Transcription
Okay, so, as you see up here, my name is Red Heelless. I'm at the University of Texas at Dallas. I'm a plasma scientist and experimentalist, mixed with a little observation and theory. I realize everyone is from rather diverse backgrounds, and all of you are, in one way or another, embedded in your own little box to conduct your PhD research work. So my objective here is not to encourage you to step outside your box in order to do your research. My expectation is not that you're going to learn everything about ionosphere-thermosphere processes. But what I would like you to do is two things. I'd like you to leave today, after I get talking, with some information that you can carry with you for your careers about what the important aspects of ionosphere-thermosphere processes are. I'd like you to recognize that the fundamental physical principles that we use when we study the ionosphere and thermosphere are exactly the same as the fundamental physical principles that you are using in whatever box you're in. And then I'd like you to recognize one last thing, and that is you're about to set out on your careers, and I would guess that more than 50% of you will not be doing what you're doing now in pursuit of your career, much as you might like to believe you'd like to do that for the rest of your life. The chances of you doing that are small, and so your success in navigating your career is going to be dependent, to some extent, on your ability to recognize and speak the languages of people who are working in space sciences in other disciplines. And so I'd like to get you—encourage you—to learn a little bit of the language of, in this case, ionosphere-thermosphere processes, in order that you can appreciate what other people are doing in the system. Maybe you can take in a talk at a GU in a field that's completely different from one you're working in now, just to broaden your horizons and give yourself a better opportunity to interact with the community, which will help you in the short term to recognize how similar the processes are that we're dealing with, and in the long term enable you to branch out into other areas if they seem more productive, better funded, or whatever reason you need to do that later on. So those are my objectives. So this is what I want to do.
I want to talk a little bit about the upper atmosphere of the planets and the ionosphere of the planets in terms just of their constituents and how they interact with the Sun and with the planetary magnetic field, if one exists. So we'll talk a little bit about what you would see or what you do see and why you see it—the underlying physical principles. And then I'd like to talk about how the charged particles in an atmosphere and the neutral particles in an atmosphere interact with one another, and they do that by exchanging momentum and energy. And there are two particular processes that I'd like to dwell on a little bit in that interaction, and that is current systems in the—in the sister—in the ionosphere and thermosphere, and the dynamo action of neutral winds. And so this is another dynamo; there are lots that you've experienced already and in this class, and this is another dynamo that's been alluded to in a few of the talks before.
I want to get started. Before I get started, I want a couple of apologies to make. My notes or the slides will differ a little bit from the slides that you're looking at if you grab the online version. I'm sure we'll fix that, but as a result of the conversations that have occurred during the school so far and some of the interactions that that we've had and that I've observed among the students here, I'm going to change a little bit what I say. If the—if the material presented is the same, to try to have you recognize that the physical principles that we—that we apply in many cases are the same physical principles, just that maybe the origin of forces are different. So there's a lot of material in textbooks, and in particular the books from the heliophysics summer schools, which you now are in possession of, where some background and some further extension of the material that I will present here exists. And so these are the—I can get this to work—in these various volumes. He's a physics 1, 2 & 3; there are chapters—many chapters—that talk about the interaction between charged and neutral species in planetary atmospheres. I will cover the basics and so that you are familiar with what you will see and why—why you will see it—and more. The details are in these books and in—in other textbooks.
So I want to start up with a little quiz—it's a bit of information for both of us—just so that we can—I'd like to get some perspective about the things that we know and the things that we don't know when we're in a general audience like this. So I'm just curious how many in the audience here can tell me what the dominant ion species in the lower corona of the Sun is. All right, so can I just have a show of hands? Who—everybody who knows—well, and be confident—hey, what's the downside? Yeah, that I could—oh, you think you know? You think you're right, and everybody thinks they know, and they'd say hydrogen, right? Page play. Yeah. Okay, so there's a fair number. Okay. Yeah. What about the dominant species in the lower atmosphere of the Earth, say 140 kilometers? How many people think they know? Oh, there's kind of an interesting—so it doesn't matter what the—my point is that in this audience, for example, one of the things that you can get out of that is that this audience actually knows more about the Sun than they do about the Earth, right? So you know—you should look at that and recognize that, hey, that's—over something basic about the system in which you live in, and you should look at that and say, hey, that's really a gap in my knowledge. I—order not—right. I don't need to know why, but I should—I should have some basic understanding at some system level. So it's not a criticism; many people are like this. If you go to an ionosphere-thermosphere session, the show of hands would be reversed, you know, and so—but that represents sort of a gap in our knowledge—overall knowledge of the—of the system. Okay. What about the temperature of the plasma in the corona? You say—who thinks they know the answer to that question? And what would you say? Million degrees. Okay, sure. Okay. Um, what about the temperature in the planet's upper atmosphere? Though there's a similar asymmetry in the distribution of the hands, right? That in fact more of you are confidently, you know, the temperature in the corona than you—than you know the temperature of the upper atmosphere. And so—so this is just the point that I want to get started is that, you know, there's always an opportunity for you to learn a little bit about the system so you can appreciate where the—where the gaps in your insight of this Sun connection between the Sun and the planets and planetary environments are.
