The question I'm going to try and answer for you this lecture is, why do we have terrestrial planets? I tried to convince you last time around that we have small bodies because Jupiter was so massive that it, it disrupted the small bodies. It didn't disrupt them as in break them apart, but it excited their orbits. By excited we mean made them eccentric, made 'em inclined, made them have high velocities relative to each other. And so they couldn't attract each other gravitationally, and never got to be very big, and yet we know that the terrestrial planets were big. We talked about these oligarchs, these planetary embryos, these isolation masses, and said that they were something like a tenth to a hundredth of an Earth mass. So clearly, things not only got to that point, but they got even past that point, where those had to have combined to have formed terrestrial planets. Let's remind ourselves what it looked like at that moment when these oligarchs were first starting to appear. And here's one of the way that people typically tend to work on this problem. You can either go through the math, like we did in a few of the lectures. And that is critical to understand the physics of what's really going on, to make sure you know what's happening. But often, once you really want to, look in detail at what happens in a planetary system, understanding just that the relatively simple physics, is not enough. The relatively simple physics is coupled with the stochastic nature of planet formation to give you a range of different things. And the only way to really explore that is to take your understanding and the physics, put it into a computer, and watch your solar system evolve. And that's what happened here in this paper from 2002. The plots are going to look like this. There are four plots, with different time scales, 0 years, 10 to the fifth years, 2 times 10 to the fifth years, and 4 times 10 to the fifth years. So it's a fairly, I'm going to call that a very fairly short time scale, you may call that a fairly long time scale, but 4 times 10 to the fifth years is 400,000 years. So it's not even not even a million years of evolution that we've captured in here. And in these 4 snapshots, we are plotting the size of the object, the, the mass of the object, by the size of the dot that you see here, and the other important property that's being plotted is its distance from the sun, A-U, here's the Earth would be right here, 1 A-U. And its eccentricity, now remember I told you that it's the excitation of the orbit that really matters, that the eccentricities and the inclinations need to be kept small, so that the, the planetary embryos can, can get to grow. And let's watch this process happen here. Everything starts out very small, and you can see just a bunch of small particles [UNKNOWN] here. Nothing, nothing big at all. Eccentricities going from 0, which is essentially circular, up to some very, very small values. Suddenly, press the grow button on your gravitational simulator and see what happens very quickly. Large bodies get to form through here, and notice that the large bodies form closer, faster. Over here the large bodies haven't really started to form yet. But as soon as the large bodies start to form, they excite the small bodies up to higher eccentricities, but, remember that the small bodies keep those large bodies at low eccentricities and and that allows those large bodies to continue to grow even faster. So notice that these large bodies by let's go down to 400,000 years. These large bodies are totally isolated, they didn't really actually grow between here and here very much at all. And it took a while for these to finally isolate themselves. These are, these are just now becoming isolated. These are probably not quite isolated. They're continuing to have the small bodies out here that they are, continuing to eat, as their eccentricities remain low. Okay this is a good start at 400,000 years we now have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12ish planetary embryos. At something like a tenth of an earth mass or, or maybe a little bit bigger down in here. How do these eventually become the Earth or the other terrestrial planets? Well, we argue that these are now far enough apart from each other, that that they can't suck each other in gravitationally like they could suck in all these smaller particles. These are isolated, but isolated doesn't mean that they don't interact with each other. They still have gravitational interactions as they're going around the Sun. And eventually, because there are so many going around the sun, packed in such a tight configuration, they begin to excite their own orbits. And again, exciting an orbit means eccentricities, inclinations, getting arrays. Once they start to excite their own orbits, they will eventually merge, and in most cases they'll merge if you do a simulation with about the right mass, they'll merge into 3 or 4 planets. Maybe the size of the Earth, maybe a little smaller, typically 4, maybe the size of the Earth. It's hard to get Mercury small, it's hard to get Mars small. These will be things that we'll worry about in the future, but it's basically this process of spending all this time making these oligarchs, and then spending perhaps another 100 million years of slowly settling down, before you finally have formed all of your terrestrial planets. It's a very slow process, remember we talked about Jupiter forming in something like 3 to 10 million years. Now we're talking about the terrestrial planets not forming for a very long time after that. [BLANK_AUDIO]. Let's watch that entire process now, and let's watch that process where we have Jupiter, a