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.