We talked about a lot of meteorites, the things that fall from the sky. And we have implicitly talked about the fact that they are from the asteroid belt, that they come from asteroids. We haven't really talked yet about the asteroid belt other than the formation of it and the question of why there's just small bodies there, instead of big ones. Let's look in more detail at the asteroid belt and lets start by looking at where the object in the asteroid belt are. Here's a plot using data of all the asteroids known as about 2007, but you can easily make an updated one. The problem is there's so many points in there it really wouldn't look any different, so I'm just going to use this one here. And here it's showing you three critical parameters. We've talked about these parameters before in terms of orbit but let's remind ourselves what they are. Semi-major axis, this is the average distance of the asteroid from the Sun. If it's a circular orbit, semi-major axis is the same as the radius. If it's not a circular orbit, semi-major axis is the average of the distance from the orbit. And it's also equal to the average of the closest approach, which we call the. And we derive little cube and the most distance approach which we call which we use as a big Q. Take the average of those two you get the semi-major axis, that's the best way to measure the distance away from the Sun, the average distance. But also is a direct measure of the energy that the orbit has. The other two parameters are the eccentricity, which you can see right here. Eccentricity of course shows you how eccentric it is. Eccentricity ranges from 0 if you're a circular orbit all the way up to 1 if you're on a parabolic orbit. Notice that it goes up to 1 right here, although nothing is on a parabolic orbit. And you can be greater than 1 if you're on a hyperbolic orbit. Remember, hyperbolic orbits are ones that are not even bound to the Sun. Finally, you have the inclination, if I take this orbit and I look at it sideways, here's the Sun, here's the orbit let's say of the Earth out here at 1 AU, going in this disc. Inclination is this angle with respect to the Earth or in this case with respect to a slightly different angle but we'll just call it the Earth of the orbit. Something that's down here at 0 is going to be in the plane of the solar system. Things up here as high as 40 degrees are going to be quite tilted with respect to the plane of the solar system. Let's see what we have. Well, first off remember, we have the Earth. The Earth is at 1 AU and it has essentially 0 eccentricity and zero inclination, so this is the Earth. The other thing that's on this plot or at least the region of it on this plot is Mars. Mars, Mars is out here at about 1.52, a little more eccentric, not really very inclined. So Earth and Mars, and then all the asteroids that are out there, where are they? Well, for the most part, you can see these dots are between Mars and Jupiter. Jupiter would be out here at 5.2 AU on it's circular un-inclined orbit. And there are a few asteroids scattered out throughout here that you don't but the population is not very big. What you mostly see is a ton of asteroids between about 2 AU and about 3, 4 AU, this is called the main asteroid belt. And as you can see it's not just a random collections of things in random orbits, there's quite a bit of structure in through there. Let's talk about where that structure is, when is comes from. The first thing to notice is there's these labels. 3:1, I'll call that 3 to 1, 5 to 2, 2 to 1. Those labels are things that are the resonances with Jupiter. A resonance is when an object in an orbit goes around a precise number of times compared to another object. It's 2 to 1, that means that the asteroid which is closer here, it's around 3.5 AU, asteroid goes around twice, one, two, for precisely every one time that Jupiter goes around. Why it does matter? Well, notice first that it seems to matter a lot, 2 to 1, 5 to 2, 3 to 1. These are regions where there are essentially walls in the distribution of asteroids, where asteroids clearly aren't allowed to live, why. Why? Because if Jupiter goes around, let's talk about the 2 to 1, if Jupiter goes around one time and this object goes around some random number of times. Let's not have it in the 2 to 1 resonance. Let's just have it in somewhere here where it goes around maybe 2 and a half times 2 and a quarter times. No nothing, no round number goes around once, goes around again and it ends up right here, Jupiter is back here. Next time it ends up here, next time here, next time here, next time here, next time here. Every time the asteroid and Jupiter go around they meet each other in random locations, where they meet each other matters a lot. Every time the asteroid and Jupiter line up with respect to the Sun, the closest to each other if we lived on the asteroid we would call that Jupiter is at opposition. Every time Jupiter is at opposition for that asteroid the asteroid gets a little bit stronger tug by Jupiter than it would otherwise. That little tug modifies the orbit ever so slightly. Now