A question we should probably ask ourselves before we get started going through the small body populations and talking about what they're telling us is, why do we have these populations of small bodies to begin with? We talked a lot about the formation of giant planets. We haven't talked yet about the formation of terrestrial planets, but we'll talk about that right now, too. But, how in this process do these small bodies form? Why didn't all these materials come together and form their own terrestrial planet, or giant planet? In fact, it's an interesting historical story that the first four asteroids that were discovered, first one we discovered, Ceres in 1801, the next three were discovered quite quickly over the next couple of years. And it was recognized that these were strange things, not like planets, not like the planets. In fact, they were called planets at first. But that these four things were on these tilted and elongated and crossing orbits, unlike the other planets. And they all sort of crossed each other, they were all in the same region of space, unlike the planets. And so the hypothesis, in the early part of the 1800s, was that these things used to be a planet, and they exploded, and this is the remnants of that explosion. That idea has been popular for a long time. In fact, you can still find people around who think that things like the asteroids used to be a planet and exploded. And that idea, although it's actually wrong in detail, there are things about it that are actually a little bit correct. There are things in the asteroid belt we'll talk about that used to be mini planets that did get hit and exploded into pieces, and we see those pieces today. But for the most part, it's not that things like the asteroid belt were once planets and then got broken apart and they're no longer planets, it's that they never had the chance to coalesce into planets. And in this lecture, we're going to explore the general reasons why that's true. To do that, we have to go back a few lectures to when we were talking about the creation of the cores of giant planets. Then I'm going to walk you through, I'm not going to go through the math again this time, but I'm going to walk you through the ideas of what happens and see where we go wrong from trying to make a big core which is definitely not a small body. Instead, we only get these small bodies out there. So, here's what happens. Remember, we had dust all over the place. That dust was slowly coagulating. It would collide with other pieces of dust that would stick together. They would get bigger, they would get bigger. And eventually they got big enough, the chunks got big enough that they had enough gravitational attraction that when something came along, it would be gravitationally attracted there and come like this. These would come here like this, come like this, and they would grow bigger and bigger. The bigger they were, the more gravitational attraction they have, the bigger they got. And, a very critical factor happened in through here is that the large ones got slowed down, the small ones got sped up as they interacted with each other, as they partitioned their energy together, as the small ones got scattered around to high velocities by these big ones. The big ones had to slow down, too. So the big ones are going slow with respect to each other, and if they're going slow with respect to each other, they have a chance to then gravitationally combine, also. So this was the process that we called runaway growth. The big ones got bigger faster and collected all the material in their space. And eventually, we got to what we had called isolation masses. And these isolation masses were when you have basically collected all of the material in your vicinity, and the next place you could get material is so far inward towards the sun, or so far outward away from the sun, that you don't have enough gravitational pull to get it. And so, you are isolated. So you can imagine in a simplistic view of the solar system that we started out with all this dust and gas. The dust started to coagulate, these bodies started to grow. A few ones got to this stage of runaway growth and became isolated and that there was a stage when there were hundreds of these isolation masses. And these isolation masses are things like maybe a tenth of an Earth mass, a hundredth of an Earth mass. The actual mass that you get isolated depends on where exactly you are in the solar system, how far away from the sun you are. And outside at Jupiter's distance, these isolation masses are potentially big enough to actually become the cores of the giant planets. The other thing that you'll often hear these called, instead of isolation masses, you'll hear the term oligarchs, for what these things are. A term which I just kind of thought funny. Now, a funny thing about these oligarchs, these isolation masses, the tenth of an Earth mass. A tenth of an Earth mass is bigger than every single small body we have in the solar system. So these small bodies, the region of, say, the asteroid belt, the region of the Kuiper belt, never got to this stage of having isolation masses, of having oligarchs. Or, if it did, it barely got to this stage of having these isolation masses or oligarchs. So what happens? How would you stop this stage? Why would you not get to the stage where all the small bodies are getting sped up and larger ones with very slow relative velocities are starting to combine