we've discussed that General history of 
the solar system. 
And we're going to start now a process of 
trying to look at 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, 
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 science 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 with about 
twenty percent molecular oxygen. 
and then below both of those is a rocky 
surface, a crust that 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 an 
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 an 
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 5500 kilos per meter3. 
cube. 
remembering that rock is about 3,000 
kilos per meter3, cube, 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 it, 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, 
pressure has become very, very high, 
density's 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 molten 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 and in. 
Particular indicates the size and mass 
fraction of the inner core which is solid 
and the outer core which is liquid 
because they have different properties as 
regard sound propagation. 
So within the understand the inside of 
the earth and one of the things that we 
know is that not only pressure and 
density increases you move deeper into 
the earth but temperature the inside of 
the earth is an extremely hard place, 
even the mantle is very hard molten rock 
and so what generates this heat. 
Well, there's Kelvin Helmholtz sheet 
that. 
Heated the earth as it was forming, 
remember, because gravitational potential 
energy was being converted into, heat. 
But, it turns out that the dominate 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 you're 
concentrated in the core. 
So the core is generating heat and this 
heat is carried up through the manto by 
convective process is we have here the 
process that we said we might discover 
some day. 
Here we have a fluid the manto heated 
from below by the harder core by the 
radio active and to some extend still Kat 
Von Helmholtz process is going on 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 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 looses the heat to radiation. 
Every square meter of earth looses about 
87 watts of. 
about the amount of energy is 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 [INAUDIBLE] drags the crust 
around. 
Whereas, crust is broken into plates, and 
the motion of these plates tell us a lot 
about the nature. 
Of geological processes on earth, the 
fact that earth has this 
Plated crusts and that these crusts are 
moving leads to recognizable features. 
For example the mountain ridges. 
The linear ridges of mountains. 
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. 
Uh,, 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 techtonic 
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 our features on Earth, mountains 
and valleys subject to erosion by air and 
water and natural processes, but the very 
atoms that are formed across 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 that most of the atoms we find on the 
Earth's crust today are only a few 
hundred millions years old, and 
By, geologic standards that's quite 
young. 
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 understanding, and her's 
a nice application of the physics we 
learned. 
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 you 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, if [INAUDIBLE] 
decreases. 
And then, that causes the sunlight to 
continue to heat it. 
In equilibrium, this is stable 
equilibrium. 
And one expects the rate at which earth 
absorbs energy, and the rate at which it 
loses energy to be equal. 
And you can use that to figure out how 
warm earth should be. 
So earth is a dense object. 
As a first approximation, let's imagine 
the earth as a black body. 
How does it 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 in 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 sits 
perpendicular to the direction to the 
sun, and has a radius equal to the radius 
of the earth, then this disc would, 
May 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 u03c0r^2. 
And remember, that the, the full surface 
of the Earth is 4u03c0r^2 but it absorbs 
as though its area were u03c0r^2. 
And so, now I have the area, I have the 
incoming 
Power per unit area I can f- figure out 
the total incoming flux by multiply them 
and the total rate at which the Earth 
absorbs energy from the sun is therefore 
pi R squared. 
Times. 
The solar luminosity divided by four 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 
four 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 
fourth power of the solar temperature. 
So I can plug this into that. 
And I obtain when I put this expression 
into there. 
I get. 
U03c0*the radius of Earth^2*4u03c0s 
cancel all over the place* u03c3 fourth 
power of the solar temperature, and then 
I get the radius of the Sun^2, divided by 
the distance to the Sun^2. 
So this is my expression. 
I will rewrite it more neatly, but this 
gives me a. 
[INAUDIBLE] expression for the total rate 
at which the earth receives sunlight. 
Some pi's have been cancelled, and I've 
rearranged the factor slightly, but 
notice that this is, depends on both the 
sun size and temperature and our distance 
from the sun as well as the radius of the 
earth. 
Okay, this is the rate at which earth 
would absorb energy, how about the rate 
at which it looses energy, well that too 
is not very difficult to realize. 
the earth is a black body. 