as long as those tugs are happening at random times in random locations, they sort of cancel each other out. You do have wobbling of the orbits around changing around a little bit but over long periods of time, they basically don't change. What happens though if Jupiter is here, goes around once, shows up here, and in that time this object goes around precisely twice, shows up right here. Next time, that gets a little tug. Next time, does it again. It's another little tug exactly in the same direction. Next time, another little tug exactly in the same direction. Eventually, you can imagine that this is going to elongate the orbit of this object until eventually, something bad is going to happen. It's going to cross Jupiter's orbit, it's going to be ejected from the solar system. It's going to get pushed into the Sun, it's going to impact the planet, something bad is going to happen. Living inside of one of these resonances is a bad, bad thing, it's so bad that it doesn't happen. Notice that there's nothing inside these resonances at all, there's one other one. Notice this envelope, right here, where things for the most part, the main part of the asteroid belt doesn't exist above this envelope unless it's well above this envelope. This is called, this one's a little bit more obscure. This is called the new six resonance. The six refers to more or less, the sixth planet, Saturn. So this is due to the effect, believe it or not, of Saturn. And it's a little bit complicated, it's because Saturn is not on a perfectly circular orbit, it's on an eccentric orbit. And like everything in the solar system or in mechanics that's on an eccentric orbit, that orbit precesses. It's a complicated theory to explain exactly how it precesses and how fast and why but it precesses. So imagine Saturn is precessing, everything else is also precessing and it turns out that an object that was on this red line here would have a precession rate exactly the same as Saturn's. So though it's not lining up time, after time, after time, after time, after time, over a long period of time the orbit of this, the, an object right here and the orbit of Saturn would be aligned as they both precess around the Sun. That effect, over enough times, would eventually do the same thing that these resonance here, these are called mean motion resonances instead of secular resonance. That would do the same thing, it would eject the object from the solar system. So we have this envelope, you're not allowed to be in this area, you're not allowed to be inside these resonance. And other than that, do we fill things uniformly? Well, this area looks pretty unifromally filled. This is often called the inner main asteroid belt and through here you'll see sort of clumpy things. There's a clump, there's a big clump, be clumped into here. We'll look very detailed at some of these clumps in a minute. Down here, you know, there's not much in this region at all except for this little clump down through here. And then there's some clumps here, clumps here, it's a very structured region. It'll be important if we could understand why. Before we do that, let's look though at things beyond the main asteroid belt when we say asteroid belt, these are the objects we mean. These are the objects we mean but there are other things out there that are beyond the main asteroid belt. Some of them are in the same semi-major axis range as the main, main asteroid belt. But they are way up here in eccentricity and important things happen. If you have eccentricity above this line and the semi-major axis where you are, that means that your closest approach to the Sun is within the Earth's orbit. All of these objects above here are Earth-crossing asteroids, near Earth asteroids, we call them. All these objects, which are inside the Earth's orbit are eccentric enough that their most distant approach from this on crosses the Earth's orbit. Everything in this ridge has the ability to impact the Earth. These are the objects that are the source of impacts. These are the objects that are the source of meteorites. These are the objects at the source of big craters that we can see on the Earth and on the Moon. Interestingly, the numbers of objects in through here is relatively small. Relatively small compared to the numbers that are here. Relatively small compared to their lifetime. You can imagine that things like this will not exist in these orbits for very long. You can't exist in an orbit very long if you come close to planets. Why is that? Well, you could impact a planet, you'll be removed or you could just have a close encounter with a planet. And that close encounter can give you a gravitational slingshot which again, will push you maybe out towards Jupiter. Getting near Jupiter, always a bad idea maybe push you in towards the Sun. Getting too close to the Sun, also a bad idea. So these things have short lifetimes, short dynamical lifetimes. Short doesn't mean ten minutes but it means much shorter that the age of the solar system. If you have a population with short fly times, there needs to be a way to get that population