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Edited Lecture Transcripts
provided by Derek Grainge during session 002, 2013-2014
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6 Earth is a Planet
Well, we've discussed a general history of the solar system and we're going to start now a process of
trying to look at the some of the outcomes in what we find in it today. And a natural place to start is the
planet we know best the little blue marble we live on. Pedagogically, this makes sense because it's going
to be interesting to see what the physics we understand and the natural history of the solar system that
we've learned tell us about living on Earth. Scientifically, intellectually, it makes sense because we know
more about Earth than about any other planet. Whatever theories we develop should first be tested
where we can actually measure things, which is on Earth. So let's do a quick pass. Of course, Earth
Sciences is a huge field that I wouldn't be qualified to teach even if I had the time, but let's do a quick
pass and see what we can say about Earth as a planet.
So first, first thing you see when you look at Earth. Is that, most of its surface is covered with liquid
water. As we know that means, that, it has an atmosphere because liquid water can't exist without it.
And indeed, the Earth is covered with an atmosphere mostly nitrogen, about 20%, molecular oxygen.
And then, below, both of those is rocky surface, a crust which is made mostly of silicates. Now, we don't
expect this to be a good description of the composition of the entire earth, because the earth melted.
We see that it is round because it melted. This means it underwent chemical differentiation. We expect
the inside of the earth to be different chemically and structurally than the outside. And indeed we find
that the Earth has a inner core, which is rich in iron and nickel, and heavier materials. And then the
silicates that make up the crust of the Earth, also make up the, the layer below the crust which is called
the mantle. And so, we have the very densest, heaviest elements having sunk differentially to the center
and formed a core. And outside that, mantle. Now this gives the earth an average density of 5,500 kilos
per meter cubed. Remember that rock is about 3,000 kilos per meter cubed. This is your first indication
that there's something denser underlying the earth. The Earth is an equilibrium system. Gravity, as we
remember, is trying to crunch it down. The Earth is at least mostly a fluid, it is not a rigid object held up
by its tensile strength. The reason that Earth does not collapse under the force of gravity is just like our
slinky. Is that, pressure increases as you go deeper down into the earth, each layer holding the layer
above it against the, the force of gravity, and so, as you go down into the earth, pressures become very,
very high. Densities become very high. We have density so, pressure so high at the center of the Earth
that despite the fact that as we'll see, temperatures are very high. The center of the Earth is essentially
solid metal, that's the inner core, this is surrounded by an outer core of liquid metal. And you can see on
the graph at the bottom of the slide, that jumps in density as a function of distance from the core,
distance from the center increases to the right and density is the vertical axis. And you see the, the
different layers of the earth, an inner solid core, a slightly less dense liquid outer core, a mantle that is
essentially both rock and floating above all of it a crust.
How do we know so much about the internal structure of the earth? Nobody's ever been there. Well, it
turns out that we can learn a lot about the mechanics and the structure of something by the
propagation of sound waves. Earthquakes generate sound waves that propagate through the interior of
the earth, we can measure them way over on the other side of the earth. Studying the time delays and
the intensity patterns with which they propagate teaches us a lot than in particular, indicates the size
and a mass fraction of the inner core, which is solid and the outer core, which is liquid, because they
have different properties as regard to sound propagation.
So we think we understand the inside of the Earth, and one of the things that we know, is that not only
pressure and density increase as you move deeper into the earth, but temperature. The inside of the
earth is an extremely hot place. Even the mantle is very hot. And so, what generates this heat? Well,
there's Kelvin-Helmholtz heat that heated the Earth as it was forming, remember, because gravitational
potential energy was being converted into heat. But it turns out that the dominant heat producing
process of the Earth today is radioactive decay. The heavy elements which are the ones prone to
radioactive decay would have sunk under chemical differentiation and are concentrated in the core. So
the core is generating heat. And this heat is carried up through the mantle, by convective processes. We
have here the process that we said we might discover someday, where we have a fluid, the mantle,
heated from below by the hotter core, by the radioactive, and to some extent, still Kelvin-Helmholtz
processes going down in the core. And so this causes warm fluid to rise in some places, cooler fluid to
sink in other places, and sets up, these circulation cells, convection cells, in which, the fluid circulates.
This has several effects, one is it carries the heat out from the core, heating the surface. The surface
loses heat to radiation. Every square meter of Earth loses about 87 watts, about the amount of energy it
takes to run an average light bulb, to radiation, because of inner heating; 80% of that is radioactive.