It has a temperature T(f) and if the 
earth is at some temperature then each 
square meter of earth radiates according 
to the Stefanu2013Boltzmann law at the 
rate sigma T to the fourth in the space 
multiply that by the radiating worth 
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, re-writing 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, they 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 the 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 two when I break inside the 
square and this tells you no I computed 
for earth and sun than any object in 
equilibrium with the radiation of any 
star if you know the temperature and the 
size of the star and your distance from 
the star you can compute in equilibrium 
temperature. 
So now I can apply this to earth and I 
find. 
278 degrees Calvin. 
This is eight degrees Celsius. 
It's pretty chilly so maybe some of our 
approximations need to be looked at. 
But it's not outside the ballpark. 
So roughly earth is in equilibrium with 
sunlight. 
This is good. 
Let's refine our calculation a little 
bit, and the first thing you notice is 
that Earth is not black of course, Earth 
is blue. 
It's blue because it reflects sunlight. 
If Earth absorbed all of the sunlight, 
the only radiation it emitted would be 
infrared, and to our eyes it would appear 
black, not the beautiful blue color it 
appears. 
In fact, Earth reflects about a third of 
the light that hits it, this is 
characteristic of any astronomical 
object. 
We call it the albedo, and we donate it 
by the letter A. 
What this means though is that about a 
third of the sunlight never goes to 
warming Earth. 
It just bounces straight back out into 
space making us look beautiful. 
And what that means is that only about 
two thirds, a fraction of one minus A, of 
the incoming radiation is available to 
warm the Earth. 
This means the Earth needs to be cooler, 
to be in equilibrium. 
plugging that back into our equation, we 
find that we get the same expression as 
before, for the Earth's equilibrium 
temperature, except when we take 
everything to the one-fourth power. 
we find that this factor of 1-A, about 
two-thirds to the power of one-fourth 
comes up. 
This further lowers the expected 
temperature and given the reflected light 
you'd expect the earth surface temperate 
to average out to a chilly 248 degrees 
kelvin. 
This is way below the freezing point of 
water. 
if this were the temperature of earth, 
life on earth would be very different at 
least than it is now, of course There's 
another thing we've neglected in our 
calculation and this is the effect of the 
atmosphere. 
Or the infamous greenhouse effect. 
So what does this mean? 
Again we can do the physics so lets try 
to look at what it means. 
the nature of the greenhouse effect is 
that the incoming light, the sun at 3,000 
degrees kelvin produces most of its 
energy in visible light and this 
Penetrates the atmosphere, we talked 
about visible light penetrating the 
atmosphere, and is absorbed by the 
ground, heating up the ground. 
The ground in turn radiates mostly 
infra-red light because the ground is at 
300 kelvin, not 3,000. 
And this infrared light we with saw when 
we talked about the optical properties of 
the atmosphere is a large extend absorbed 
by the atmosphere. 
Well this heats the atmosphere and the 
atmosphere then radiates because the 
atmosphere is one by some of the heat 
that the atmosphere radiates goes out in 
the space. 
Some of the heat is re-radiated back 
towards the surface moving the surface 
the net result is that the surface is 
warmer then would be a black body that 
lost as much energy the spaces does the 
earth. 
This might sound, or should sound 
confusing to you. 
I know it confuses the daylights out of 
me. 
But what usually helps me is to do a 
calculation. 
So let's try to do a calculation and see 
if physics explains to us how this 
greenhouse effect works. 
So lets do a simple model, a simple model 
will have two components. 
It'll have an atmosphere that is 
transparent to visible radiation but 
absorbs a fraction G, I'll call it the 
green house fraction of infrared 
radiation that hits it and then will have 
a surface and so here's how my simple 
model looks. 
I have here the surface of earth and 
above it decoupled from it other than 
through radiation. 
I'm going to imagine, is something called 
the atmosphere, and between some 
transparent medium. 
So, of course, this is an approximation, 
but it will give us a ballpark of what is 
going on. 
