The Kuiper Belt, as you recall, is the material outside of the orbit of Neptune. The Sun is here, once again, all the other planets, and then finally Neptune out here, and the Kuiper Belt are the small bodies that are in orbit beyond this region. And as you recall, the reason that they're there are the reason that there is no large body out beyond Neptune, is that Neptune itself when it was formed, started to excite the orbits of these objects. They started to have higher eccentricities, higher inclinations, they started colliding together at higher velocities and they stopped growing. They were left in a state of arrested development. When people first started talking about a hypothetical Kuiper Belt and that eventually talking, discovering things in the real Kuiper Belt. There was this idea that perhaps things close to Neptune, would be highly excited. But as you moved further out the orbits of the objects would get more and more circular, until finally you were in a relatively undisturbed region once again. And the reason, only reason that things wouldn't have formed in this very distant undisturbed region would've just been that there wasn't enough material. Let me show you what I mean by that. One way of thinking about that is again looking at the orbits of the objects in terms of semimajor axis on this axis, and eccentricity over here. And these are the same things again, semimajor axis is the average distance away from the sun. Eccentricity tells how elongated it is from zero, meaning it's the most circular orbit all the way up to one, meaning it's on a parabolic orbit. To calibrate yourself, I'll remind you that Neptune itself is over here at 30, and if we can go in another ten Uranus would be in there at about 20 astronomical units. The first Kuiper Belt object that we discovered in the modern era was found right around here, around 42 AU. I actually don't remember exactly where it was but it's somewhere, right around that region, and it was on a moderately eccentric orbit, just like you see here, and, it was also on a moderately inclined orbit. I'm not showing you inclination but you should think of inclination as, as sort of equivalent to eccentricity. Things are elongated and tilted with respect to the plane of the solar system. And this is, these are not real data this is my made up version of reality in which things that are close to Neptune are elongated and have high eccentricities. And as you move further away those start to decline, start to decline until they finally get to be a nice circular disc. All of these objects are in near circular orbits, and if you looked at their inclinations they would all be in inclinations right in the plane of the solar system. This is the way we thought it was going to be. It was just a really big shock when the first few dozens and then a few hundred Kuiper Belt objects were discovered. And this region of space got to be mapped out for the first time, and it doesn't look anything like this expectation. Instead it looks like this, this doesn't look anything like the expectations. There are no circular orbits that we know of out in these regions out through here, and not only that, there is very eccentric orbits here. There are very eccentric orbits coming out through here, and a lot more structure than what was originally anticipated. In fact, even if you don't know what any of this stuff means and, and where it comes from. When you look at this plot of where objects sit in space in semimajor axis and eccentricity space, I think your eye is immediately drawn to probably three structures. The first one is the most obvious one, is this cluster of objects sticking up like this. They all have the same semimajor axis, that means they all go around the sun with the same period. Because you remember, period is proportional to semimajor axis to the three halves power. They all go around with the same period, but they have a range of eccentricities from moderately eccentric down here to around 0.1 to very eccentric up here to about 0.25, 0.35 even almost. Very strange and really tightly constrained in semimajor axis. Interestingly, Pluto sits somewhere right around here at exactly the same location, semimajor axis of right around 39 AU and with a moderate eccentricity. As I said you don't have to know anything to know that something's going on here. The other structure that you might notice as an interesting structure is this tail of material going out to very large distances in semimajor axis space, but also very large eccentricities. And because they have these large eccentricities and large semimajor axes. We actually discovered them when they're at perihelion, perihelion again is closest approach to the sun, and they are not as far away as they seem, they're not at a 120 AU. This, this object with a semimajor axis of 120 AU and a eccentricity of let's call it 0.65. The closest it ever gets to the sun is 120 times 1 minus 0.65, and that's equal to almost a third so that's about 40, the actual answer's about 42 AU. These, this thing never comes any closer than 42 AU, and it's discovered at 42 AU because at a 120 AU it would be way too far away for us to see it. But there's this slew of objects on these sorts of orbits, and I should have mentioned before that this line right down the middle here. The only reason this slew of objects looks a little bit like it has a bend right there is because I changed the scale here, originally this was 