big massive object sitting here at 5.2 AU where it is right now. Now we will spend a lot of time in the future talking about Jupiter and watching it move around different places, but for now, let's just stick that big mass right there at 5.2 AU. Let's start out a process where we have a bunch of small particles strewn all the way from the location of approximately Mercury, all the way through the asteroid belt. Now we, we don't stop here at Mars which would be at about 1.55 we have all these things in the asteroid belt here. In this particular simulation, they're worried about the delivery of water to the Earth and the planet so they have color coded things by how much water they have. They put a lot water in the outer asteroids, a little bit of water in the middle and no water in here. And the question is, can things like the Earth acquire water that way? We're not going to worry about that question very much right now, we're going to first just watch what happens, now what's going to happen? Two things are happening at the same time. As time goes by, here's the first million years. Masses have begun to isolate. In this case, it behaves a little bit differently, because now it's harder to have as many small masses, [INAUDIBLE] there's so many masses and we have such a big area, that the simulation is running. That the, the smallest masses you don't see at all. And they don't have any effect at all and so, you, you have a little bit slower evolution it looks to me like, because it's taking more like 3 million years before these things really start to get going. But you start to have these, these isolation masses in through here, you don't really have any large masses growing out in through here. But what do you have? You have excitation. You have large eccentricities in these regions and what is it caused by? You guessed it, it's caused by this guy. Causing all these problems, because you have this excitation, nothing big is ever allowed to form now through here. Normally there's nothing big ever allowed to form out through here. Jupiter actually physically removes objects that are closer than about here, it takes them eventually has a close encounter; they could eject it from the solar system. They go into the Sun, they go into Jupiter, they go somewhere. This is part of all that material that hits Jupiter early on, and it gives it all that extra material that we talked about before. 'Kay, let's get up to to 30 million years, 30 million years is a pretty long time. Now after the beginning of the, the, the solar system, Jupiter's been minding its own business for, for quite a while. And we now are down to 1, 2, 3, 4, 5, 6 planet-ish sized things and still a ton of small bodies going around here. This is the stage that we call the, the clearing out of the inner solar system. That clearing out occurs when these planets, these these planetary embryos start to merge and go into single ones. This one maybe and this one that's hard to know exactly who goes into who. Maybe some objects here go into here. And eventually, these planetary embryos become after they were already isolated dynamically here but you can see that their orbits are getting excited in through here. And they clear each other out, they combine, they also clear out all the rest of the stuff in through here. You don't see any more small bodies in through here and instead, you see 3 in this case, planets. Now, you may say 3 planets, 3 terrestrial planets, that's wrong. We have 4. Well, you press the Start button on the computer again, you might get 4, you might get 5, you might get 2. They might have little mass here, a little more mass there. It's a stochastic process. What you end up with and where they end up is really subject to total chance, totally what happened in this instant here. Did this object happen to get close to this one? And make this one who knows? And you could have, [UNKNOWN] our own solar system, our terrestrial planets could have been any number of different configurations. It's kind of nice the way that we got the one that we did because I kind of like living here on the Earth, but it need not have been that way. Let's look what else happened. You have in addition to these giant planets, you now have a few objects left over, in the asteroid belt. Now you might also ask, why so few objects in the asteroid belt? And the answer is, because again, we're only able to track, moderately large particles in this simulation. The asteroid belt is also filled in with a ton of small bodies. But those ton of small bodies have been generally removed from this region here, and they will be in the region that we now know is occupied by the asteroid belt now. So, what's the difference between the small bodies, and the terrestrial planets? The the terrestrial planets were not bothered enough by Jupiter, to keep from going to this second process, that process of taking the oligarchs and combining them into even larger and larger real planets here. The small bodies are the ones that stayed small. They stayed small because nothing large was ever allowed to grow in this region, where eccentricities first started getting high, and there were no small objects that were pulling things back down again, and no small objects were allowed to form. This is all a great theory, and you put it on the computer and it looks about right. And you get time scales. Over here we get 200 million years for how long it takes for the, the planets to form. Is there any way to go back in time 200 million years and answer the question of whether this is really true? The answer is, and, and the answer for a lot of these questions about the inter-solar system and time scales. The