Astronomy isn't my particular field of study, but it has always been of interest to me on a hobby level... So I've spent considerable time in university libraries poreing over a book on the stars and planets while I sohuld have been reading boring economic policy or briefs off of Westlaw. ;-)

As a result, I did have an opportunity to look into this and ask some friends at ASU, U of A, and the Oak Ridge facility, who have a considerably more personal relationship with the subject... I'll see if I can do the answers they gave me any justice here.

As I understand it, this "third magnetic pole" is more a phenomonon caused by the realities of quantum physics and string theory than what we would consider (or experience as) a "true" magnetic pole. It's not so much as if, were you standing on Neptune (which they assured me - quite needlessly - would be very uncomfortable ;-) your compass would need a three-pointed needle, or anything... It's just that you would get some really unpredictable results from your compass... And, even stranger, a person standing next to you, while they would get equally unpredictable results, they might be quite different from your own.

This peculiar situation arises from a few individually unlikely circumstances that have the even more unlikely coincidence of occurring in close proximity to one another.

First, Neptune itself is quite large, and quite massive... At some 17 times the mass of Earth, it's the fourth-largest planet by diameter and the third-largest by mass. Add to that the fact that it's the furthest planet from the Sun, so it sufferes less "pertubation" than the other, nearer planets... Which means it enjoys more of it's own gravitational autonomy, so to speak, than the nearer planets.

Next, like most of the large outer planets, Neptune has a large family of natural satalites - thirteen of them that we know about so far... But, unlike the other larger planets, most of it's satellites lack the size and density to even form a spheroidal shape... This means, again, less perturbation for Neptune... More gravitational autonomy, if you will.

Third we consider the only one of it's satellites, or "moons" that is massive enough to have a spheroidal shape... Triton. Now, it turns out that Triton is a very odd duck, indeed... Not only is it the only large, 'planetary' moon in our solar system to have a retrograde orbit - which is to say, it orbits opposite Neptune's own direction of rotation - but it's also the single coldest object we've ever measured in the solar system... Colder than the vast balls of ice and dust we call comets, colder even than little Pluto or Charon, which are sometimes nearly twice as far from the Sun.

It's here that things get a bit fuzzy... Here we have a large, massive world with very little in the way of gravitational perturbation, and the only really significant perturbation it does have - outside the Sun itself, of course - is this strange planetary moon that is somehow synchronously locked into a degrading retrograde orbit. That, in and of itself, plays merry hell with the magnetic field of Neptune... Were the other Neptunian satellites larger, they might even out the influence, and make things more "normal", but as it is, we would expect Triton's influence on Neptune to be so pronounced that her magnetic polar axes might be "bent" as much as 15 degrees off true... Which is to say that Neptunes "north" and "south" poles would not be opposite each other, as they are on Earth, but rather that they would be on a kind of bent line, similar to, but far less pronounced than a "greater than" sign, like so... >

That explains the first part of it... And I've reached maximum post length. I'll finish in another post.

Might I help explain more that last bit:

Firstly, we have this big playground called space-time, or the 3rd and 4th dimensions (and perhaps the other 6 defined by string theory). When you have a bird's eye view, looking at all the big things, you see everything in perfect harmony, like a ballroom dance. But when you start inspecting the very small particles of an atom, you see that it is very tempestuous and unpredictable. Those forces affecting the large things are called Gravity and Electromagnetism. The ones affecting the small things are the Strong and Weak nuclear forces. Ergo, the line between the two regions is very fuzzy.

However, let me bring up Electromagnetism, the strongest force in the universe. When you put your hand on a table, the only reason it doesn't go clear through is electromagnetism; there is a small amount of Electromagnetic field around every atom, and some can have very large fields, as in magnets. This leads me to explain Triton. We know that it is composed of potentially magnetic metals that we believe to have come from several asteroids. As it passed through a retrograde orbit, the metals slowly build up an electromagnetic field. Over the billions of years of Neptune's existence, Triton has gained a charge nearly equivalent to that of the Earth. This charge influences metals in the region of Neptune it is over. Even though you may think that the third needle of your compass would point to Triton, it doesn't. Do to the covalence of Neptune and Triton's magnetic fields, there is a varying charge amongst the particles, thereby causing a compass needle to fluctuate greatly.