GG 140: The Atmosphere, the Ocean, and Environmental Change

Lecture 02.?Retaining an Atmosphere

https://oyc.yale.edu/geology-and-geophysics/gg-140/lecture-2

Escape Velocity [00:02:59]

Which planets have atmospheres and why? And it turns out that the key physics, the key process that determines this is whether molecules at the top of the atmosphere can escape the planet's gravitational field. The molecules in this room are traveling a very short distance and then they encounter another molecule and they collide, and then another short distance and they collide. So there's no chance that these molecules in the lower part of the atmosphere could ever escape, at least not immediately, because they're surrounded by other molecules.?But the molecules at the top of the atmosphere, if they're heading upwards--and some of them are--they might just leave. They may just get fed up and decide to leave the Earth's atmosphere.?

We need to define something called the escape velocity. It's defined as the velocity needed to escape from the gravitational field of a planet.?

If I'm at the top of the atmosphere, there is the Earth. There's the atmosphere. And if I've got a molecule at the top that happens to be heading upwards, if it has a velocity less than this number (11,180 m/s), it's going to go up for a while and then stop and then gravity's going to bring it back into the atmosphere. If I have a molecule that's moving faster than that speed, it's going to leave. It will never be seen again in the vicinity of planet Earth. So this here is when the upward velocity is greater than Vescape, and this is when v is less than Vescape.

Something interesting about this formula--notice that the mass of the object does not enter into that formula. So this would apply for a molecule or for a rocket ship. When they launch a rocket into orbit or to another planet, it's exactly that same speed. But they have to accelerate the rocket in order to get it to escape from our planet's gravitational field. So this is kind of a universal number for the planet, independent of what the object is.

Molecular Velocities [00:08:48]

We have to know something about what the molecules will be doing.?

Before we go any further, let me just give you a little table of these molecular weights for some--for a few of the gases that we might be interested in.?This will be the column of molecular weights, going down here. For a single hydrogen atom by?itself, it has?just?one?proton in its nucleus and no neutrons, so its molecular weight is 1.Hydrogen usually occurs in the diatomic form, two atoms fastened together with a bond. And of course the molecular weight for that would be 2.?Helium has two protons and two neutrons in its nucleus, so it has a molecular weight of 4.?

Nitrogen--and most of the gas in this room is nitrogen--appears in the diatomic form, two nitrogen atoms together. Each one has a mass of 14, so the molecular weight of the N2 molecule is 28.?Oxygen, which composes most of the rest of the gas in this room, again occurs in the diatomic form. Each one is 16, and so that's going to be 32. And carbon dioxide, which you're breathing out--carbon is 12. If I add that to two Os, I'm going to get 44 for the molecular weight of carbon dioxide.?

And let's do it immediately for nitrogen, because that's the one that's relevant to this room. So for a molecular weight of 28,?It's going to be 3 times 8,314 times 288, but in this case divided by 28 inside the square root . And that comes out to be 506 meters per second.

So now we've got the two sides of this argument started. It's time to do some interpretation of it. I wanted to consider for a moment what would happen if vesc?was approximately equal to vmol. In other words, if those two numbers were about the same value in an atmosphere, what would happen?

• At the top of the atmosphere, some of the molecules are moving down and some of them are moving up. Now, I have to say, this is a typical molecular speed but some of them are moving slower and some of them are moving faster. There's a complete distribution of speed. So it's not every molecule that would be aiming up and have a speed equal to or greater than the escape velocity. Probably only 1/4 or 1/5 of the molecules up there would happen to be aiming up with a speed that would be fast enough to leave.

• But remember, they would leave in an instant. In a fraction of a second, they would be gone. In another fraction of a second, the molecules remaining would have had more collisions, and now some of them would be aiming up with a speed faster than the escape velocity, and they would leave. And this would continue.

So in fact, if this were the case, if the average molecular speed was about the same as the escape velocity, we would have an explosive loss of the atmosphere. It would be gone within moments. So when we're asking about whether a planet can retain an atmosphere, we have to use a more restrictive criteria than this. Because remember, the Earth has been around for something like 6 billion years, so we have to use a conservative estimate.