And then, sunlight, visible sunlight, 
which I'll draw in blue, is impinging at 
some rate for every square meter 
something like a quarter of the solar 
constant effectively, is impinging upon 
the atmosphere. 
The quarter common of the geometric 
factors that we talked about. 
Now, the atmosphere is transparent to 
this. 
So this light goes right through the 
atmosphere. 
And, indeed, some fraction of it is 
reflected. 
Some of it might bounce off the clouds. 
So there's some contribution by clouds to 
the albedo. 
Some contribution by the ground and the 
oceans and ice caps. 
And the visible reflected radiation goes 
off into space. 
The net result. 
Is that there is a flux which I will call 
fn which is something we computed that 
amount per the, the, the power per square 
meter of visible light that comes in and 
is absorbed by the ground heating the 
ground. 
So far the atmosphere has played no 
essential role but here things become 
interesting. 
Now the ground of course being a warm 
object radiates that light up as infrared 
radiation so there's 
Fact power sigma, T ground to the fourth 
will give the ground to temperature of T 
ground. 
Lets give it a temperature of t ground 
and we will give the atmospherial 
temperature t atmosphere which need not 
be the same and the ground will radiate 
at the rate that different Boltsman tell 
it to radiate and now the news is that 
this doesn't go into space it pinches 
upon the atmosphere where a fraction G of 
this radiation is actually absorbed and 
goes to heating the atmosphere whereas 
the fraction 1-G. 
Goes out into space. 
So far so good, but now we have a warm 
atmosphere, at a temperature ta, and this 
too radiates we'll imagine that it too 
radiates like a black body, so there is a 
flux of sigma times the atmospheric 
temperature to the fourth. 
In every direction, emitted by the 
atmosphere, this layer, this imaginary 
layer that I've called the atmosphere. 
And of course, this gets lost to space. 
The infrared light that's directed down, 
is directed in all directions, but 
eventually what's directed up, goes out 
to space. 
What's directed down will eventually hit 
the ground and be absorbed. 
Because the ground is absorbent of both 
infrared. 
And the visible radiation, and now, what 
do we need to do? 
This is our picture, and what we need to 
do, is use the fact that both the 
temperature of the surface and of the 
atmosphere are going to be constant. 
To find equilibrium conditions, we can do 
some elaborate Physics here and I, I 
consider this a good thing. 
And so what do we have? 
Well We have equilibrium conditions for 
the surface and for the atmosphere 
separately. 
For each of them, the incoming, power 
must equal the outgoing power. 
So for example for the ground the 
incoming power has two pieces. 
It has incoming, visible radiation from 
the sun at a rate Fn which we computed 
before, plus the infrared light it 
absorbs from the atmosphere, and that 
must equal the rate at which the ground 
radiates, and for the atmosphere, it 
loses at a rate energy both to the. 
To space and back down to the ground. 
And thus it must equal the rate at which 
it absorbs energy. 
So we have two sets of equations. 
I'll erase the model, so that we can see 
them more clearly in a minute. 
But this is the equilibrium condition 
that says that what the ground emits is 
equal to the sum of the two sources from 
which it absorbs. 
And this is the equation which says that 
what the atmosphere emits in both 
directions is equal to what it absorbs. 
Let's clear out this nonsense. 
And now we have just two equations to 
solve. 
And these will determine both the 
temperature of the atmosphere and the 
temperature of earth. 
And so 
The first thing I will do is I will move 
this two over here. 
And now I recognize that I can take this 
sigma t a to the fourth. 
Plug it in for that sigma T to the 
fourth, get an equation that has nothing 
about the atmosphere in it. 
And it's all about the temperature of 
the, of the surface. 
And it will be sigma T surface to the 
fourth is equal to G over two, sigma T 
surface to the fourth. 
Plus F N. 
And then moving that over to the left 
I'll get an equation for the temperature 
of the surface to the fourth and then the 
other thing I realize is that the 
temperature of the atmosphere to the 
fourth is just g over two temperature of 
surface to the fourth. 
