Frank Landis' Blog


More fun with Pandora
February 8, 2010, 1:04 am
Filed under: Uncategorized

There were a bunch of other things bugging me about Avatar.. Some of my fussing was unfounded.

This had to do with the fun of designing a livable moon that orbits a gas giant.  Pandora, or the world I’m working on: Nysus.  This has to do with three things: Roche limits, Hill Spheres, and tidal locking.

I’m a biologist, so I actually have to look these up.  Fortunately, Wikipedia has the relevant equations, and when I was designing Nysus, I set up simulations in Excel to figure it all out. Right now, based on my memory of the movie, I’m trying to figure out if they got it right.

Here are the issues:

The Roche Limit is the minimum orbital distance where a moon breaks up due to stresses from the gravity of the big planet. That’s where Saturn’s Rings came from. The fun part is that the rigid Roche Limit is based on the densities of both the gas giant and its moon, so on a soft and fluffy gas giant, the rigid Roche Limit’s actually inside the gas giant. While Pandora’s ridiculously close to its primary, it’s outside the Roche Limit, because it’s orbiting a gas giant: Polyphemus.

The Hill Sphere is where the gravity of the gas giant and the gravity of the sun are equal. If a moon’s orbit is outside the Hill Sphere, the sun yanks it away. Pandora doesn’t have this problem.

A moon that’s anywhere near its primary tends to be tidally locked so that one face of the moon always faces the primary. From that moon, the primary basically sits at one point in the sky, never rising or setting.

If you want a 24 hour day on your exomoon, it’s got to orbit its gas giant primary every 24 hours.

One thing I noticed fiddling around is that, while the equations are complicated, things tend to be proportional. If your moon is orbiting a big planet, it goes a little faster, so it’s further away from the planet. Assuming you don’t fiddle with the density of the gas giant, it gets a little bigger, and it so the gas giant appears roughly the same size in the sky.

Now, we get to that fascinating question: how long was Pandora’s day? If it’s 24 hours, Polyphemus covers 25-35% of the sky, not half the sky, which is 90 degrees. If Pandora’s day is 12 hours, Polyphemus covers 40-50 degrees.

Now in the movie, Polyphemus sometimes covers something like 90% of the sky, and sometimes there’s a lot of blue sky showing. This suggests that Pandora actually is spinning, which is not a good thing. If by some weirdness, Pandora actually rotated with respect to Polyphemus, it would have truly godawful tides. How big? I don’t know, but when I calculated them for Nysus (which as about a 48 hour day), the tidal bulge was around five kilometers high. If Polyphemus is rotating, that means the tidal range is several kilometers. As I said, it’s bad. Fortunately, moons get tidally locked pretty fast.

And then we have the issue that the Alpha Centauri system has two stars, not one, and B’s orbit around A is highly elliptical and takes about 80 years to complete (distance varies between 11 and 35 AU, roughly). Therefore, the energy input to Pandora would vary enormously over that time, but it’s more than what Earth experiences. I’m not yet sure whether it’s possible to have a livable planet in this system, but since we only saw one sun, I think it’s safe to say that a real Pandora in the Alpha Centauri system would be weirder than James Cameron imagined. Oh well.

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