We learned in the last lecture about what comets are made out of and we see that they are made out of these ices that much have formed in the outer part of the solar system. The next question is, where do they come from? And, this is a really interesting part of the questions. So first, we have to look at the comets that we have found in space and look at their orbits and try to understand what that sais about the origin of comets. So, let me draw you a few orbits to give you a general flavor of what sort of orbits, comets have. Everybody has this general impression that, we'll put the Earth right here going around the Sun, that comets are on very elongated orbits around the Sun. It's true, they do something like this. They come around maybe very close to the Sun. They go much further out this way. This is when we see them, particularly when they get inside of three A.U. this is when they have their coma, they get super bright here when all the things start to evaporate. They fade out as they go further out through here. What do they do out through here. Well it would be an important part of the picture there are really two, at least two different types of comets. Dynamically. By dynamically I mean based on looking at their orbits. There are two different flavors of orbits right now. And to over simplify, I'll say it this way, if I'm looking at the solar system from the side, often I draw the top down view with the planets going around like this. And here I'm not here the planets are all in these plain Right here. We'll put the Earth here and Jupiter out through here. All the other ones, you know where they are. There are one flavor of comets who have orbits that are very close to the plane of the solar system. And who have elliptical orbits that go out to Jupiter, a little beyond Jupiter, but back and forth this way. Back and forth this way. That's one type of comet. These are actually called Jupiter family comets. And as you might guess from the name they're associated in many ways with Jupiter. But there's another entirely different type of comets. And those comets, instead of being stuck in the plane of the solar system and at relatively modest distance, these are the ones that come from very far away, from all directions, and they come around the Sun and go back out. And we never see, their outer distances are extremely huge, they come from everywhere, they seem relatively isotropic. These are called, not surprisingly, isotropic comets. For a long time it was assumed that the relationship between the isotropic comets and the Jupiter family comets was that. The isotropic comets would come in, go around the sun, come out, and every once in a while one would happen to get close to a giant planet as it was coming in, and that giant planet would alter the orbit and pull it into the plane of the solar system, and so this was an evolutionary effect. Turns out, that's not actually true. This is one of those things that seemed true when you sat down nd wrote the equations out looked like it might work out and it took until computers became fast enough that you could follow the dynamics in a computer, calculate the forces in the computer, see enough of these things to happen. They realised is actually not true, they're two separate sources for comets. We'll get to those in a little bit. Let's first talk about the Isotropic comets. The key question about the Isotropic comets is you know, we see them coming in from very far away and going out to very far away. Where did they come from? There's a way to know the answer that which is to very precisely calculate their orbits during the period time when they're close by. And they're on an orbit, they're on orbit around the sun and so if we can figure out exactly what their orbit is like here we'll know what their orbit was all the way out here in the tail of this orbit. Now I'm drawing these things purposefully not showing you how it's closed over here. Because there are really three possibilities and I'll draw those three possibilities for you now. Orbits can be elliptical. And again, in an orbit, the ellipse has two foci, there's a focus here, there's a focus over here, and the Sun is on one of those foci that comes in close. This could be really far away, but it's still an elliptical orbit, it goes around forever. The extreme version in the ellipse, if you take the eccentricity greater, greater, and greater, in fact to officially eccentricity, these have eccentricities of less than one. I'm going to now draw you what happens if you have an eccentricity is equal to one. You get a parabola and parabolas look like ellipses for a while but they never close. They go of to infinity, always further away. parabolas are. You have to be exactly perfect orbit to be the parabolas. So real parabola orbits never exist. The real option is eccentricity of less than one as an ellipse. Or an eccentricity greater than one is mathematically called a hyperbola. What is a hyperbola? Hyperbola would look more like this remember your high school geometry, a hyperbole also has another branch over here. But we're only talking about one branch of the hyperbole and the difference between hyperbole and an ellipse are critical. Ellipses are things that are bound to the sun, they are totally confined to the gravitational pull of the sun and they go around the sun like this. A hyperbola is something that comes from interstellar space and goes flying by the sun but's not captured. If something has an orbit of something like 0.99 or 1.01, these two things are both so close, maybe this is actually an ellipse that I'm going to close at the