there. Where do these object come from? What is the replenishment of these objects? The obvious source is of course the main asteroid belt but how do you get things from the main asteroid belt to here? In particular, the main asteroid belt, the reg, regions where things survive in the main asteroid belt are where they are stable. Most of these objects in the main asteroid belt will be in exactly the same place if you came back after another 4.5 billion years. Their orbits do not change significantly just like the planets are in relatively stable orbits. Yes, they have eccentric orbits. Yes, they have inclined orbits because they did interact with planets in the past. But one of the reasons they're alive now is because they are, the small fraction of things that are stable. So how do you get these near Earth asteroids? How do you get the meteorites delivered to us? A clue comes from looking in more detail at these clumps in the asteroid belt. All right, here's a blow up of the asteroid belt where you can see a little bit better. I'm now showing you semi-major axis and only inclination. I'm not going to do eccentricity but we could have look at the eccentricity too. And let's look again at these things, we recognize the, the gaps caused by the resonances here. We can see even some of the minor ones in through there that we didn't see before, the outer edge here and we see now these clumps in more detail. Look at this, this line of objects here is sudden over density, another one that looks like this, things like that, things like that. They're really very easy to pick out by eye and they are all over the place, what are they? Well, they were identified nearly 40 years ago now, as what are called asteroid families. They're asteroids that all have very similar orbits, similar semi-major axis. Similar x in, inclination and if I showed you, you would also see that they have similar eccentricity. Similar orbits doesn't mean that they follow each other around in space. It means that they have the same orbit in space but they maybe anywhere, randomly, within that orbit. How do you get all these asteroids to have the same sorts of orbits? Again, worked out about 40 years ago by looking at the objects themselves in addition to looking at the orbits. And realizing that in all cases where you have a clump of objects not only do they have similar orbits, that they have similar compositions. We'll talk about compositions in the next lecture but for now, just take it that you can look at objects, figure out what they're made out of. And their difference and yet these are all the same, these are all the same, these are all the same, these are all the same. The implication is that they all came from the same source, how does that work? Well, if there was one larger asteroid right here that had an impact with a smaller asteroid and it shattered into pieces. What happens when it shatters into pieces? Well, it's an orbit. Here's it's initial orbit, there's an impact, shatters into pieces. All the pieces go flying off into different directions. The speed that they go flying off is not particularly big compared to the orbital speed of the asteroid. So it's not like they go flying off and have crazy orbits that don't look very similar to the old one. They have almost identical orbits but slight changes and those slight changes come in very strict patterns. They come in patterns where you keep nearly the same inclination and change your semi-major axis. Or you keep nearly the same eccentricity and change your semi-major axis that spread is a little bit easier to see. And you can very easily trivulate, calculate what it should look like and they should look exactly like this. This is exactly the signature of an impact somewhere around in here that spread things off in all directions, these asteroid families are due to collisions. Now, we've known that collisions were an important part of at least an early part of the solar system and the building of objects. But we also know that collisions are an important reason why asteroids have not been able to get bigger. Collisions happen now and they shatter rather than coagulate things. This shattering is still going on when an asteroid gets hit by another big enough asteroid, the entire thing shattered, a new family is created. And you can see these things are allover the asteroid belt, you might already see where this is going. Imagine this impact occur and objects get strewn all over the asteroid belt or at least up and through here. And some of them would've ended up in this resonance right here. What happens when the resonance. Well, they can get very eccentric, very inclined and eventually hit Jupiter or hit the Earth they can become near Earth asteroids. The problem is that these impacts occurred a long time ago. These families can be quite ancient if all of the delivery into the near Earth asteroid system up here, came about during these impacts themselves. We still wouldn't have any near Earth asteroids left. Luckily, there is one more process that goes on, that is, I have to say, crazy sounding. There's a nice