So now I'm pretty confident that the show of hands will go down because now I'm going to be talking a little more about the ionosphere-thermosphere processes, but what about the dominant neutral constituent at 300 kilometers in the Earth's atmosphere? There's a smaller number of hands, that's—and that's fine. So—and then one point I want to make here is that this neutral constituent in this atmosphere, as in other planetary atmospheres, is not a native neutral constituent of the atmosphere we breathe or the atmosphere that originates at the planetary surface, and I'll get back to that. And just—though if I took that around the same altitude and asked what the relative neutral and charged particle number densities in the atmosphere were—in the Earth's atmosphere—and many people would know—sorry, where are you at? 350? It doesn't matter; doesn't matter; it's not a big function of latitude. Who? So again, maybe a little gap in knowledge. And then as far as the dynamics of the species are concerned, I want to go through these—these details, but how these are—this is information about the—how the ions—charge—the neutral particles interact with one another, and there's probably just a few people that have some insight into these questions. So the point I'm trying to make here is that you can, by attending a talk in some area where you are not familiar, you can always use that as an opportunity to broaden your—your horizons. So let me just leave this slide by encouraging you: next time you go to the AGU meeting—and I'll discuss this with other instructors—you've been to enough AGU meetings, I hope everybody—all of you—vintage meetings—you can probably make an assessment of how many—of the presentations in your field you could have neglected to go to and—and wouldn't have made a big impact to the—to the benefit that meeting had on your—on your research. And I'll be willing to bet that that number—I've done the polls in—might for my students—and the numbers about 25 percent at least. Okay, so you could take the time that you spend on 25 percent on the sessions that you attend in the area of your expertise, and you could just thumb through the other sessions at AGU and say, you know, I—I know absolutely nothing about the impact of the Sun on climate, and there's a whole special session on that, and that first paper—there's a review paper by some notable in the field—I think I'll just go hang out in that session and learn a little bit about Sun-climate. And so you can—you can broaden your horizons, learn a little bit more about what's going on, just by dividing your time. You don't have to know all the nitty-gritty; you can just learn some of the basic physical principles, and if you listen well, you'll find—and write down what you hear—you'll find that the physical principles that are applied are exactly the same as the physical principles you apply in your field. They're not that different; they can be cast in different ways, and I'll come back to that as we go along here, but there are not very many physical principles that you apply, right? Conservation of momentum, conservation of energy, conservation of matter—that's about it. Okay, and if you happen to be in a plasma, you have to throw in Maxwell's equations, right? But those are the fundamental principles. You have to recast them in order to make them apply in the area you're applying in, but you can relate those fundamental principles to whatever people are talking about.