10 AU across here and now I'm down to 10 AU like this. So I doubled this axis here so you can see these things. Lot of strange structure in through here, and finally there is that a similar sort of thing like this a bending up through here, but then a clump of material in through there. What is going on? I put a few suggestive lines on here to help us understand what's going on. First off, these things piled up right here, and in fact you can see things piled up right through here, too. They're not in random locations, these are in resonances with Neptune. Remember we talked a little bit about resonances with Jupiter, when we were talking about the asteroids three to two, you can't read what I just put there. Three to two, means that Neptune goes around three times precisely for every two times that the Kuiper Belt object goes around. Interestingly, we talked about that being a problem in the asteroid belt and yet, here instead of having it be a problem, we have an abundance of things here. Two to one, same thing. There are places where Neptune goes around two times and the Kuiper Belt object goes around one time, and if you looked at all of the other little resonances in through there, you'd see piles of objects piled up in there. So we have resonances. We also have an important line that I can draw right here just like I drew for asteroids of things that are eccentric enough that they would cross the Earth's orbit. These are objects if you are, if you have this eccentricity or higher, you cross Neptune's orbit. Notice that for the most part, these things that are here are not crossing Neptune's orbit, but they're quite close. A couple of them do, these guys all cross Neptune's orbit, and they won't be around for long. If you cross Neptune's orbit, you're going to be either ejected outward, or you're going to be injected inward and you have even more planets to contend with when that happens. This other region of this clump in through here. We actually call the classical Kuiper Belt, and classical Kuiper Belt, because in a sense, that's what people were looking for when they first started thinking about the Kuiper Belt. A relatively low eccentricity, relatively low inclination set of objects in through there. These days we divide it into two different types and you'll, we'll talk about that in a minute. We have hot, classicals, and a cold classicals, and this doesn't refer at all to their temperatures, it ref, refers to their dynamics, is that all, as I said we'll talk about. Okay, big question, why do we have these objects in the three to two resonance, why do we have these objects in the two to one resonance? Well this question was actually answered before it was asked. Well it answered for Pluto because Pluto is sitting right up here in the three to two resonance. And for a while people asked why is it that Pluto this only object in the outer solar system, why does it happen to be in a three to two resonance with Neptune. And the only answer anybody had for the longest time was, it's just a coincidence. It had to form somewhere, it happened to form exactly where it was in the three to two resonance. Not only is it exactly in the three to two resonance, but it's in a funny one. It crosses, if you notice where I drew it here, it crosses Neptune's orbit, as do these other objects in the three to two resonance. You would think that crossing Neptune's orbit would be a bad thing, but Pluto and all the other guys in this resonance do a very special thing. When they cross Neptune's orbit, as they do, they're on an eccentric orbit like this. When they cross Neptune's orbit like this, when they're in here, Neptune is always over here, or over here. Neptune is as far away as it can possibly be. How is that possible? Because they're in the resonance the same orbital configuration happens time and time and time again. If they were not in the resonance, and they were just a little bit outside, they had a little bit longer period, a little bit inside, there's no chance they wouldn't have encountered Neptune and they wouldn't be there. In fact, looking very carefully, there aren't objects there. There are no stable objects in these regions of Neptune encounter up in these distance. These guys are there, but as I said before, they're not going to be there for long. So while it's true being in a resonance can be bad for you because you encounter Neptune at the same time every time. In this case you encounter Neptune as far away as possible every time, and that's actually good for you. You are stable in that configuration. Pluto and these other objects actually come closer to Uranus than they ever do to Neptune. So why, so why is Pluto there? Why are the other objects there? As I said, when Pluto was known to be in the three to two resonance the first ideas were it was just a coincidence. The coincidence idea was never a very good idea, it's just too strong of a coincidence. The first plausible idea was put forward by Ranuma Haltred just before the discovery of these objects in the Kuiper belt. And she suggested that it was not because of dumb coincidence, but it was because of a consequence of the planets migrating. This was a crazy idea at the time, maybe people hadn't really thought very much about planets moving, giant planets moving around. And yet this was just about the same time that exo-planets were first being discovered and those planets, those hot Jupiters, were being discovered. They