Avatar's flying mountains

[Robert'); DROP TABLE *;]

So I got involved in a "Superman vs. Batman"-style discussion, and these came up. Shortly, I realized that, although they're obviously impossible, I couldn't come up with a satisfactory answer as to why they're impossible, because I didn't know enough electromagnetics.

As a note, the in-canon explanation for why they work is that Unobtanium, (I thought it was funny. ) which composes most of the mountain, is a room-temperature (or higher) superconductor, and the Meisner effect means that it excludes Pandora's magnetic field, and so levitates.

However, each mountain is, well... mountain-sized, and easily weighs thousands of tons. They also float what is quite clearly multiple of hundreds of metres, if not multiple kilometres off the ground. My intuition says that, at some point, the Meisnerr effect must fail and leave the mountain to crash to the floor, but I can't really explain why that would happen or what the result would be, re: superconductivity. Is anyone here more knowledgeable?

As a bonus question, are there any physically conceivable properties that unobtanium handwavium could have that would let it support the mountains? (Other than cheats, like negative density.) As someone pointed out, "you can't have a better than perfect conductor," so I'm struggling to come up with even a hypothetical. Do even impossibly-perfect materials (say, zero penetration depth, the density of aluminium, and a magnetic permeability better than steel) help at all?

[Xanthir]

The Meisner effect won't "fail", but it's not magical either. The magnetic field exerts an upward force, and gravity exerts a downward force. You'd have to do calculations to figure out which one wins for a particular size of mountain/amount of unobtainium.

[Robert'); DROP TABLE *;]

Oh, oops, that was my "immovable object" thinking. Do you know happen to know how to calculate (even an approximation of) the force in that situation? (And does this have anything to do with magnetic pressure?) There doesn't seem to be any agreement on Google about how to calculate it, or how fast it drops off with height. One person suggested r^{-2}, someone else suggested that because it's a electric dipole-based, it's r^{-4}, and someone else said r^{-3}.

[idobox]

It will vary with the magnetic field, which is in r-3.

If your permanent magnet is the planet itself, the variation will be tiny over a few kilometers.
With the magnetic pressure formula, you can do the maths yourself. Use a spherical flying mountain in a vacuum to simplify computations. I don't feel like doing them, but I suppose it will require a freakingly large magnetic field. Remember, 1T is a lot, and your average Neodyum magnet will produce much less than that..

[Robert'); DROP TABLE *;]

So it basically involves assuming that the mountain is sitting on a cushion of magnetic pressure, in the same way that a ship sits on the pressure of the water?

[idobox]

I think it closer to how you "fly" in an indoor skydiving thingie.

Because the superconductor rejects the magnetic field, a force is created. Because your body rejects air streams, a force is created.
In fact, the superconductor magnetize itself to nullify the field, so it behaves like a magnet with reversed polarity. I don't understand why it is stable, while it's impossible to be stable with two magnets.
Most experiments will make a magnet fly above a superconductor. I'm not sure a superconductor could be stable over a magnet, also, it appears the magnetic field has to be vertical. But I'm not sure, it's been a long time since I last did some magnetostatics.

It would be possible that the moutains are magnetic, and the ground below superconductive, but the moutains would soon be attracted to each other.

[Xanthir]

Yes, a superconductor can be stably suspended over a magnet just fine. Here's a particularly awesome example: http://www.youtube.com/watch?v=5el1A5B-h3Q

[SlyReaper]

Unobtanium is cavorite?

[Robert'); DROP TABLE *;]

I think it closer to how you "fly" in an indoor skydiving thingie.

Because the superconductor rejects the magnetic field, a force is created. Because your body rejects air streams, a force is created.
In fact, the superconductor magnetize itself to nullify the field, so it behaves like a magnet with reversed polarity. I don't understand why it is stable, while it's impossible to be stable with two magnets.
Most experiments will make a magnet fly above a superconductor. I'm not sure a superconductor could be stable over a magnet, also, it appears the magnetic field has to be vertical. But I'm not sure, it's been a long time since I last did some magnetostatics.

Ah, yes, that explanation makes sense. Thank you, I'll have a look at how magnetic pressure behaves there.

It would be possible that the moutains are magnetic, and the ground below superconductive, but the moutains would soon be attracted to each other.

To psuedoquote Mythbusters, "Jame get big boom?"

Unobtanium is cavorite?

Fair enough, I suppose, but that causes new problems.

[BlackHatSupport]

Gravity-resistant minerals? Technology installed by some ancient race? Or maybe just really damn weird?



I vote grav-rwesistant metals or ores.

[letterX]

OR! What about a mountain made of gravito-magnetic superconductor which resists changes in the gravitational flux through its volume, analogous to the video of the regular superconductor resisting changes to changes in magnetic flux currently making the rounds. Ignoring the fact that gravito-magnetism isn't very well observed, and I am totally just making things up to pretend that it can form a current, and have superconductors.