Okay, so I thought what I do here is—soon I'm going to play a little movie. This movie repeats. It's a picture taken with a Nikon camera in visible light from astronauts in the space station, but you just take a—it's not an inexpensive Nikon camera—stick it out the window and take a movie. You may have seen these movies on YouTube; there's a lot of them. Some of them played to very dramatic music, but this is an orbit around the space station—of the space station across the equator, moving from southern—from northern latitudes to southern latitudes over the continent of India. And what you can see here is you can see the surface of the Earth; it's this very dark limb here, and you can recognize that because you can see the stars rise behind the atmosphere. So this is the limb of the Earth, and above the rim of the Earth here there's something that looks yellow, and that's because they don't have a very good infrared filter on the Nikon camera, and so the infrared emission—this is actually infrared—the heat from the atmosphere shows up as this yellow sort of glow above the atmosphere. And then the top of the center of the upper atmosphere, where—where we are going to understand it—try to understand how the atmosphere and the ionosphere interact with the Sun—is—not—by this green line here, and above that there's these—this red features—a red emission which also comes from the atmosphere of the Earth, and you can see it's got lots of waves in it. And various times—various times of the day as we pass by here, you can see variations in the intensity of the image of this emission, which is produced by an interaction between the charged and the neutral particles. So there do exist images of the upper atmosphere. So you used to use—looking at images of the Sun are recognized—and—and images of the magnetosphere and images of the aurora—these are images of the Earth's atmosphere, and they're seen because they're—the atoms in the atmosphere—because of their interaction with the Sun and the ionosphere—are raised to excited states, and as they decay to the ground state they may emit visible light. So this light is sensitive enough to record on a camera; it's not sensitive enough for your eye—more to see though. Yeah. So—um—let me just go back. So I put a scale, and it kind of goes away when I play the movie for reasons I haven't figured out yet, but this layer is at the bottom of the atmosphere, about 120 kilometers, and this layer—the red layer—is at the top of that—of the atmosphere or the middle of the upper atmosphere, about 300 meters. So you could see—just by looking at that—this movie—I encourage you to go on YouTube and take more looks at it—you can see—like—as you—I hope—I hope you saw lightning flashes across the oceans and across the land masses and very dynamic pictures as it—as it changed in—in local time where the amount of the Earth was sunlit changes. Okay, so—um—well, I want to do first is just take a simple look at the properties of the neutral atmosphere. So this just shows some profiles of the density of the various species in planetary atmospheres. This—this is Venus—for Venus; this is for Earth; this is for Mars. And there are several things like that I want you to notice—or I'll ask you to notice. So the first thing is if you look at the upper atmosphere of the planets—the upper atmosphere of the planet—you'll see neutral species—in this case atomic oxygen here, atomic oxygen here, atomic oxygen—that are unrelated or—or have very small concentrations—in—in fact, maybe zero concentration—at the surface of the Earth. So near the surface of the Earth—of Venus, Earth and Mars, for example—the atomic oxygen density is very, very—luck—there's almost no atomic oxygen at Venus and Mars. The dominant constituent everywhere is carbon dioxide, and yet in the upper atmospheres of the Earth, in addition to carbon dioxide, there are other neutral species—atomic oxygen and—and CO in the case of Venus, in the case of Mars, and atomic oxygen in the case of the Earth. So the upper atmosphere of the Earth can differ from the lower atmosphere of the Earth, and the reason for that is that all these gases are subject to solar radiation, and they absorb solar radiation, and in the process of absorbing full solar radiation, the energy of the incoming photons can be larger than the binding energy of the molecules in the gas, and so the gas can dissociate. So—so dissociation—molecular dissociation by the absorption of UV photons—is a common phenomena in planetary atmospheres that gives you a distribution of neutral gases in the upper atmosphere that's different from the source gases. Okay, so remember that.
The second thing that you'll notice in all these pictures, I hope, is that the altitude distribution of the gases in a planet changed dramatically as a function of altitude. So if you look here at Mars, for example, you'll see CO2, O & CO all drop off at the same rate in altitude until you get to about 120 kilometers. I'm going to have a trouble pressing the wrong button. On the Earth it's not so obvious, but you can see these two profiles turn over. I'll show a little bit more detail here where they both have that decrease at the same rate until you get to about 120 kilometers. In Venus, the crossover is higher up, but you can see CO2 and CO drop off at the same rate until you get to about 150 km, and then they have different—they drop off at different rates. So the distribution of the gases in a planet change with altitude, even though these gases are gravitationally bound to the planet. Okay, so the gravitationally bound to the planet, and so you would think in—in a—in a sensible—most sensible way—that the balance of forces in a situation like this would just balance the pressure gradient of the gas with the gravitational force. And so what does this mean? It means all the gases behave the same way up into some altitude, and then they behave as if they were separately distributed. So what that means is close to the planet surface—up to 120 kilometers or so—all the gases are mixed together, and that's because near the surface the atmosphere interacts with the surface itself, and the surface topography of the—of the planet mixes the gases together. And as you rise in altitude, the—the gas density decreases, and molecular diffusion—that is the diffusion of the individual particle collisions with one another—exceeds the diffusion rate—exceeds so-called eddy diffusion—and that is the ability of turbulence to stir the gases up. So okay.