were the first ones, they were very close to their parent star. People immediately jumped on the idea that these had migrated. So the idea of our own planets migrating suddenly made more sense. We'll even see why they migrate in a minute, but let's at least talk about what happens if they do migrate. As if Neptune formed in much closer here's the sun again, Neptune again it goes around. If Neptune formed closer, its three to two resonance would be closer, there'd be a lot of Kuiper belt objects out in through here. And some of these would be in the three to two resonance. The three to two resonance with Neptune is sticky if Neptune is moving outward, it's not sticky if Neptune is moving inward which is an interesting derivation that we could do. But it is sticky as it moves outward if Neptune moves outward slowly. So what happens by sticky, what do I mean by sticky? Imagine Neptune's orbit slowly spiraling outward getting further away from the sun all the time. These objects are going in orbit around the sun also, but the ones that are in the three to two resonance stay stuck in the three to two resonance. As Neptune moves out, its resonance moves out and these objects move out with it. They sort of undergo a snow plow effect. Interestingly, as they get snow plowed outward, their eccentricity also increases. And in this hypothesis, their eccentricity increases proportional to how far they've been pushed by Neptune. So if you looked at these objects right here, these ones with high eccentricity would have been pushed the furthest. They would have started in close. The ones with lowish eccentricity would not have been pushed very far. They would have been only recently captured, and you are looking at the effects of this migration of Neptune. Let me show you a quick movie of how that really looks, just so you can get a feel of how these sticky resonances work. The other resonances are, are equally sticky too so you'll see things sticking in those. Okay, here's the way it's going to work. First let me tell you that this simple simulation is courtesy of Hal Levison of Southwest Research Institute. And what Hal has done is he has taken a simple planet, this is Neptune, at 27 AU, and a slew of Kuiper belt objects out through here. And all he's going to do is slowly push Neptune with time, and watch what happens to the Kuiper belt objects. For your own entertainment, you can watch, this is the three to two resonance, right there, and this is the location of the two to one resonance. So here's what I want you to notice. I want you to notice that as Neptune moves outward the three to two resonance, resonance moves outward. The two to one resonance move outward, and these things all move interestingly at the same time. Okay, here we go, watch what happens. Even on the very first time stamp, we've got some things captured up in to the three to two and the two to one resonance, they've been pushed outward. Things that are not in the resonance, they're getting excited, eccentricity, a little bit of wavy action going on through here. But they're not moving, they're staying the same in semimajor axis. Watch them go here. Excitation, but not movement unless they are caught up into the resonance three to two, there's more resonances in through there, another resonance, another resonance. Those guys are being snowplowed out, and everything else is just getting excited as time goes on. Look what happens here after 200,000 years. In this particular simulation, almost everything is caught inside of a resonance except for the things outside of the two to one resonance out through here. Let's compare this to what the real Kuiper Belt looks like, this is same as the picture that I just showed you. Here is the simulated Kuiper belt, the real Kuiper belt, all these objects in the three to two resonance, all these in the two to one. Sometimes you see people write it two to three instead of three to two, means the same thing. Other resonances that we hadn't labeled that are stuck inside here, that's this one. There's another one there. Here are those inside ones that are going on here. It's a beautiful verification of the hypothesis, the hypothesis being that if Neptune is pushed outward through some process, and it's pushed outward through a sea of Kuiper Belt objects, that those Kuiper Belt objects will be captured into these resonances just like you see here. It leaves you though, with one question, which is, why did Neptune move? And here's the answer, the one thing that we didn't see in that last plot was we did we see all these things in the resonances here, but we didn't notice any of these objects going through here. What are these objects and where did they come from? Well you can see kind of by their name they're called scattered Kuiper belt objects and they come from scattering by Neptune. You can see that they come very close to Neptune's orbit, at one time they must have had a relatively close encounter with Neptune, got scattered out into the outer part of the solar system. Their perihelia closest approach took them back close to Neptune, but they're now just a little bit far enough away from Neptune that nothing's going to bug them too much, and they're going to stay in these orbits for a long time. But that scattering process that, that Neptune scattering these objects is actually what drives Neptune to migrate. Let me show you how. Here's the sun again, and I'm going to draw Neptune's