Bad and good science in Avatar!

[Niwantaw]

The floating mountains of Pandora float apparently because of the strong magnetic field levitating them. A magnetic field strong enough to levitate mountain-sized superconductors (assuming they are pure unobtanium) should be strong enough to suck all of the RDA machinery to the Tree of Souls.

Unless they are non-ferrous. At which point they aren't magnetic and as they were expecting strong magnetic forces there's a good chance that they would take precautions against it.

[Irtaviš Ačankif]

To solve the mystery, I should mathematically calculate the magnetic field strength from the Tree of Souls at the distance of the mountains.

Assume that the rock in the Hallelujah mountains is purely unobtanium superconductor and has a density of 3,000 kg/m³. Also assume that each mountain is a cube measuring 1,000 meters across.

This means that each mountain has a mass of 3,000,000,000 kilograms and weighs (according to Pandoran gravity = g=7.84 m/s²) 23,520,000,000 newtons.

That is a LOT of weight. What would that mean then? We can calcuate the required pressure on the rock to levitate it: pressure equals force divided by area. The base area of the mountain is 1,000*1,000 = 1,000,000 m² and the force required to levitate it equals the weight, 23,520,000,000 newtons. Therefore, pressure required equals 23,520 Pa.

We use the following equation to calculate field strength (B):



Plugging in P_mag = 23,520 and mu₀ = 4π×10⁻⁷ N·A⁻², we get

B₂ = 93,538,000,000 T²

B = 305,840 Teslas

Since we used tons of approximations, just remember this value as 300,000 T or three hundred thousand Teslas. Or if you want to do it Navi-style, do so as ^o1,000,000 Teslas

This is WRONG. See posts below.

[Eyawng te Klltepayu]

Yep, this is unfortunate. Other than invoking a different physical mechanism there seems to be no way around it. I chalk it up to artistic license. Those mp3s are genuinely worth listening too, BTW. You should listen to them.

[Irtaviš Ačankif]

To solve the mystery, I should mathematically calculate the magnetic field strength from the Tree of Souls at the distance of the mountains.

Assume that the rock in the Hallelujah mountains is purely unobtanium superconductor and has a density of 3,000 kg/m³. Also assume that each mountain is a cube measuring 1,000 meters across.

This means that each mountain has a mass of 3,000,000,000 kilograms and weighs (according to Pandoran gravity = g=7.84 m/s²) 23,520,000,000 newtons.

That is a LOT of weight. What would that mean then? We can calcuate the required pressure on the rock to levitate it: pressure equals force divided by area. The base area of the mountain is 1,000*1,000 = 1,000,000 m² and the force required to levitate it equals the weight, 23,520,000,000 newtons. Therefore, pressure required equals 23,520 Pa.

We use the following equation to calculate field strength (B):



Plugging in P_mag = 23,520 and mu₀ = 4π×10⁻⁷ N·A⁻², we get

B₂ = 93,538,000,000 T²

B = 305,840 Teslas

Since we used tons of approximations, just remember this value as 300,000 T or three hundred thousand Teslas. Or if you want to do it Navi-style, do so as ^o1,000,000 Teslas



Now this is an insanely huge number - the strongest field ever created by man was less than 10 Teslas - and that was enough to levitate frogs. 305,840 Teslas would be enough to levitate all of the wildlife on Pandora and uproot trees. Tiny movements would induce terrible currents in any conductor, including neural pathways, and Eywa will be very mad getting zapped by thousand-ampere currents just because the Tree of Souls moved a millimeter after getting blowed on by the wind.

By the way, since the trees are all connected to a network, the huge currents generated here will travel all around Pandora, potentially destroying every tree on Pandora and zapping the fornicating Na'viyä under the Tree of Voices 

Editing reason: Forgot to include my postly Na'vi word!

[Tsyal Maktoyu]

Don't forget the Meissner effect, occuring both from the mountains themselves as well as the ground under them, which leads to flux trapping behavior that has never been tested or observed on Earth (only between superconductors and regular north/south magnets). How would that effect things? I also remember reading somewhere that the cross-section of unobtainium also plays a role in magnetic flow. So maybe other, unknown  mechanics would be at work, possibly something involving Lenz's Law. I read somewhere to that gravity is a little lower in that region due to the flux. So maybe while the levitation between two superconducting hunks of unobtainium is enough to cause the mountains to float, the flux's effects on non-superconducting objects (CFC airplanes, living creatures, etc) are minimal. Meh, all on the mysterious nature of unobtainium I guess. Tbh electromagnetism was never my strong point, just hypothesizing out-loud I guess.

IDK, all I know is that it looks cool.