The other effect, of course, is that the horizontal component of the flow at the top of the mantle drags
the crust around. Earth's crust is broken into plates. And the motions of these plates tell us a lot about
the nature of geological processes on Earth. The fact that Earth has, this plated crust and that these
crusts are moving, leads to recognizable features. For example, the mountain ridges, the linear ridges of
mountain, the Rockies, and the Andes, that line plate boundaries where plates are coming together and
one of them gets pushed up, or the Alps and the Himalayas. These are linear mountain structures that
reflect the fact that plates are being crunched together. On the other side, when two plates come
together, one of them will typically fold up. The other will fold under and crust will be subducted and
the result of this plate tectonic process is that the Earth's crust is by and large, very young. This is why
we never found old rocks on Earth not only are features on Earth, mountains and valleys subject to
erosion by air and water and natural processes, but the very atoms that form the crust are in a geologic
sense very young and constantly being interchanged, crust is constantly subducted and reabsorbed into
the mantle. And then new crust is constantly formed by volcanic processes.
So we have heat rising from the bottom, and then heat being radiated out into space. And this is the
beginnings of Earth's energy balance. Of course if Earth relied on internal heat. It would have been a
very cold place by now. It's been around losing energy for billions of years. What keeps Earth from
freezing is the sunlight. So, we can set up an understanding, of what maintains the constant
temperature of Earth, by setting up a sort of balance problem. Earth absorbs energy from sunlight as
radiation. With this additional small contribution from internal heat, but if we remember, that every
square meter of Earth absorbs about 1300 watts in sunlight, the 100 watts in, internal energy is not a big
deal. At the same time, Earth is losing heat because it's a dense object sitting in space, it has a
temperature. It radiates a black body spectrum out into space. If Earth is too hot, if Earth gets warm, it
radiates more because of the Stefan–Boltzmann law, and that cools it down until the rates are equal.
If Earth gets to cool, it's Stefan-Boltzmann radiation decreases. And then that causes the sunlight to
continue to heat it. In equilibrium these, this is stable equilibrium and one expects the rate at which
Earth absorbs energy and the rate at which Earth loses energy to be equal and we can use that to figure
out how warm Earth should be.
So Earth is a dense object is a first proximation. Lets imagine the Earth as a black body. How does this
work? Well here's the Earth. It's a sphere of radius R. And it's orbiting here in space. And if I imagine that
the sun is over to the left then there is a flux of sunlight impinging on the Earth from the left and this
flux is given by the solar constant which is related to the solar luminosity by our energy conservation
relation that says the solar flux is distributed uniformly over a sphere. Whose radius is the distance from
Earth to Sun, so D here stands for one astronomical unit. Now how much of this light does the earth
absorb? Well it's clear that only half of the Earth at any given time is absorbing any light at all, because
the right half of the Earth is not absorbing anything. But it's also true that radiation is not uniformly
absorbed. Depends on where you are on Earth and this equinoctial configuration, light is absorbed most
efficiently at the Equator. And this is easiest to understand by realizing that if I replace the Earth by this
disc, which sets perpendicular to the direction to the Sun, and has a radius equal to the radius of the
Earth, then this disc would, make, produce the exact same shadow over to the right as does the ball that
is the Earth. Basically if I chop off everything but the central disc, then I am not changing the shadow,
and so effectively as an absorber, the absorbent area of the Earth is the same as the absorbent area of
this as the actual geometric area of this disc. Which is just pi r squared. Remember that the full surface
of the earth is 4 pi r squared but it absorbs as though its area were pi r squared, and so now I have the
area, I have the incoming power per unit area. And the total rate at which Earth absorbs energy from
the sun therefore, is pi r squared times the solar luminosity divided by 4 pi times the square of the
distance to the Sun.
I can improve upon that calculation Because the Stefan-Boltzmann law tells me that the solar luminosity
is equal to 4 pi times the radius of the Sun squared. That's the surface area with which the Sun radiates
times sigma. The Stefan-Boltzmann constant. Times the 4th power of the solar temperature. So I can
plug this into that and I obtain when I put this expression in there. I get pi times the radius of Earth
squared times 4 pi’s cancel all over the place times sigma 4th power of the solar temperature. And
then I get, the radius of the Sun squared, divided by the distance to the Sun squared.
So this is my expression, I will rewrite it more neatly, but this gives me, a expression for the total rated
which the Earth, receives sunlight, some pis have been cancelled, and every arrange the factor slightly.
But notice that this is, depends on both the Sun's size and temperature, and our distance from the Sun
as well as the radius of the Earth. Okay, this is the rate which Earth would absorb energy, how about the
rate at which Earth loses energy, well, that too is not too difficult to realize. The Earth is a black body, it
has a temperature, T Earth. And if the Earth is at some temperature that each square meter of Earth
radiates according to the Stefan-Boltzmann law at the rate sigma T to the 4th in this space. Multiply that
by the radiating area of Earth which is the full surface of Earth since Earth radiates in all directions. And
that will give you an expression for the rate at which Earth loses energy by radiating it out to space.