The one that I like to use is to say, the escape velocity-- if that is greater than about ten times the molecular speed, then an atmosphere can be retained. It's kind of a rule of thumb to put that factor of ten in there, to take into account the fact that some molecules are moving faster than the typical molecular speed. And we have to retain it not just for an instant. We have to retain it over millions and millions of years.

• So let's take a look at Earth for a second and see what we can conclude from that. If I multiply this by ten, I get 18,940 meters per second, about 19,000 meters per second. That is actually greater than this. And so we conclude from that, that hydrogen could not be retained on Earth, could not be retained on Earth.

• Let's do the same thing for nitrogen. If I multiply this number by ten, 506 -- that's about 5,000 meters per second. That's only half of this number. So we conclude that nitrogen could be retained. Well, as it turns out, there's very little hydrogen in our atmosphere, and that's probably why. Because any hydrogen that was there in the beginning has been lost by this process. Instead, our atmosphere is dominated by nitrogen, mostly, but also oxygen that would move even a little bit slower, because it has a molecular weight even greater. So that could be retained. There's some carbon dioxide in our atmosphere. That could be retained.

So we've already learned something about the Earth with this little exercise. It's probably lost its light gases like hydrogen and helium, even if it was there in the beginning, which I think it probably was. But it's been able to retain the somewhat heavier gases such as nitrogen, oxygen, and carbon dioxide. ?

Which Planets have Atmospheres and Why? [00:22:43]

Now, let's consider?take all the planets and moons in the solar system. And I did an estimate for the temperature of each one. And we know something about the gravitational field and the radius of each planet. And so I came up with a ranked list where it's basically the ratio of the escape velocity to the molecular velocity. So if a planet has a large escape velocity, and a small expected molecular speed, I ranked it high on the list. If it has a low escape velocity--like a small planet, not much gravity, fast-moving molecules--I put it low on this. So this is a ranked list, my ranked list, of where I would expect to find atmospheres in the solar system.?

Jupiter's going to be first since?Jupiter has the largest mass. It's also fairly far out in the solar system, so the gases are not particularly hot. So this is large and that's pretty small, so indeed Jupiter is first on the list. And right behind it comes Saturn for similar reasons. Neptune, Uranus. Then comes our planet, Earth. Venus. Pluto--poor Pluto, no longer a planet. Triton, which is a satellite of Neptune--or say, a moon of Neptune. Then comes Mars, then comes Titan,?which is a satellite of Saturn.

And let me continue the list a little bit longer. Ganymede, Io, Callisto, Europa, Mercury, and our moon. And then I stop there. Of course, I could go on and on, because there's lots of other smaller moons in our solar system. But I wanted to get at least to Mercury, which is the other planet, and I wanted to get to our own moon in order to make the list interesting for us.

So that's the ranked list. Now what's--we know a lot about this, because we can detect planetary atmospheres from a distance. We can detect it by going there with an unmanned vehicle. So we know, pretty much, whether these objects have atmospheres now. From observations, we think that the planets before?Titan?have atmospheres and those after Titan?do not. So our ranking based on that was pretty successful. Maybe not quantitatively, but at least qualitatively, it gave us an idea of where we could find atmospheres in the solar system.?

So now let's consider this molecular weight effect, the heavy gases versus the lighter gases. For mercury, it turns out that both would be lost. I'm going to put two arrows here, and I'm going to label one L and one H. L for the light gases, like hydrogen, and H for the heavy gases like nitrogen, for example.?

Mercury would lose them both, because it's a pretty small planet and it's quite hot. So if there were molecules there, they'd be moving quite fast. Venus--the light gases can leave but the heavy gases are retained. So I've drawn that molecule trajectory coming back into the planet. The same for Earth. The light gases leave, the heavy gases come back. The same for Mars.

Planetary characteristics in relation to their atmospheres [00:29:47]

So while we have this up here, let me talk about a couple other characteristics of planets that have some interest in relation to atmospheres. If you sent a spaceship to Jupiter and tried to land on the surface, you would penetrate down into this massive atmosphere. And it would get denser and denser and denser, and after a while you'd begin to wonder whether you were in a gas or a liquid. But there wouldn't be any particular interface.