Since G is a number smaller than one it's 
a fraction. 
this tells me the atmosphere is cooler 
than Earth. 
This is how the model works. 
Basically some of the radiating part that 
space sees is the atmosphere which is 
cooler than the surface. 
So it doesn't lose as much as if it were 
a black body at the atmospheric, at the 
surface temperature. 
And indeed, solving the equation for the 
temperature of the surface we find this 
equation which is. 
Essentially the equation we found before 
that sigma to the fourth is equal to the 
flux with this little factor of one minus 
G over two in front of it. 
And this means the earth has to be warmer 
because this is a number smaller than one 
then it would otherwise by precisely this 
factor. 
The temperature you find with greenhouse 
is bigger than the temperature you would 
find without it by this factor of one 
minus over two, number smaller than one 
raised to the minus one fourth power. 
So that raises the temperature. 
This is how the greenhouse effect 
Causes the surface to be hotter. 
I don't know if that helped you but it 
certainly clarifies things for me. 
That's a simple model in truth there's 
all kind of complications and different 
mechanisms of heat transfer. 
This is 
More complete version. 
the salient part, though, the big fat 
arrows. 
the ones that count are precisely the 
ones we mentioned. 
We see here, the energy emitted as 
infrared radiation by the surface. 
Some fraction of which travels out into 
space. 
And the rest is radiated back and 
reabsorbed by the surface. 
This is that greenhouse effect that we 
were talking about. 
And so putting that into our equations 
this is what we found, I take the old 
equation and modify it by this green 
house factor and I find that with all 
these factors in place I can determine 
the surface temperature of earth of 
course I don't measure the green house 
factor what I've done here is fudged I've 
adopted a green house factors such that 
the resulting so temperature of earth is 
the agrees with your measured 292 kelvin. 
Comfortably above the freezing point of 
water. 
And so the atmospheric greenhouse effect 
without an atmosphere earth would be 
frozen and uninhabitable and 
The comfortable temperatures we enjoy 
depend on the precise values of A and G 
that we currently have. 
A can change due to different amounts of 
cloud cover, ice cover. 
G can change due to changes in the 
chemical composition of the atmosphere. 
We hear a lot about this. 
This can change the temperature, notice 
that even though A and G appear only in 
this one fourth power which makes the 
temperature relatively insensitive. 
Because we're dealing with a temperate of 
300 degrees, one part in a hundred change 
in temperature is a three degree 
centigrade change which completely and 
drastically alters climate conditions. 
Moreover the real thing that people are 
worried about when they talk about 
changes in the earth's greenhouse 
scenario is that a small change in G. 
For example increasing G makes this 
denominator a little bit small. 
What this causes is the earth's 
temperature on the surface to rise a bit. 
This might cause 
polar ice caps to melt, reducing A, which 
further raises the temperature and can 
lead to non-linear effects that enhance 
the change. 
This is but, but, that's why people think 
we're very sensitive to the precise value 
of A and G, with which we live, in order 
to keep our temperatures stable. 
So, we've managed to understand one 
property of the physics of earth, based 
upon the physics that we learned last 
week. 
So it's good that we have an atmosphere, 
but given what we've tal, said about the 
creation of Earth, one could ask where 
did it come from. 
When the Earth formed, it was forming as 
silicates and aluminum and calcium., And 
I didn't say anything about water. 
Some amount of water can be trapped in 
minerals, we know. 
And I didn't say anything about gases. 
Earth was too small a planet to trap 
hydrogen and helium, which were the only 
gases plentiful. 
And indeed, when Earth formed, it would 
have had a very tenuous atmosphere. 
But when you cook rocks, earth formed it 
was very hot the rocks on the surface 
were cooked and they released carbon 
dioxide and nitrogen that can be trapped 
in minerals and is released when you heat 
them. 
this gave us the beginnings of an 
atmosphere of nitrogen and mostly carbon 
dioxide, much was released when the 
cooking rocks on the interior of earth in 
the manto were a, a, a available by vo, 
volcanic action and so this releases 
gases from the interior of the planet and 
we get bergining atmosphere of carbon 
dioxide. 
where water came from. 