And so again rewriting that more cleanly, we have now an expression. And thermodynamic equilibrium
will determine the Earth's temperature in such a way that these two quantities are equal. So my job is to
equate this to that, that will give me an equation for the surface temperature of Earth in terms of
properties of everything else. And, let's see, well we have some cancellations here. Fortunately the
sigmas cancel, that's good. We don't need to remember the value of sigma. The pis cancel. Most
importantly, the radius of Earth cancels. The size of Earth is completely irrelevant. Any object, asteroid,
Jupiter, Earth. Whatever you put at Earth's distance from the Sun, will have the same equilibrium
temperature. And rearranging things I find an expression that says the temperature of Earth to the
fourth power, is the solar temperature to the fourth power, times this ratio. The radius of the Sun
divided by the distance to the Sun and then I want to square this so that four will turn into a two when I
put it inside the square. And this tells you, note I computed for Earth and Sun but any object in
equilibrium with the radiation of any star. If you know the temperature and size of the star. And your
distance from the star, you could compute equilibrium temperature so now I can apply this to Earth and
I find 279 Kelvin. This is about 6 degrees Celsius, that's pretty chilly. But, the first thing is that it's not
outside the ballpark. A rough approximation of Earth as a black body in equilibrium with sunlight has
given us a temperature value that is not outside the range of what is actually the temperature on Earth.
We're on the right track, maybe we should try to improve our approximations.
Well we know one approximation we've made, that is clearly false, we've assumed that the Earth is
black. What that means is that it absorbs all of the incoming sunlight and emits thermal radiation with
Earth's ambient temperature of around 300 Kelvin. This is obviously infrared radiation. We can use
Wien's Law to figure that out. What this means is that if Earth were really black, viewed from space
emitting only infrared radiation, it would be a black object. We've all seen the beautiful pictures of Earth
from space. Earth is a beautiful blue marble. How does it get to be blue? Well, the reason Earth is blue
is, because some of the sunlight, the visible sunlight, that impinges on Earth in fact, is reflected by cloud
tops, by oceans, by Earth's surface. This fraction about a third in the case is called the Earth's albedo and
denoted by the letter a. It is a property of any astronomical object. That some of the light impinging
upon it is reflected and albedo is the term we use to denote this property.
Now, with Earth's albedo of about a third. That means that the amount of the sunlight that goes to
heating Earth, the amount of sunlight that is absorbed by the Earth heating it is only about two-thirds of
the incoming light. That means that the amount of light Earth absorbs, which we will denote by I
absorbed, is only about two-thirds, a fraction 1 minus a, of the incoming radiation. And so when we take
that into account. What will that do to Earth's temperature? Earth is absorbing only about two-thirds of
the solar radiation that falls upon it. That means to be in equilibrium it must emit about two-thirds of
the amount of energy that we computed that we used previously to compute its temperature. Oh, this
will make Earth, cooler, because, to emit less it must be cooler. That's what the Stefan-Boltzmann, law
tells us. Since, the power radiated is proportional to the fourth power of the temperature, to reduce, the
emitted power, by, a factor of about two-thirds, we'll have to, we'll have to reduce the temperature of
Earth, by a factor of about two-thirds, to the one-fourth power. So the T to the fourth. Is two-thirds of
what it previously was. Inserting that we find a prediction for earth's temperature of 254 Kelvin. This is
not an improvement on 279. 254 is well below the freezing point of water. If this would really the
ambient temperature on Earth. Life here would be very different than it currently is.
Luckily, this is not correct for Earth. We will turn in a moment, to discussing how Earth's atmosphere
allows us to actually enjoy temperatures quite a bit more balmy than 254 Kelvin. But let us stop here
and note, that for a planet without an atmosphere, for example, were we to be discussing the Moon.
The Moon is about the same distance from the Sun as Earth is, the Moon does not have an atmosphere.
We would expect the average temperature on the Moon to be about 254 Kelvin. And for any planet
orbiting any star if we know the star's temperature, the planet’s albedo and its distance and the
radius of the star, then we can compute a predicted equilibrium temperature for that planet.
Arquivo da conta:
astronomo
Outros arquivos desta pasta:

Week 5 - 7 Our Moon.mp4 (165802 KB)
Week 5 - 6 Earth is a Planet.mp4 (188351 KB)
Week 5 - 8 The Atmosphere and Beyond.mp4 (172336 KB)
 Week 5 - 1 Introduction.mp4 (175178 KB)
 Week 5 - 3 The Solar Nebula.mp4 (228955 KB)
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Outros arquivos desta conta:
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_repetidos
 01
 02
 03
 06
Relatar se os regulamentos foram violados
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