Eventually, as you came further down, you're pretty sure you're no longer in a gas. You're almost certainly in a liquid. And as you kept going down, it's going to get a bit--more and more like a solid.?But never with an interface. So the point is that there's no surface. There's no solid surface on these outer planets, whereas the inner ones you can land on it, walk around. They may be hostile in terms of their environment, but at least there is a place to stand.

What about the temperature? Well, extremely hot and no atmosphere on Mercury. This one is--Venus is extremely hot as well. Mars may be OK but it's a little cold for us. It's below the freezing point of water most of the time. And for these others, well, I don't know what to write down. Because here I'm kind of assuming that I can stand on the surface and break out a thermometer and measure the temperature.?So I can't really fill this in, because it would get hotter and hotter and hotter as you go down deeper and deeper in the planet. There isn't any particular reference point from which to say, Jupiter's a hot planet, or Jupiter's a cold planet.

What about habitability? I think you can pretty much guess for yourself, then, that these wouldn't be habitable for a number of reasons. And neither would Mercury and Venus. Ours--our planet, Earth, probably, certainly yes, and Mars would be,?it'd be a question mark. There's not very much atmosphere there. You might be able to build some kind of enclosure and live within--inside some kind of a pressurized enclosure. But it wouldn't be a very pleasant existence for us. So habitability is pretty much limited to Earth, and maybe Mars if you want to extend the definition a little bit.?

It's convenient to break up the planets into two general categories. The so-called terrestrial planets, which are a bit like Earth--they comprise Mercury, Venus, Earth, and Mars. They're small, they're dense, they have rocky surfaces, they rotate relatively slowly on their axis. For Earth, it takes, as you know, twenty-four hours to go around. The atmosphere--well, none in the case of Mercury, but the heavier gases in the case of Earth, Mars, and Venus, with molecular weight somewhere in the range of four to fifty, I would say.

Whereas, the Jovian planets--that is, the planets that are like Jupiter in some way--are much larger, much lower density. They have soft surfaces, they rotate more rapidly than Earth, and their atmosphere is primarily composed of light gases. Mostly hydrogen with a molecular weight of two in the diatomic form, and helium, just independent helium atoms with a molecular weight of four.

So there are the terrestrial planets. I'll show you more about this, but that's Earth, Venus, Mars, and Mercury. And the outer planets, the Jovian planets. That's the list. I already have it on the board, so you don't have to write that down again. This is also a review. I think we've been through this. But Mercury has no atmosphere. Venus has a massive CO2 atmosphere. It is entirely covered by clouds. 100% cloud cover all the time, which makes it a very bright planet.?

It turns out, though, that it also has a super greenhouse effect. And it's a little bit closer to the sun than we are, but its temperature is even hotter than you would expect based on that proximity to the sun. It has a really super greenhouse effect that brings it up to a temperature that's in the order of 600 Celsius, way, way, way above the boiling point and so on and so forth. So a very hot planet because of the greenhouse effect.

The Earth we know has a nitrogen-oxygen atmosphere primarily. Partly cloudy. Water can exist in the liquid form. We have life, and we have ice caps. We have frozen water, in this case in the form of snow or frozen seawater, at the caps, at the poles of the planet.

Mars has a CO2 atmosphere but not much of it. There may have been water there once. We don't know if it's still there now. There may have been life there once. We don't think it's there now. But it too has some ice caps. If you look at the planet, it has these kind of snowy regions near the poles. We don't think it's frozen water. We think it's frozen C02. What's frozen CO2 called? Dry ice. Dry ice is what we call frozen CO2. Mars seems to have dry ice ice caps on the poles that change a bit with the season.

Vertical Profile of Temperature in the Atmosphere

We're going to be talking about the vertical temperature structure on Earth.?This is the temperature in the Earth's atmosphere as a function of altitude. And it starts around fifteen degrees Celsius, and that's the example I used today, and then it cools off, warms up again with altitude, cools off again, warms up with altitude. Think about that profile, and in a day or two, I'm going to be asking you to speculate about why it is that the Earth's atmosphere has this peculiar structure.

The other planets, by the way, have a structure that's a bit simpler. It cools and then warms, just one cooling trend and one warming trend in the atmospheres of most of the other planets. So there's something unique about our planet that gives it this layer cake structure of temperature.