Well there's some water as I said trapped 
in the rocks. 
But calculations show that, that probably 
would not have been enough to 
Create the oceans that we see on Earth 
today. 
And what there was of water would have 
been baked out and lost to space early in 
Earth's history. 
So it is, imagine that most of the water 
that forms our oceans, was in fact 
imported from farther out in the solar 
system. 
In the form of ice, where it formed in 
the form of ice and then fell in and 
impacted Earth during that heavy 
bombardment period 3.8, 3.9 billion years 
ago. 
And so the fact that we have water, is 
the result of import. 
And water creates a dynamic water falls 
as ice on the surface of Earth, it boils 
off. 
Up it 
accumulates as water vapor in the 
atmosphere. 
It condenses and creates the oceans that 
we see. 
And the rain that 
Falls from the atmosphere where the water 
condenses. 
Dissolves carbon dioxide. 
Which is then dissolved in the ocean and 
is fixed in sediments. 
This process is accelerated by the 
emergence of continents about three and a 
half billion years ago. 
And that, amount of carbon dioxide in the 
atmosphere is gradually removed. 
Leaving us with an atmosphere of 
nitrogen. 
That'd three-fourths of the atmosphere 
already there. 
With traces of water vapor, we need 
oxygen. 
The other quarter, oxygen. 
Free oxygen on earth is produced by the 
beginnings of plant life actually. 
initially this goes to oxidize sediments 
of iron and sulfur. 
But eventually as these are fully 
oxidized, free oxygen takes begins to 
exist in the earth's atmosphere starting 
about 700,000,000 years ago. 
And 
The, the level of oxygen approaches 
twenty% that we comfortable breathe 
today. 
There is therefore the. 
The atmosphere both enables the existence 
of life and is shaped by the existence of 
life all the oxygen we breath was 
produced locally in photosynthetic 
processes. 
So. 
This is how we think about, about the 
chemistry of the atmosphere. 
What does the. 
Physics tell us about the atmosphere. 
Well the atmosphere like the mantle is a 
convective system. 
It's heated from below because the ground 
is warmer than the atmosphere. 
So air down close to the ground is heated 
by conduction through the atmos through 
the from the ground. 
And then we have a fluid which is being 
heated from below. 
This drives convection patterns 
The differential heating shapes where the 
convection cells are going to fall, so 
globally, Earth has in each hemisphere 
these three large convection cells. 
The air, hot air rises near the Equator, 
cooler air sinks at mid latitudes, and 
this there's one more instance of hot air 
rising at upper latitudes. 
And, of course, at the poles there, is 
sinking. 
And so, we build these three convection 
cells, this drives northerly or southerly 
surface winds, and Global pattern of 
circulation cells will repeat and be 
generic and so. 
We should enjoy what we can of the 
physics of it. 
So, we've talked about the Earth's 
surface. 
We've talked about the Earth's interior. 
The Earth doesn't stop at the atmosphere 
which tapers off into planetary space. 
There's one important property of Earth 
that extends way beyond the extent of the 
atmosphere, and this is the Earth's 
magnetic field. 
As anybody who has used the compass knows 
that there is a magnet. 
Earth is a magnet whose poles roughly 
align with the axis of rotation. 
in fact, the earth's self magnetic pole 
is roughly aligned with the earth's north 
geographic pole. 
These are just a matter of convention we 
call north pole of a magnet, the part 
that faces north since opposite poles of 
a magnet attract, this means that it's 
being attracted to the earth's south 
magnetic pole. 
So here's a picture of the earth's 
magnetic field. 
The fields, remember, start at the north 
magnetic pole and 
enter into the South magnetic pole. 
And what this picture suggests us, other 
than the South pole is in the North, is 
that the source of the magnet is in the 
earth's core. 
This is indeed true. 
the process by which the earth's core 
generates a magnetic field are 
non-trivial one. 
It's called the geo dynamo, and it has to 
do with confluence of three factors. 
One is that the core is being heated from 
within. 