end. Maybe this is actually a hyperbola that's going on forever. Maybe it's a parabola, they look very similar when they're in close. So you have to get their orbits very precisely. And when enough of these isotropic comets were measured, a fairly astounding thing was discovered. This is a plot showing you an important parameter in the orbits of comets. And now, instead of showing you the eccentricity, which would maybe make it easier for you to understand, we're actually plotting one over the semi major axis. So, small numbers mean they have really large semi major axis. Officially a has a semi major axis of infinity, and so zero right here is a perfectly orbit. These are ellipses, and mathematically a hyperbole has a semi-major axis of less than zero and negative semi-major axis. These are over here. These are hyperboles. And, as you can see, the key differences between things that are bound and things that are unbound. And what do we find? Well, notice that this bin, of all these objects, is actually, it's not at zero, they are not parabolic, it's slightly greater than zero. Every single one of these objects through this bin is bound, it's an ellipse. It's not on a parabolic orbit, it's on an elliptical orbit. All of these are bound on elliptical orbits, a few of them are on hyperbolic orbits. But, in fact, in every single one of these cases on the hyperbolic orbits, the hyperbolic orbit you can tell. Occurred not because the object came from interstellar space on a hyperbolic orbit, but because it was perturbed by a giant planet onto a hyperbolic orbit. For all of the well-measured comets that are not perturbed by giant planets. They come from elliptical orbits but with 1 over a incredibly small which means a is incredibly large. In fact, let's look how large. I should have point out a bit last plot as well as this one. It means very nice review article by Luke Downes and company called Comets 2, when you can take a look at that chapter in that book and learn a lot about where these or cloud comets have come from. Now, I'm showing you semi-major axis, which is a, not 1 over a. So, you're actually seeing what the semi-major axis is. And again, number of comets. And these are the ones that are coming into the solar system from really far away. 10,000, 20,000, 30,000 AU maybe. Some of them up to 100,000 AU. AU is the distance from the Earth to the Sun. These things are on orbits where they're semi major major axis 30 000 au. And the semimajor axis is 30000 au and they come all the way to the sun that means the outer extend of the orbit is 60000 au. It's a tremendous distance that things are coming away from. Not all comets do that, there are these ones that are called returning comets and these are ones that. The story is presumably these were comets that came, new comets, came in for the first system. Got again, perturbed by giant planets and got pulled on to slightly smaller orbits too, but we're not going to worry about those. Mostly we're going to worry about the new comets in through here. What's going on out there? How can there be comets coming from 30,000 AU? Well, one answer might just be that there are comets that are at 30,000 AU or on orbits that go on all the way to 60,000 AU. And they just go around the sun and go around the sun and go around the sun. The problem with that idea is that something that has a semi-major axis of 30,000 AU, we know that the time of the orbital period, the time it takes to go around the sun, Is a to the 1.5 power. So, we take 30,000 to the 1.5 power. We get something like 5 million years. We also know and we'll talk some more in the next few lectures how we know those. But, we know that the solar system is something like 4.5 billion years old. So, if something is on a 5 million year orbit It's gone around the sun many, many, many times in the history of the solar system. And yet, we see that when these new ones come in, they are often ejected from the solar system by Jupiter, pulled into these smaller orbits. Something happens to them. So, it's highly unlikely that these things have been going around the sun for all of this time. It seems more like there is a cloud of material that's near the outside of the solar system where occasionally something comes in from that cloud of material. Now this idea was proposed nearly a century ago. People thought there might be a cloud of material that was out there caught, I say cloud of material, but a cloud Comets, and cloud is not even the right word, a collection of comets on the edge of the solar system, people argued for a while whether it really was comets at the edge of the solar system or comets coming in from interstellar space, the problem with comets coming in from interstellar space is that they would have been coming in very very largely negative. Hyperbolic orbits, largely negative semimajor axis, and they're just not seen. Comets are not coming from interstellar space. Comets are coming from 30,000, 100,000 AU. And it appears that they're coming out there for the first time. It was a very strange thing, how is this possible, how did they get there? Some ideas were that they just, this is the edge of the solar system, they just condensed out there, out of material We are now pretty clear that can't be true. We've talked about how you make solid objects in the solar system and it requires all these collisions and building up and the amount of material out in the outer part of the solar system is so small that this would have never happened. So, why would there be all these objects out there where they weren't there to begin with? We'll find out in the next lecture.