orbit very small so we can really watch what's going on, going around the sun, minding its own business. Except it's not really minding its own business, because there are all these Kuiper Belt objects out through here, and occasionally one will have a close encounter with Neptune. And, and what's going to happen? Well it's either going to get, have a close encounter, and get flung outward on an orbit scattered outward like that, or the other possibility, it could be scattered inward like this. That's what happens. It will come back to the same location that it got scattered, we've talked about that before, but it will be on a new orbit either smaller or bigger. Okay, what happens if it goes on a bigger orbit? Well to get on a bigger orbit it has to be given energy. Where does that energy come from? Has to come from Neptune, Neptune actually has to move inward. To get scattered inward, Neptune has to take energy away from the Kuiper Belt object, and Neptune moves outward. Now as long as Neptune is scattering things inward and outward with equal efficiencies, which it should, it's a random process, then Neptune's not going anywhere. But, this is not what happens, let's think about what happens to this object that got scattered outward. This object that gets scattered outward, well, it comes back in and has a chance to get scattered again. It's either going to get scatter inward or scattered outward, it gets scattered outward, comes back in has a chance to get scattered again. That's the stochastic process, It'll either it'll, it'll be 50/50 either way. After that first scattering, it might go in, it might go out who knows what's going to happen. Let's think about that object that gets scattered inward, that object that gets scattered inward pushes Neptune out a little bit. Normally it would come back to Neptune, and then it could get scattered inward or outwards or Neptune could go in or out again, and the net effect would be nothing but, that's not true. What happens if you scatter inward from Neptune? Well you might encounter Uranus. And, same thing happens at Uranus you might encounter Saturn, you might encounter Jupiter. Once you encounter Jupiter though, game is over. You are ejected from the solar system pretty much if you get too close to Jupiter or, or pushed into the sun or something. The net effect of that is, is that Neptune scatters things out, Neptune scatters things in. Ones that come out, that get scattered out, come back again, get scattered one way or another, there's no net effect of scattering outward. Because Neptune is a little bit not massive enough to scatter things all the way out of the solar system to eject them from the solar system. But if it scatters inward, Neptune never sees it again, Neptune gets to keep that energy of that scattering inward and Neptune moves out. The same process actually happens to other planets, Uranus we could make the same argument with. Uranus sometimes if it scatters outward it sees it again because it doesn't come by Neptune, but Neptune on the bulk scatters objects inward to Jupiter and Saturn and so Uranus moves outward, too. Saturn moves outward a little bit. Jupiter actually moves inward by a tiny bit, because Jupiter basically scatters all the objects out of the solar system giving them energy, meaning it has to move in. This is a process that was first proposed long before the Kuiper Belt was discovered. It was proposed by Fernandez and, and, and it was a paper that, that people read and, I think, ignored. People looked at it and said, oh yeah sure, I'm sure that happens, but somewhere deep down inside, nobody really believed that giant planets could move. And it was not until this paper a decade later from Renu Malhotra who took the idea that Pluto was in three to two resonance. Who then, remembered and had read the Fernandez and Ip paper and knew that these things had, had, should have been moving, and hypothesized that that was the reason why Pluto was where it is. Not only did she hypothesize that that's why Pluto were, it was where it was but, this was just as the Kuiper Belt was beginning to get discovered. She also predicted that there would be other objects found in this three to two resonance, boom there they were. This one discovery this discovery of the Kuiper Belt and its object's and the resonances led to a profound rethinking of what the solar system history was like. We would have never really seriously considered that Jupiter, Uranus and Neptune had moved by significant amounts in the early solar system until that Kuiper Belt showed us that it must have been true. Not only did the Kuiper Belt show us it must have been true, the Kuiper Belt showed us what was the mechanism for that motion, that mechanism was the Kuiper Belt. Now, I just told you what is in some ways the classic story of the Kuiper Belt, and of Neptune's migration and of resonance capture in the Kuiper Belt. And I will tell you also that there are new ideas that are percolating that that rewrite this story a little bit in some interesting ways. So the details of what I have told you may or may not be exactly true his, historic details are true this is the way it came out. But in general the Kuiper Belt and the the structures within it demand that the giant planets had moved. These days the question is did they move in that nice smooth fashion that I told you that Neptune had to have moved, or did something more catastrophic perhaps occur.