Then the last thing I want to talk about in terms of the neutral atmosphere is just the heat sources and sinks. So that once you're armed with this information, you'll be able to look at profiles of density and other information about an atmosphere and figure out what's going on. Once you understand the basic principles that must apply, you can look at data, and it can be useful to you because you can interpret it in terms of what must be going on. So the other thing is to recognize what the sources of heat are in a planetary atmosphere, and the first ones—rather obvious one—right—the absorption of solar radiation. And you've heard from previous talks, particularly the one this morning from—from friend—that particle precipitation from the magnetosphere—high latitudes—it's manifest itself in the aurora, for example. Those energetic particles lose their energy in the atmosphere, and so they heat—what we'll see later on is that frictional heating—because the forces that drive charged particles and the forces that drive neutral particles are different—the ion and neutral velocities can be different, and so they will collide with one another, and when they do they can exchange momentum and energy, so that can be a heat source. And I've already talked to you a little bit about the Earth's topography—or the planet's topography—that stirs the gases up, and that's—that stirring mechanism—and can produce a distribution of waves in the neutral atmosphere, and those waves have to conserve momentum, and so as the density goes down with altitude, the wave amplitude must increase, and at some point those waves break—just like sea waves break when the density gets low—and they dissipate heat in the—then the other important thing to remember in any fluid is conduction. Conduction is capable of transferring heat from one place to another. So the thing to keep in mind when you're looking at an atmosphere is conduction along a temperature gradient. So I have a hot spot here and a cold spot over there; I lose heat here and deliver it there through conduction. What we want to be able to do is to relate—can—the heat sources and sinks to the temperature in the atmosphere. Okay, so can anybody tell me—do you have a good feel for the difference between heat—internet—in a fluid and the temperature of the fluid? If I increase the heating in a fluid, does the gas get hotter? Sounds like a trick question. Yeah. Okay. So the point I want to make is when you think about heat—the heat—it is a property of the volume of a gas. You'll—you'll frequently hear the term heat capacity—how much heat can a gas—and a gas contain? It's a property of the volume of the gas. The temperature is a property of the individual particles in a gas. So if I have a lot of heat and a small number of particles, the particles are very hot; they have a very high temperature. If I have a lot of heat and a large number of particles, then the particles don't have to have as high a temperature to accommodate the same amount of heat. Okay, so just remember that the—the temperature depends on the heat per unit mass. Okay, so with that information, we can look at a profile of the—of the temperature—in—this is a temperature in the Earth's atmosphere, and you can see—rather than the temperature just decreasing as we expect it to do—it—from the surface—at some small distance above the surface—15 kilometers or so—the temperature starts to increase, and we go a little further, and the temperature starts to decrease, and then we go a little further, and
Temperatures now actually increase again. And so there's some information here in a profile like this that allows us to identify where the heat sources are. So remember, this is going to be heat conduction in the fluid, so there always there'll be some transport of heat from the hot spot to something colder. Okay, so what do you think makes the temperature decreases as we rise in altitude? Yeah. So I mean, so that's a good way of describing how the temperature changes, right? Is the lapse rate. Well, it was what makes the—why does the temperature decrease as you go up in altitude? And so this is the amount of heat in a given volume. So here what we know is this tells us two things, right? It tells us the heat sources down here at the surface. Okay, and as we move up in altitude, we move into a much larger volume because we're expanding into a sphere. So there's a lot more particles. Yeah, and there's only a certain amount of heat that can be conducted from the surface up into those particles, and those particles have to go into a much larger volume, and so they're not as hot. These words here—this is just for your information—all come from either Latin or Greek roots.