to the ever, ever bigger ones. Well this stage, it's probably better to draw not a little box of the solar system here, but to step back and look down at the orbiting things in the solar system and think about what's happening. So we're at a place in the solar system where we have the sun right here and we have a bunch of bodies. And before, I drew them going in all directions, but really what I mean is, of course, they're all going around the sun. And to have low relative velocities as you're going around the sun, two things that are going to, when they collide, they're going to collide at a very low velocity. Or when they meet, they meet at a low velocity. What does that really mean for things going around the sun? What that really means is that they're in circular orbits with no inclination with respect to each other. Let's think about why it means that. Let's first make circular orbits that are inclined. When circular orbits that are inclined at the spot where those two orbits meet, this object's going this way, this object's going this way, they meet at a pretty high velocity. They meet at close to the orbital velocity of these objects. That's enough that the gravitational focusing, which takes two things that are at low velocity and preferentially pulls them together, gravitational focusing doesn't work very well. They just move on past each other, they don't combine. If you're down to zero inclination, if you are meeting each other, you're almost going exactly the same velocity around the sun and you meet each other at very low velocities. The other thing that you need to have is very low eccentricity because if you have two objects with large eccentricity, I'm going to draw them here instead of drawing you pictures here. If you have two objects with eccentricity, here's an object that's going around the sun like this. Here is an object that's going around the sun like this. They're both very eccentric. They meet in these locations. And again, this one's going this direction, this one's going this direction. They have quite a high velocity of meeting, same as in all these other locations. If they are just on circular orbits, or orbits that are really close to circular that are just right next to each other, when they meet they're almost going at zero velocity. So to have this gravitational focusing won't work. To have this runaway growth work that leads to these oligarchs, we need to have very, very pristine circular orbits. Now, we didn't really talk about this when we talked about the giant planets. But why do we have circular orbits to begin with? The reason we have circular orbits to begin with is because all of this dust, all of these smaller bodies are beginning to get formed in an environment that has dust and a lot of gas in it. And that gas, you can imagine, that gas is just kind of this soup through which the dust particles have to continue to move. And they want to move at the same speed as the gas. If they move a little faster than the gas, they feel a headwind, they slow down. They move a little slower than the gas, they feel a tailwind, they speed up. And gas, well, gas is gas. Gas doesn't have an orbit around the sun that's inclined or eccentric, it's just a big mass that's going around the sun at the time, and it's supported by pressure, it works in a very different way. So these small particles are confined into the gas in that way, they're forced to have that same sort of velocity, that same sort of circular orbit that the gas does. And what that really means is that when things form, they all form on very, very circular orbits. It also means that when we're reaching that phase of runaway growth where I say that the big objects are getting bigger and are being slowed down by the small objects, by being slowed down, what it really means is being put into very circular orbits. The big objects have circular orbits. The small objects are being strewn around to higher velocity orbits, which really means higher inclination orbits and higher eccentricity orbits. In general, that doesn't matter because eventually these big guys are so big, they gobble up all the small particles anyway and they take over everything. So we still haven't figured out a reason why that wouldn't happen. Looking through the processes and looking through what's important, there's one clear place that things could go wrong for these things trying to become runaway, trying to become oligarchs. And that is, it is critically important, that these large objects are slowed down by the small objects so that they can be on nice circular orbits that cross each other. And that always happens. If you have a sea of small particles, they will drain the energy out, the orbital energy out these bigger ones. But, this is not all that's going on in the solar system at the time. And this is where things can go wrong. Or, go right, if you like to have small bodies. What happens if all this is happening here in this region here at the same time that just outside this region here there was that snow line. And remember what happens outside the snow line. Outside the snow line suddenly cores, which were starting to form, I shouldn't say cores. Suddenly these runaway masses, these oligarchs, these isolation masses that were starting to form have access to even more material because they have access to ice. Ice is now a solid material that will condense. Before, it was just a gas inside of here. So you start just get a sudden jump in the size of your isolation masses, and they can form very quickly. They form very quickly, they become cores of giant planets. And let's say that in a relatively short amount of time, Jupiter forms out here. Relatively short amount of time, while we don't know the exact time that it took to form Jupiter, but as we discussed before, it's something like from 3 million to 10 million years. How do we know that? We know that because that's how long we think that gas still exists in disks around stars. When we look around other stars, we see gas still there. 