Eclipse length and realism

[PetWolverine]

I have a little mini-rage every time I get an eclipse, not because it's game-breaking or anything, but because eclipses don't last for days in real life - and I'm pretty sure they can't, for any hypothetical star system. I decided to do some math to try and back this up.

The length of an eclipse depends on the apparent size of the moon and sun in the sky and their respective orbital periods (and the planet's rotation, which I won't take into account). The apparent size of an object depends on its radius and distance from the observer:

θ = 2 * tan^-1(r/d)

Each object moves through the sky at a certain angular speed, which can be calculated from the orbital period:

ω = 2π/p

The angle the moon has to traverse from the start to the end of the eclipse is the sum of the two angles, and the time it takes depends on the relative angular speed of the two bodies:

t = (θ_moon + θ_sun) / (ω_moon - ω_sun)

Here I'm subtracting the two angular speeds on the assumption that the two bodies are moving in the same direction across the sky, which is usually pretty close to true; if they're moving at some angle relative to one another the math gets more complicated, but the eclipses only get shorter.

For eclipses on the Earth, with numbers from Wikipedia, this works out to:

t = (9.037e-3 + 9.301e-3) / (2.6617e-6 s^-1 - 1.9910e-7 s^-1) = 7446.6 s = 2 hours 4 minutes 6.6 seconds

The Earth's rotation, again, shortens this a bit, depending on latitude.

How can we arrange to have an eclipse last for days? We want both the sun and the moon to appear huge in the sky, something that is helped by having them be nearby. We can also make the two periods be very similar, so that instead of having a 365.25-day year and a 27.3-day month as on Earth, our rimworld has a 60-day year and, say, a 55-day month. This longer period means the moon would have to be a bit further away, and would therefore have to be larger in order to have the same apparent size; or the planet has to be smaller (and lighter) than the Earth - but it's not out of the realm of possibility. The shorter year means we must be much closer to the sun, which must be a lot smaller and cooler than the one we're used to; or else the sun must be much more massive, which seems like a problem.

But in Rimworld, not only do eclipses last for days, but the total part of the eclipse lasts that long! On Earth it's more like 7 minutes. To make this longer, we don't want to maximize the total of the two angles, but rather maximize the angle of the moon while minimizing that of the sun. We also still need the two angular speeds to be very similar. The total time works out to:

t = (θ_moon - 2 * θ_sun) / (ω_moon - ω_sun)

The denominator is the same as before, but for the numerator, instead of adding the two angles (to count from when the two discs just touch until they no longer overlap) we subtract twice the sun's angle from the moon's (to count from when the sun is completely obscured until it just starts peeking out the other side).

We could actually calculate the relative apparent sizes of the sun and the moon based on the time it takes for solar panels' output to drop to zero, compared to the total length of the eclipse. I'd estimate the ratio to be at least in the thousands.

So the sun has to be so small and far away as to be almost pointlike, but so incredibly massive that the planet still orbits in only 60 days, and bright enough for plants to grow.

Tynan: Get rid of eclipses and make solar panels not work when it's raining or cloudy. A multi-day period of cloudy weather is entirely believable, though it would be biome-dependent. It also explains why we can't predict these events, whereas eclipses should be predictable.

[Seeker89]

Could be more than one moon, or rimworld is the moon.

[Hans Lemurson]

A good analysis.  Eclipses always bothered me a bit as being "random" events when they occur in reality in easy to predict cycles.

I agree that "Bad Weather" of some sort or "Mysterious Dark Cloud" would be a better way to describe an event that occurs at random and plunges the land into darkness for unknown amounts of time.  Not very eclipse-like.

[loc978]

Referring back to previous versions of the game, an eclipse happened when the gas giant your world is orbiting came between you and the sun... said so right in the event dialog. Not sure why the dialog is different while the game mechanic remains the same...

So when thinking of your rimworld, go with less Earth, more moon of Jupiter.

[Limdood]

don't forget an equally large drawback of the eclipse is losing a day of plant growth...and for me that's almost always the WORSE of the eclipse effects, compared to solar power loss...and plants tend to grow fine in cloudy weather.

[Bozobub]

The eclipse mechanics in Rimworld are pretty damn silly.  To replicate their irregularity and extreme length, you pretty much obviate any possibility of an inhabitable biome.  You'd need multiple suns and/or VERY chaotic orbital systems and/or a very distant sun to make them both as irregular and long-lasting as in the current implementation; such worlds are incredibly unlikely to be able to sustain human life, without rather extreme direct modification and/or heavy-duty, high-tech support and engineering.

This would be easy to fix:  Just have the game pick a proper recurring eclipse period, within set limits.  Even more than one is perfectly fine, although that would complicate the model.  Calculating actual eclipse data isn't even remotely easy — you'd have to generate "virtual ephemerides", so to speak, for the Rimworld, any orbiting/orbited large bodies, and its sun(s); ouch! — but you can easily simulate something of the sort by having one or more relatively regular "cycles" of eclipse(s).  With one much longer and one shorter cycle, for example, you could easily suggest "Earth-sized moon of a Jovian, with its own moon".  The shorter cycle, in this case, would have longer duration, and would represent the Jovian parent's eclipses, while the "moon of the moon" would have a long cycle but very short (1-5 hour, say) duration.

This would make eclipses a lot more realistic, in my opinion, without adding much calculation overhead or coding work.  To make them even more realistic, you could add a small amount of variation to each cycle (eclipse mechanics are...complicated ) and "partial" eclipses (which should be significantly more common than full eclipses for small moons, but very rare or nonexistent for the Jovian parent in this example).  In fact, this would allow a very small moon to ALWAYS generate partial eclipses, if desired or randomly determined.  And last, this would still make it rather difficult to exactly predict eclipses — and they could "stack"! — but it would give them the "recurring cycle" feeling they currently don't have.

[Dorian]

I think this is overthinking it.  After all, anything could explain it.  Rimworld could be a minor-planet moon, as in, the moon of a moon orbiting a larger planet the size of Jupiter.  Or even a binary minor planet, where Rimworld is orbiting the moon of a set of binary planets.  This would make seemingly random eclipse events that could be quite long, or even be the result of two back-to-back eclipses thanks to the binary grandparent planets.

Sci-fi sometimes needs no explanation