But then once we get above this, the troposphere here, drop with pause, it's so named because the temperature starts to increase. So what does that mean if the temperature starts to increase? Then it must mean that there's a heat source above you, right? Okay. So now we can ask, okay, let's get rid of all the considerations about heat from the magnetosphere and all these other places. Where do we get the heat from? That we get the heat from absorption of solar radiation. Well, this tells you, right in this region here, heat from the solar radiation is being absorbed by the atmosphere, and the atmosphere is being heated. Yay! So we'll come back to this. I'll just mention it now, right here, the principal absorption comes from O2 and O3, ozone, and like kilowatts. This is the so-called ozone layer. It turns out, as you well know—hopefully you know—that the absorption of the radiation from O2 and O3 occurs in the UV radiation, in the UV wavelengths. And so that's very fortunate. I'll leave it to you to decide whether it's fortunate that we're that we're sensitive to UV radiation, and that UV radiation that we're sensitive to happens to be absorbed by the atmosphere, or whether we evolved that way because we were not subject to the UV radiation that would harm it in this region where the heat is deposited. Now the temperature starts to decrease again, and we get to a certain point where the temperature starts to increase again. Oh, where's another heat source somewhere up here, right? That turns this decrease in the temperature, which is what we would expect, turns around in the temperature starts to increase again. So there must be a heat source here, and here is where the atmosphere of the Earth absorbs radiation from the Sun. In the absorption is by O2 and O, the atomic oxygen, and that absorption results in the ionization of the species. So in this region here, not only is the solar radiation absorbed by the neutral atmosphere, but the neutral atmosphere here is ionized as a result of that absorption. And so in this region here, we start to produce charged particles. Yeah. Okay, good question. So leads me to my next slide. Thank you. Okay, so I think that's all I want to say beyond this.
So if I were to take—if I were to take this all this structure in the radiation away and ignore the scale here—hopefully you would recognize this intensity of radiation as a function of wavelengths that goes up like this and drops like this. You'd recognize that intensity spectrum of radiation. Everybody recognized that shape. What is it? This is a blackbody radiation. So this is a shape of a blackbody radiator. It's not quite certain—the accurately the shape of a blackbody radiator because it reflects the absorption of the radiation in the atmosphere. So yes, I'm going to translate that. Okay, so imagine you have a blackbody radiator from the Sun incident on the atmosphere, and then you ask where and what wavelengths will be absorbed and where will they be absorbed. That reflects you a question here. Okay, so now you have to ask yourself what is required for the absorption of radiation by a molecule or the ionization by by a photon. So how many of you did quantum mechanics in undergrad and grad? How many of you've forgotten all the quantum mechanics you did in grad—you graduate? There we go. Okay, so but so let me just say that you all know, I hope, that there are simple simple models of the molecules, right, that have the electrons surrounding the nucleus of an atom and the molecules that are all in discrete energy levels, right? And so what is the absorption of a photon require? The absorption of a photon to produce a molecule with a different energy or to dissociate the molecules requires that that photon be able to displace an electron from one shell to another shell or to displace the electron completely from the atom to produce an anion and an electron, right? So photons are only absorbed at discrete energies. So only certain bands—only certain energies in this blackbody radiator—will be absorbed by the molecules in an atmosphere, and it will depend on the electron energy levels in the atmosphere. Okay, it turns out that all those energy levels are in this wavelength regime here between say 60–80 nanometers and 180 nanometers. Yeah, everybody knows how to convert wavelength to energy, right? So if if you needed to do the quantum mechanics, then you could quite easily convert this by multiplying by h-bar over C, you could convert this wavelength to energy. If you did that, you will see that this energy range here is from about—oh, I'm gonna guess—any V2O—horrifies—something like that. So in this energy range, the molecules in the atmosphere match with the photon energies and they're observed—absorbed—and of course there are certain molecules at certain altitudes, and so this tells you where the absorption of the photo of that energy takes place in altitude. So if you just go to 90 or angstrom and 90 nanometers here, that's absorbed in the Earth's atmosphere at about 120 kilometers and it produces N2+, O2+, atomic oxygen, and other molecules—ions. So here in this wavelength regime here above 200 nanometers, the radiation is absorbed at much lower altitudes—below 50 kilometers—and this is the absorption—the UV radiation that's harmful to human cells—that's absorbed by O2 in the atmosphere and by O3. The O2 is dissociated into O and O, and O2 come together to make O3. Okay, so that just tells you that it's absorbed lower down in the atmosphere in this way. So this is the spectrum of radiation, and this is the altitude at which that radiation is absorbed by these molecules to produce these constituents.