answer will come from, things like meteorites, which we'll talk about in detail, and actually even looking at isotopic ratios, on the Earth. There's one in particular, which I think is a, a, a beautiful demonstration of the power of isotopic geochemistry that answers some really profound questions about things like timescales of the formation of the Earth. Let's go into that one in a little bit of detail and and see how it works. This is called hafnium, tungsten, tungsten is a W. I'm sure there's a reason for that, I don't know what it is. Hafni, hafnium tungsten dating. Hafnium tungsten dating is, is I think super cool because, it exploits a couple of random but in, incredibly important and and clever properties of the element hafnium and the element Tungsten. And these two are also connected through radioactive decay. So, here's the way it works, it's actually [UNKNOWN] tell you, super cool. Hafnium is an element that is called a lithophile. For all of you who know you Greek out there, phile means friendly, litho is rock. These are rock friendly elements. That means, if it has a choice of where it's going to go, if it's, if the, if the mantle were, were molten or, or things were freezing out or something, hafnium would go into the rock part. The other option is, something like Tungsten, Tungsten is siderophile. Okay, we have the same file, it's friendly to what, this is iron, it is iron friendly. At some point in time, driven by all these impacts, as the Earth was being formed, the Earth differentiated. It was probably at first this big ball of things that were iron and rock in many different places strewn throughout, and as we know now, it is iron on the inside and rock on the outside. That process, as this process occurred, the hafnium would stay here, and the tungsten, would go down here. Most of the tungsten that was a, available in the Earth should have sunk to the core, back when this happened. An interesting thing happens, though. Hafnium 182, has a half life, of 9 million years. And when it decays, what does it decay into? Tungsten 182. Why is this good? Let's think about this for a minute. Let's think about all of this hafnium and this tungsten in the originally all mixed up, hafnium is decaying into tungsten. Finally differentiation occurs and it doesn't matter where the tungsten started out with it is siderophile, so when tungsten goes away leaving just a little bit of hafnium left. Now we have all the tungsten in the core, the hafnium is in the mantle now, and, what happens? Well, whatever hafnium is left, a 182 still starts to decay, or continues to decay. And suddenly, there is tungsten stranded in the mantel, tungsten 182 is in the mantel when it shouldn't be. Why does this help you? Well, it gives you a time scale. This 9 million timing scale is perfect for this. It gives you time scale because if the differentiation happens really fast, all of the tungsten goes down really fast, then there's still a lot of hafnium 182 around, and it creates a lot of tungsten 182. So if you find a lot of tungsten 182, differentiation occurred really super early. What if differentiation takes a long time, it takes a long time for the planet finally to get to it's final state. Well, by that time the hafnium is all decayed into tungsten 182. The core happens and all the tungsten goes away and you look in the mantle of the earth and you don't see any tungsten 182. And what's the answer that you get when you do this? Well, something like 30-100 million years for that last differentiation event. Now, it's complicated, there're, there're many different ways to interpret what this hafnium, tungsten date really is telling you, but, I find it intriguing that this 3200 million years is not dissimilar from those time scales that it takes dynamically for all these, these planetary embryos to pull themselves together, to finally make themselves, into a planet. Those big impacts would have, have left entirely, potentially entirely molten planet, and it would be after those big impacts, when you could finally differentiate and make this iron core. When did that happen? Well, maybe 30 to 100 million years, which is just what we expected. Something really strange about hafnium tungsten though, if with respect to Mars. We know the Mars hafnium-tungsten age because we actually have meteorites from Mars. We'll talk about, again, talk about meteorites in detail. What do you get if you try to figure out the hafnium tungsten age of the differentiation of Mars? You get something like 5 million years. That is a quite a bit shorter than these time scales here. Basically, that means that the Martian meteorites are filled with tungsten 182 because the differentiation happened so fast, Hafnium was still all very active and all that 182 strapped in the mantle. Why would these have a very different timescale? [SOUND] That's a complicated question, and we will get to it, in some of the very last lectures of this unit. But it's it's a hard one to, to try to answer. But, let's recap here what we know now. We know now that terrestrial planets form the way they do because they're being protected from the influence of Jupiter by being just far enough away, and that they form those oligarchs really fast, just like everyone else does. But then they take of order 100 million years before they really become the planets that we see around and love today and that time scale is nicely matched with the hafnium tungsten age of what we think these planets might really be. Okay, now that we know where these terrestrial planets came from and where the small bodies came from, we can start to look at the bigger picture of how much of this stuff is really there.