3 million years later, we see a little bit there. After 10 million years, we don't see anything. So we know that Jupiter must have formed in that period of time. These things are still in this phase of trying to form together, and suddenly there's a giant planet right out here at, let's say, 5AU. We don't know exactly where Jupiter formed, maybe even a little bit closer. Giant planet out there at 5AU, and what's it going to do? Well, just like Jupiter does today for the small bodies. Jupiter is the enemy of small bodies of asteroids, in particular, in the sense that Jupiter is so big and the asteroids are so close to where Jupiter is that they get gravitationally tugged by Jupiter every time they go around. So Jupiter goes around once every this stage, goes once around every about 12 years. These asteroids go around much faster because they're closer in here. Every time they go past Jupiter, they get a little gravitational tug. And a little gravitation tug can be in many different directions and, for the most part, they sort of average out and adjust causes these small bodies to have eccentricities, to have inclinations. In fact, to do the exact thing we said they can't do. If you start to give bodies eccentricities and inclinations, because you have a big body out through here, you will break this process of gravitational focusing and runaway growth. So imagine that the story is something like this. All the bodies in the solar system are starting to form. Everything is going through this process of getting bigger and bigger, maybe even starting the process of runaway, maybe even starting the process of isolation in a few places, and suddenly Jupiter appears on the scene. When Jupiter appears on the scene, things that are close to Jupiter get stirred up by Jupiter's gravity. They no longer are on pristine orbits. And when I say pristine orbit, I mean really, really circular, right in the plane of the solar system. They can't stay in that orbit, they get pulled by Jupiter, they get tugged, they get pushed, and all of the bodies in them just get stirred a little bit. And so they continue to have higher eccentricities and higher inclinations. And when that happens, they cannot get bigger. That runaway is broken. The asteroids were never allowed to coagulate together to form a planet because of Jupiter. We'll talk a lot about the asteroids, we'll talk about the Kuiper Belt. The Kuiper Belt is the exact same story. The Kuiper Belt is, instead of right next Jupiter, is right next to Neptune. Put the sun back here, here was Jupiter now, way inside here, and we'll put Neptune out like this. Kuiper Belt is all this material out through here. It would have loved, I'm sure, to have been able to form into a planet, to have been allowed to form into a planet, but it was just a little bit too slow. Neptune is not nearly as massive as Jupiter, but because we're further away from the sun, the relative effect of Neptune is huge on the Kuiper Belt. So imagine all of these small bodies in the Kuiper Belt trying to do what the asteroids are trying to do. Trying to build up, to reach runaway growth, to begin becoming oligarchs, to eventually combine together to form the core, if there was still gas around they could have formed a core, and then had another giant planet. Maybe the gas was gone by the time these got their act together and started to form and they would've had to form a large icy planet, which would've been sort of a fun thing to have had out there, but they never got the chance. Neptune formed first and started stirring these things up into higher eccentricity orbits, higher inclination orbits, and it broke that process of runaway growth. And that's what we have left. Now, this is the main reason why we have small bodies, we have the small bodies in the asteroid belt. We have the small bodies out here in the Kuiper Belt. We also have comets that are much further away out in the Oort Cloud. They formed in this same region, and basically through the same process of these. Small bodies you can think of really as failed planets. If the small bodies had been left alone, if the giant planets of Jupiter and Neptune, in particular, had never been around or had been able to get ejected or, I don't know, imagine some crazy process, they weren't there. They would have made a planet. They would have made planets that were the sizes of the other planets that we have around. But because of the influence, the gravitational influence of all these giant planets, the small bodies that were on the edge of where the planets formed and inside where the giant planets formed just never had a chance to form. In the next lecture we'll actually look instead at the terrestrial planets and see, okay, if the asteroids were not allowed to form, how can you form terrestrial planets? What's the difference? It's a very interesting story. And we'll see that next.