Okay, so the other thing I want to make sure you understand about the neutral atmosphere is the concept of the gas being gravitationally bound to a planet. Hopefully you're all familiar with this. I don't need to spend a lot of time on it, but it's just again think of it in terms of force balance. Force balance in a quasi steady state is a remarkable tool that you can use. We talked about it with when we were doing force balance in a plasma, and it works perfectly well in the neutral atmosphere too. And the forces in the neutral atmosphere are a pressure gradient—there are other forces—but the major forces, particularly those acting vertically, are the pressure gradient in the gas and the gravitational force. And if you balance those two in equilibrium in a steady state, then the pressure is distributed out in altitude by in a simple exponential way where the e-folding distance of the density is called the scale height. So you'll see in different textbooks the scale height written in different ways—KT over mg or sometimes it's written—if you're a fluid dynamics person—you write it in terms of the gas constant—RT/mg—where this is the mass density and not the mass. Okay, so so I just written this completely so you can use it either way if you apply it in the textbook. So this is a very simple picture. And so what this tells you here is that these gases—I've shown you these—skin this before—just going back—each one of these gases above about 150 kilometers has its own scale height that's determined by its mass. So on Earth, for example, is the oxygen scale height, and the O2 scale height is a factor of two smaller than than oxygen scale height because the mass difference is a factor of two. Below 120 kilometers, because the gases are all mixed together, they have a mean mass that depends on how much gas there is and what the mass number is, and all the gases are distributed in that way. So there's a magic place here where the gases make a transition from being well mixed to they're having their own diffusive—their own hydrostatic equilibrium—and that's called the turbopause—where the gases are well mixed below and individually diffusing or individually have pressure balance between their gas and gravity above that. This separation boundary is called the turbopause. And just note that on the in the Earth—all these regions—the troposphere, the stratosphere, the mesosphere—all these regions are below the turbopause, so they're all the well-mixed regions. And once you get above the turbopause, which is about 120 kilometers, is where the upper atmosphere and the thermosphere begins. Yes. So yes, so the turbopause marks the boundary between the homosphere and—about—it's the same—different word with the same thing. Okay. This is just for your information, and I had a little homework exercise for you to go—just to get some education in our field—in the ISP thermosphere because it's fairly rich with measurements. There are international standard models. So if you want to get some information about our atmosphere—the Earth's atmosphere—you can go do that. I don't website here—I'm new—web—GFC—nasa.gov. And I want to make a note of this—you can get information about the interplanetary field—Indesit—all kinds of indices—probably most of you who—if you're in space science—know about this website. You can go to, and you can select by day where you are in latitude, longitude, and time. You can say what kind of resolution you'd like in a in a particular profile, and and obtain as a listing file or as a plot and in what kind of information you need—all the information about the constituent densities in the atmosphere and the temperature in the atmosphere. And there's a lot of information you can get by recognizing that a planet in quasi-equilibrium will be in hydrostatic equilibrium. What does it mean? It means that you can measure the density anyway, and if you know something about the temperature—say that the temperature is constant or something about the temperature—then you can just—you can calculate the densities everywhere else in altitude. This is just a little exercise, for example, if the temperature was constant in altitude and I knew a certain scale height of atomic oxygen, I knew the density—this atmosphere looks like Mars—contains CO2 and O, and I know what how they're distributed at a peak altitude, then I can find out what these densities are at some other altitude. So this is a little exercise that just says, hey, if you knew what they were at a hundred kilometers, what—where would the densities be the same? Okay. And so in your—this is a little animation—I'm just gonna go through it here—um, once you know the how these neutral densities are distributed, then you can say, okay, well, this is the how the O density is distributed because it's ten percent of the oxygen of the total, and this is how the CO2 is distributed because it started as ninety percent of the total. So if I just want to know where the height where they're the same, I want to be quite either side—either side of this equation—I need to be equal. And so you can rearrange in a fairly simple way these—this—this equation to put the height difference on one side and all the information you know on the other side, and then you can do the algebra. If you do that, you end up with the 50 kilometers. Oh, if there one is 10% and the other is 90% at 100 kilometers and the scale height is 40 kilometers for atomic oxygen, these two species will have the same density 50 kilometers later. Okay, so the densities of O and CO2 are the same at 150 kilometers. And so you can go back and check your picture of the neutral atmosphere of Mars and verify that it's true. So there's a lot of information you can find out about an atmosphere just from the assumption of hydrostatic equilibrium and knowledge of the scale heights. There's a little homework question here along the same kind of lines, but to derive some more information about—okay—and this is the little tasks that I'd like you to take a look at—the second homework—and that's just to go to this website and look at the profiles of the of the density from immoral and just look at the scale heights of the atmosphere, and you can derive the scale heights in two ways—one by looking at the density and by differentiating the density—and one by calculating the scale height from the temperature in the mass—and it'll be interesting to see if there are any differences, and if they are—if there are differences—why you think the differences occur.