paper that demonstrates this process by Bill Bottke, who is best known, well, at least best known to me, as my former office mate in an office right across here in Caltech. Before I was a professor, he and I were both post doctorate fellows in the same office at Caltech. So all the cool things that he's done, I attribute to my great influence on he couldn't have been anything else, I'm sure. Anyway, what what Bill and his colleagues figured out very interestingly is, is that other people had proposed this process that is called the Yarkovsky Effect. And it's, it's such a small thing that it seems like it wouldn't make any difference at all and yet it makes a huge difference. Here's how it works, you have an asteroid and the Sun is off in this direction. And let's say that asteroid is rotating in this direction, that asteroid heats up on this side. And as the rotation comes around, it's still hot on this side. It's hotter on this side than it is on this side, what happens then? Well, it's a very, very tiny effect but this actually turns out to matter. If an object is hot, it radiates, black body emission. We've already talked about this sigma t to the fourth, its radiations photons coming off. There are also photons coming off this way, sigma t to the fourth but because the temperature's lower and the energy is less. That is essentially like a tiny, tiny little rocket engine on this side of the object. Now, if the object were rotating the other direction, it would be hotter over here. You would have a tiny, tiny, tiny rocket engine on this side. Now, I'll remind you, this rocket engine is made out of photons, it's made out of light. It's made from the slight difference in temperature between one side and the other tiny insignificant. If you'd ask me, does this matter? I would say, no. Why could this possibly matter? And I would've been wrong. Here's why it possibly matters, if you take into account this Yarkovsky Effect of asteroids and small asteroids in particular they have to be small. If you're going to have a light as a rocket you better be pretty lightweight. If you start those objects in a particular place and you just track how they evolve in their orbit over time. Here's eccentricity again, I'm changing up on you, I was showing you inclination before semi-major axis again. And this is that set of objects that was on the outer edge of the asteroid belt in this clump right here. And these are the objects that is identified as part of this clump of this yellow dots or objects that have been identified as this clump. Here's the 5 to 2 resonance again, we've talked about that. Here's another of these secular resonances, those ones were you process at the same frequency, it's a complicated one but again, one we don't want to end up in. And object is this simulation, objects are started right about here in a, in a family surrounding the asteroid Koronis. Koronis has been ar, identified as the largest of the objects in this family in through here. It's the one, it's the one that was hit that ejected all these other particles here, so these are all chunks of Koronis in this theory and what happens? Well, even if you start them out at pretty slow velocities, this impact not much occurs from them. This Yarkovsky effect slowly moves them over time, the small ones in particular in along these blue trajectories. Here's the first 100 million years, takes a while over 300 hundred million years they keep on spreading. They spread in one direction mostly, they spread in a semi-major axis, like this in one direction, the other direction. So here, how they, they move here and the first one has hit the 5 to 2 resonance and boom it's gone. When it goes up like that, that means the excentricity is high which means it's bound to cross Jupiter or cross the Earth or both. Same thing happens here when it crosses this resonance, they go up but they don't go up all the way. They only go up to this region here would start to populate up here where other objects are. Over 5 7 hundred million years, more and more objects start to cross out of here. These get ejected into some other region of space and more and more of them populate these regions up through here. It's a beautiful simulation of how this very very tiny effect over something like a billion years can lead to these interesting dynamics we see in the asteroid belt. More importantly, what is leads to is a mechanism that allows particles in small asteroids to continue to dribble out of the asteroid belt. Even though most asteroids are what we think of as stable, these small effects will allow them to cross this 5 to 2 resonance and other resonances. And once they cross it, all bets are off, they can become these Earth crossing asteroids. So this is how, even though we are way inside of the asteroid belt. These small effects are enough that this is going to continue forever to have us have these near Earth asteroids crothing, crossing our path. You might ask yourself, this sounds a little scary. Is there something we should do about it? I give the astounding answer to that question in a couple more lectures.