By the hotter inner core. 
So we have a liquid, metal-rich outer 
core full of conducting 
Elements like iron and nickel, its being 
heating from below which drives 
convection along with the rotation of the 
earth... 
This drives this conducted flow leads to 
instability that generates a spontaneous 
magnetic field 
It's not a trivial problem. 
It's not one that I'm going to write the 
equations for. 
But it's true that it's, it's 
Understood phenomenon, that rotation 
along with convection leads to 
spontaneous magnetic field. 
and that this field will roughly align 
itself with the axis of rotation. 
What is not true is, that the South Pole 
needs to be at the Earth's geographic 
North Pole. 
And indeed the geologic records shows 
that it always hasn't been that way, the 
field reverses polarity in a rather 
unpredictable way On average every 
500,000 years and here's a geologic 
record of the earth's polarity. 
Regions that are in black indicate a 
polarity 
Sorry. 
Regions in white indicate a polarity the 
same as the current polarity. 
Regions in black indicate the opposite 
polarity. 
And you see that the intervals are 
somewhat random. 
There are long periods of stability, 
periods of rapid change. 
We're now in a relatively stable period. 
But there are indications that the 
Earth's magnetic field might change. 
here is a, sort of, simulation of the 
Earth's magnetic field lines. 
Including the complicated structure near, 
the core. 
And here's what the field looks like. 
During polarity change, as I said, the 
process in complicated. 
What else? 
Does the field do for us? 
Why am I making such a big deal? 
the next demo might help us understand 
this. 
The interaction of charged particles and 
magnetic fields will come up again and 
again in this class. 
So this apparatus will allow us to study 
it. 
inside that glass bulb is that shiny 
horizontal metal structure. 
That's an electron gun. 
When I turn on a current. 
There is a piece of metal there that will 
be heated, will emit electrons. 
Those will be accelerated. 
And the electron gun will emit a 
horizontal beam of electrons into the 
bulb. 
Now, the bulb is nearly evacuated. 
So those electrons will be able to, 
propagate rather freely. 
But there's a very tenuous atmosphere of 
some inert gas in there. 
And this means that, when the electrons 
hit the gas, they will ionize the gas. 
The gas will glow, and we'll be able to 
trace where the electrons are going. 
Surrounding the bulb are these big coils. 
When I turn a current on through the 
coils, then as we saw eh, last weeks 
discussion of magnetism, we'll create a 
magnetic field penetrating the coils. 
So in the view we're seeing, that 
magnetic field will be directed from 
where we are sitting into the black 
backdrop. 
And we'll see what that does to the 
motion of the charged particles. 
Remember that, moving charges are 
affected by magnetic fields. 
So here, we've dimmed the light, we've 
turned down the electron beam. 
We see a, a nice straight electron beam, 
and we see that it ionizes the atoms of 
the gas. 
And the gas glows so we can trace the 
position of the beam. 
And now I'm going to turn on the magnetic 
field, which in this image, points from 
right to left. 
And we see that, when the. 
Beam impinges upon the electrons. 
The straight electron beam is curled into 
this helical shape, and as I turn up the 
current in the coils, increasing the 
magnetic field, the helix tightens more 
and more, we see what happens when the 
electrons hit the bob, the beam is 
absorbed. But by increasing the intensity 
of the beam, I can tighten the helix, 
make the radius about with which the 
electrons 
move smaller in other words increasing 
their acceleration since their speed is 
pretty much constant. 
I weaken the field and the helix opens 
up. 
This is clear perhaps in this view. 
We're viewing it from the side The beam 
is moving to the right, and when I turn 
on the magnetic field, which now points 
away from us I see a circle which is the 
projection of the helix. 
When I tilt it, you see, there's still a 
helix going on. 
But viewed from the side, it looks like a 
circle, and the radius of the circle is 
smaller when I make the magnetic field 
strong. 
And as I turn the magnetic field down, 
the radius of the circle grows. 