[Clarke]

To solve the mystery, I should mathematically calculate the magnetic field strength from the Tree of Souls at the distance of the mountains.

Assume that the rock in the Hallelujah mountains is purely unobtanium superconductor and has a density of 3,000 kg/m³. Also assume that each mountain is a cube measuring 1,000 meters across.

This means that each mountain has a mass of 3,000,000,000 kilograms and weighs (according to Pandoran gravity = g=7.84 m/s²) 23,520,000,000 newtons.

That is a LOT of weight. What would that mean then? We can calcuate the required pressure on the rock to levitate it: pressure equals force divided by area. The base area of the mountain is 1,000*1,000 = 1,000,000 m² and the force required to levitate it equals the weight, 23,520,000,000 newtons. Therefore, pressure required equals 23,520 Pa.

We use the following equation to calculate field strength (B):



Plugging in P_mag = 23,520 and mu₀ = 4π×10⁻⁷ N·A⁻², we get

B₂ = 93,538,000,000 T²

B = 305,840 Teslas

Since we used tons of approximations, just remember this value as 300,000 T or three hundred thousand Teslas. Or if you want to do it Navi-style, do so as ^o1,000,000 Teslas



Now this is an insanely huge number - the strongest field ever created by man was less than 10 Teslas - and that was enough to levitate frogs. 305,840 Teslas would be enough to levitate all of the wildlife on Pandora and uproot trees. Tiny movements would induce terrible currents in any conductor, including neural pathways, and Eywa will be very mad getting zapped by thousand-ampere currents just because the Tree of Souls moved a millimeter after getting blowed on by the wind.

By the way, since the trees are all connected to a network, the huge currents generated here will travel all around Pandora, potentially destroying every tree on Pandora and zapping the fornicating Na'vi under the Tree of Voices 

IMO, you're completely wrong about the effects of a 300kT field. It wouldn't be levitating the wildlife and electrically frying Ewya. (And everyone connected to her.  ) It wouldn't even be uprooting trees. That's because 300 kiloTelsa is apparently 1/3 or so the field strength of full-size neutron stars. That's not so much "Bye-bye Ewya", as "Bye-bye Polyphemus!" 

Since accidentally Death-Star'ing Pandora is kinda depressing, I'll say what I think is the coolest piece of science in the whole film: the ISV Venture Star. It's so massive, and so surprising that Cameron included such a realistic piece of technology, when he's used "It's future superscience, go away!" so much in the past, i.e. Terminator, Aliens. Disappointingly, the fuel economy doesn't work under completely accurate physics, but it's certainly the best attempt I've seen in yonks, and it's seven shades of cool, which forgives everything. 

(Also, am I allowed to mention Jake's wheelchair?  )

[Irtaviš Ačankif]

Why would it be kìyevame Polyphemus? Having the magnetic field of a neutron star does not make Pandora a neutron star. The reason why neutron stars destroy nearby stars is because of its mass. Pandora is just a little moon.

However, the strong magnetic field would attract nearby moons and make Pandora crash into them. Not...exactly...something...good

The ISV Venture Star really, yes, is a great piece of science. However, I can't seem to understand why it always points in the direction it is traveling...a bit of artistic license? Additionally, the shots with Polyphemus and Pandora glaring in the foreground still have dense stars in the background...more of artistic license?

[Clarke]

AFAIK, magnetic fields drag against each other, and gas giants tend to have absolutely ginormous magnetic fields. (All 4 of Jupiter's major moons are inside the Jovian field, for instance.) And that would mean that Pandora would slow down enough to crash into Polyphemus, and... well, IMO, "spectacular" would be an understatement.

And I checked your numbers, since I thought something was off. Since you can rearrange

into 2mu₀ x P_mag=B², and we've already said that P_mag is only ~20 kPa, how did you get B to be so large when mu₀ is less than 1?

And about the Venture Star, I thought we only ever saw it at either launch or landing. In orbit, it might as well face whatever direction it's moving.
(Re: stars, isn't that you would see if you were there? I know actual photography doesn't work that way, but reality is unrealistic.  )

[Irtaviš Ačankif]

Woops. Did multiplication as division.  

Re doing it:
B² = 0.059 Teslas

Whoa.

That wouldn't be insanely big. However, remember that this is at the altitude of the mountains.

Assuming the mountains are floating at a height of 2000 meters, then according to the inverse square law at 10 meters to the ground the field would be about 20 Teslas. Not enough to suck Pandora into Polyphemus, but still an immense field. A palulukan gobbling up a tree would still send an electric shock all around Pandora. Na'vi would levitate and Samsons would crash. Not to mention that a running Na'vi would zap himself with the induced EMF.

