visual.

So:  imagine a hilltop on our world.  It is a fairly random hilltop, close enough to the coast that we can see out onto the ocean for some way.  At present, we don't have much to look at except the sky, so let's look up.  There are stars in the night sky, same as our world.  There are also two moons.  One is red, the other blue (these colors are more for differentiating the moons than anything else; we might change them later).  The red appears to be a little closer to us than the blue, since it moves more quickly through the night sky.  The blue appears to be ever so slightly larger, but that might be a trick of the eye.  Regardless, the two moons both seem to move more slowly through the night sky than our own does.  They certainly move through their phases more quickly, however, especially the blue moon.  Over the course of the night, it moves from new moon to full moon, and just starts to wane as the sun comes up.

For those who are having trouble understanding why, it's because the apparent motion of the moons is dictated mostly by their actual motion, instead of our world's rotation.  In real life, Earth's moon moves through 1/27 of its orbit in a single night, but we spin around completely by the time we're facing it again, so it seems like it rises and sets in a single night.  On our world, a single rotation takes about as long as the "month" of the furthest, blue moon.  If we assume they're moving in the same direction as the lamp, that still means it will take somewhere around two day-night cycles for the blue moon to complete a rise-set cycle, and about one day-night cycle for the red moon to do the same... but remember, a day-night cycle here is almost twice as long as we're used to.  Similarly, the phases of each moon are dictated by where it sits in relation to us, the viewer, and the sun.  On our world, the sun is closer than either moon, so a phase-cycle is going to be blisteringly fast compared to Earth's moon.

The orbital mechanics are fun to get into if you're a math/astronomy nerd.  If you're not, just hold onto this general rule:  It takes one day-night cycle for the Lantern to get back to its starting point.  It takes the red moon two day-night cycles to get back to its starting point.  It takes the blue moon four day-night cycles to get back to its starting point.  And each moon will go through one full phase-cycle in about the time it takes the Lantern to "lap" it.  Because of the resonances, all three will line up every four day-night cycles.  And, because of everything else we've set up, that means the length of a blue moon "month" is just a bit more than a week.

We'll be using that relationship later when building calendars and keeping time.  For now, all you have to understand is that our world's two moons move slow and change fast.  Also, food for thought:  lunar eclipses will be common, long, and spectacular, and every once in a while, both moons will be eclipsed at the same time.

Also also, during solar eclipses, the "sun" blots out the moon, not the other way around.  So, on this world, if the sun suddenly goes dark?

Not a good sign.

Conclusion

This wraps up the parts of worldbuilding that constitute the "Outside."  From here on out, the decisions we make and consequences we explore are things that will directly impact those living on our world, rather than the conditions under which it operates.  We're still working our way inward, however, which is why our next consideration is going to be the necessity of buying an umbrella.  Until then, happy worldbuilding!