So now, we understand what the magnetic 
field can do for us, besides direct our 
compasses. 
what the magnetic field does, is that it 
interacts with that solar wind of charged 
particles that are constantly being 
emitted by the sun. 
And what happens to these charged 
particles, 
when they hit the earth's magnetic field 
is that they go into circular motion in a 
direction perpendicular to the field. 
And essentially that means that they are 
trapped along the field lines. 
They can slide along the field lines and 
rather than penetrate through the field 
and 
and pinch upon the earth. 
They are trapped along the field lines 
and they travel along the field lines in 
a sort of spiraling around them in, in 
the helices is that we saw. 
And the next calculation that I couldn't 
show you with that demo, shows that 
regions of strong magnetic field actually 
repel the particles. 
What that means, is that if you look at 
the field lines the particles in pinching 
from the sun are trapped along the field 
lines, they propagate along the field 
lines until new the poles with the field 
intensifies. 
They are repelled, they bounce back. 
So they end up bouncing back and forth 
and creating the so called Van Allen 
radiation belts. 
These are regions around the Earth where 
the magnetic field has trapped particles 
from the solar wind. 
And this prevents this intense flux of 
charged particles from impinging upon the 
Earth. 
Now, the solar wind actually it plies a 
pressure to this. 
We often talk about charged particles we 
saw what a magnetic field does to charged 
particles. 
Charged particles in turn influence a 
magnetic field when they're moving. 
we saw that for example with our 
electrons which were moving in a circle 
they themselves constituted a motion of 
charges in circles which would generate a 
magnetic field and as you can predict 
from stability. 
That magnetic field actually opposes the 
magnetic field in the cause that caused 
them to move in the helix. 
what that means is that when you have a 
magnetic field that is 
trapping a flux of charged particles. 
Those, the, that the, momentum of those 
charged particles is absorbed by the 
magnetic field and essentially pushes it. 
You can imagine sort of a hydrodynamics 
problem where the charged particles are 
just pushing on the fields and will often 
apply this sort of picture, where the 
particles push on the field. 
What this shows you is what the earth's 
magnetosphere actually looks like it, the 
earth is trying to make that nice apple 
shaped symmetric magnetic field. 
But the sun here on the left is pushing 
that field out. 
So that the field is compressed on the 
left hand side, and then extends way off 
to the right and this is the D-4 
magnetosphere. 
And what we see is that the flux from the 
sun is not constant in the course of a 
magnetic storm there's a dynamics here. 
And when the magnetics storm, when the 
stream of particles from the sun has 
enough flux then some of them break 
through the atmosphere. 
And they break through the atmosphere 
where the magnetic field line enter the 
atmosphere 
that would be near the Earth's poles, and 
then they impinge upon the gases in 
Earth's atmosphere. 
And as they did in the tube, they ionize 
them. 
And this gives rise to the beautiful 
light show we call the Aurora. 
In this case the Aurora Australis over 
Antarctica. 
So the charged particles get trapped 
along the field lines. 
When they penetrate, they enter the 
atmosphere along the field lines, 
which enter the atmosphere near the poles 
and this is why we have Auroras near the 
poles. 
And that's why the intensity of northern 
or southern lights is dependent upon the 
intensity of solar activity, as we will 
see next week. 
So let's summarize what Earth has taught 
us. 
we learned how to identify the benchmarks 
of tectonics. 
Looking, look for ridge-like structures, 
those linear mountain structures. 
Geological activity will be reflected in 
volcanoes. 
we learned the importance of an 
atmosphere and what that does to the 
temperature structure. 
We learned how to compute the equilibrium 
temperature of a planet, about a star. 
And we learn that the existence of a 
solid and a liquid core of conducting 
material generates a magnetic field, 
which allows protection, leads to 
protection from the solar wind, 
this will become very important. 
And the last thing we learned is that the 
air stressed is very young. 
So as a way to test our understanding of 
the very early solar system, Earth is a 
poor place to do the study because the 
atmospherics, the erosion, geologic, 
tectonic activity erases the past rather 
quickly on Earth. 
Maybe you can find a better place to 
study that.