This is WRONG. See posts below.

[Clarke]

That would be hilarious.  Unfortunately, there's another problem: dipole magnetism isn't an inverse-square force. IIRC, it's proportional to the inverse-cube, possibly worse.

I've not actually did the numbers yet, but I can tell this isn't going to go well. 

[Tsyal Maktoyu]

Well, at least everything else about Pandora is for the most part realistic. It's basically a prehistoric Earth with bioluminescence gone wild and a planet wide hive-mind, and land-based mountains can be just as spectacular anyway. Just look at the mountains in China that the Hallelujah Mountains were based on.

Though I still wonder if the fact that they are two superconductors interacting, rather than a superconductor and standard dipole magnet interacting, changes anything. Such strong fields are required by standard dipole magnets because of their natural state of resistance. Two interacting superconductors on the other hand...could they do the same amount of work as a standard magnet with only a fraction of the field strength? Just thinking out loud here...

[Irtaviš Ačankif]

Oh. Superconductors and superconductors don't interact. What will happen if it isn't a standard dipole magnet is that the mountains would just crash down.

Superconductors are NOT magnets - they are conductors. They are repelled strongly by magnets because of Lenz's law and the Meissner effect. Two superconductors would be like to blocks of concrete: absolutely nothing happens.

By the way, can anybody give me a heads-up on a formula for magnetic field versus distance? Such a formula seems hard to find...

[Tsyal Maktoyu]

Alright then, thanks.

Another question. What role does the fact that unobtainium is a Type II superconductor play into all of this? Now I remember that special property I was referring to earlier, that flux vorticies formed in the lattice structure of unobtainium. Therefore, type II. Any ideas?

[Niwantaw]

I think you'll find that rather than magnetism holding up the mountains it's sheer awesomeness.
screw realism. we have floating mountains.
also the engines point behind the ISV when it's accelerating but when you see it it's decelerating and ergo it's the other way round.

[Irtaviš Ačankif]

A Type II superconductor undergoes two specific heat changes from the non-superconducting state. The end result is the same - zero resistant. There are vortex lattices, but they are not FLUX vortices, which actually mean nothing. Magnetic flux only occurs when things move. Static stuff, such as the Tree of Souls, only have a magnetic FIELD, but not a magnetic FLUX. Magnetic fields in the shape of a vortex don't make sense. Probably another stupid RDA invention by somebody who doesn't know science, like Parker Selfridge.

Anyway, I did a miscalculation again - I mistaked B squared for B. Here is the correct one (which also includes the inverse-cube law instead of inverse-square):

B² = 0.059 T
B = 0.24 T
B_ground = 19,200,000 Teslas <<Whoo!

I used the inverse square law incorrectly too (I used the inverse law, not the inverse square), so here is the same calculation with the inverse SQUARE:

B² = 0.059 T
B = 0.24 T
B_ground = 9,600 Teslas <<Whoo!

As the magnetic field lines are radiating away from the magnet, I actually am more inclined to believe that inverse square is more correct. Therefore, write this down: the magnetic field strength at the Tree of Souls is 9,600 Teslas.

[Tsyal Maktoyu]

The ToS isn't under the Hallelujah Mountains last I checked. The battle started in the mountains, but I thought they were clear of them by the time they reached the pitt woth the ToS.

I haven't seen the movie in a while, so forgive me.

[Irtaviš Ačankif]

For the ISV Venture Star thingy, when it is releasing the shuttles, it is facing the direction of its orbit. When it approaches Pandora, it is also facing the direction of its trajectory. Not that this is impossible, but doing so on purpose wastes a lot of RCS fuel. For a better idea of orbital mechanics, just get the Orbiter space flight sim (real-world solar system) or its near-clone Spaceway (fictional universe).

[Irtaviš Ačankif]

The ToS isn't under the Hallelujah Mountains.

It is. Watch the final battle. The shuttles approach in the Hallelujah Mountains. In the extended version it is mentioned that the flux vortex makes the mountains float, and it is also said that the field is strongest at the Tree of Souls. 9,600 Teslas, man!

[Tsyal Maktoyu]

Huh. Guess a real ToS will have to be surrounded by grounded mountains, then. Would still be quite spectacular. I wonder if the EMF coming from Eywa alone would still be enough to jam navigation equipment? Sort of like a cell tower magnified several fold.

[Irtaviš Ačankif]

From Eywa alone? Nope. Eywa, as I understand, is a wired network, not wireless. This wouldn't cause problems with communication. Think about it: does the Internet present on Earth interfere with your cell phone?

ToS could be a big server farm, but I haven't heard of devices stopping when they enter a server farm.