If you are standing somewhere
on Earth... this is the Earth,
the mass of the Earth,
radius of the Earth,
and you're here.
And let's assume for simplicity
that there's no atmosphere
that could interfere with us,
and I want to give you one
huge kick, an enormous speed,
so that you never, ever come
back to Earth,
that you escape the gravitational attraction
of the Earth.
What should that speed be?
Well, when you're standing here
and you have that speed,
your mechanical energy--
which we often simply call E,
the total energy--
is the sum
of your kinetic energy--
this is your mass;
this is your
escape velocity squared--
plus the potential energy,
and the potential energy equals
minus mMG divided
by the radius of the Earth.
So this is your kinetic energy
and this is your
potential energy--
always negative,
as we discussed before.
Mechanical energy is conserved,
because gravity is
a conservative force.
So no matter where you are
on your way to infinity,
if you are at some distance r,
that mechanical energy
is the same.
And so this should also be
one-half m v at a particular
location r squared
minus m M earth G
divided by that little r.
And so at infinity,
when you get there--
little r is infinity,
this is zero,
potential energy at infinity
is zero--
and if I get you at infinity
with zero kinetic energy,
then this term is also zero.
And that's the minimum amount
of energy that I would require
to get you to infinity
and to have you escape the
gravitational pull of the Earth.
If I give you a higher speed,
well, then, you end up
at infinity
with a little bit
more kinetic energy,
so the most efficient way
that I can do that is
to make this also zero, so you
reach infinity at zero speed.
So this is
for r goes to infinity.
And so this E equals zero then.
And so this term is
the same as this term
for your escape velocity.
And so we find that one-half m
v escape squared equals
m M earth G divided
by the radius of the Earth.
I lose my little m, and I find
that the escape velocity
that I have to give you
is the square root
of two M earth G
divided by the
radius of the Earth.
And this is enough,
is sufficient to get you
all the way to infinity
with zero kinetic energy.
If you substitute in here
the mass of the Earth
and the radius of the Earth,
then you will find
that this is about 11.2
kilometers per second.
That is the escape velocity
that you need.
It's about
25,000 miles per hour.
Again, we assume
that there is no air
that could interfere with you.
If the total energy
when you leave the Earth
with that velocity--
if the total energy is
larger than zero,
you do better than that.
You reach infinity
with kinetic energy which is
a little larger than zero.
We call this unbound orbits--
larger or equal.
If E is smaller than zero,
that the total energy
that you have is negative,
then you will never escape the
gravitational pull of the Earth,
and you will be
one way or another
in what we call a bound orbit.
Let's pursue the idea
of circular orbits.
Later in the course we will
cover elliptical orbits,
but now let's exclusively talk
about circular orbits.
Now, this is
the mass of the Earth,
and in a circular orbit is an
object with mass m, a satellite,
and m is way, way, way smaller
than the mass of the Earth.
And the radius
of the orbit is R,
and this object has a certain
velocity v, tangential speed.
The speed doesn't change,
but the direction changes,
and there has to be
a gravitational force
to hold it in orbit,
and the gravitational force
is exactly the same
as the centripetal force--
we've discussed that
many times before.
And so the gravitational force
which is necessary
to make it go around--
I could also say the
centripetal force is necessary
to make it go around
in a circle--
that gravitational force equals
m M earth G
divided by R squared.
This is now the distance
from the Earth to the satellite,
and that must be equal
to m v squared divided by R,
and that is that tangential
speed that you see here,
which a little later in time,
of course, would be here.
I lose my m, and so you see now
that the orbital speed--
not to be mistaken
for escape velocity--
the orbital speed is exactly
the same what we have there
except the square root of two
divided by R.
This is now R.
And there it was R earth.
If you know R, then you can
calculate the speed in orbit.
If you know the speed in orbit,
you can calculate R.
And so the period
of going around in the orbit,
T equals two pi R
divided by the orbital speed,
and when you do that,
you get two pi.
You get an R
to the power three-halfs,
and you have downstairs
the square root of G M earth.
Let me move this in a little.
Two pi R
to the power three-halfs.
So again,
if you know the radius,
if you know how far you are
away from the Earth,
the period follows uniquely.
If you know the period,
then the distance to the
satellite follows uniquely.
If we take the shuttle as an
example of a near-Earth orbit,
so we have the shuttle.
The shuttle may be
400 kilometers
above the Earth's surface.
So we have to add to the radius
of the Earth 400 kilometers,
so you end up with
about 6,800 kilometers
for the radius
of the orbit of the shuttle,
and you substitute that in here,
the mass of the Earth
and the gravitational constant,
you'll find that
T is about 90 minutes.
It's about 1½ hours.
The shuttle takes
about 1½ hours to go around,
and the speed,
that tangential speed,
is very close to eight
kilometers per second.
And that holds for all
near-Earth-orbit satellites.
Whether they are
400 or 500 or 600 kilometers,
that doesn't change very much.
If you take the moon--
the moon is much further away
than the shuttle,
and you take the distance
to the moon--
which is some
385,000 kilometers--
you substitute that in this
equation, you will find
that the period for the moon
to go around the Earth
is about 27½ days.
And its speed is only
one kilometer per second.
It's much further out.
If it's much further out,
R is much larger,
and so you see
the speed will be much lower.
If you take the Earth itself
around the sun--
because we can use
all these equations--
replace the mass of the Earth
by the mass of the sun,
and then we can do this
for planets.
So if we take the Earth
around the sun,
then we have to put in
the mass of the sun,
which is about two times
ten to the 30 kilograms.
And the distance
from the Earth to the sun,
we have seen that before--
I call that the distance
from the sun to the Earth--
is about 150 million kilometers.
Forgive me for mixing up
meters with kilometers,
but you have to convert that,
of course, to meters.
And when you calculate
how long it takes the Earth
to go around the sun,
no surprise--
you will find 365½ days.
So that's simply substitution
of these two quantities
in the equation that I have here
and that I have here.
The velocity of the Earth
in orbit
is about 30 kilometers
per second.
That's a substantial speed,
by the way,
that the Earth is going
around the sun--
30 kilometers per second--
way higher than the speed
that the shuttle is in around
the orbit... around the Earth,
which is only
eight kilometers per second.
Jupiter is five times further
away than the Earth,
and so the time for Jupiter
to go around
goes with five to the power 1½.
That's about 12,
so it takes Jupiter about
12 years to go around the sun.
Notice that this period
is independent
of the mass
of the little satellite,
and that was very unfortunate
for the Americans
when on October 4, 1957,
Sputnik was launched.
They could find the radius
very easily, because they knew
the period that it took Sputnik
to go around the Earth.
That was about 96 minutes.
They could calculate
the velocity,
they could calculate the radius,
but they had no clue
about the mass, and that was a
key piece of ingredient
that the Americans wanted,
because if the mass was
very large of Sputnik,
that would indicate, of course that
the Russians had
very powerful rockets.
But you cannot tell the mass
from the orbital parameters--
it's independent of mass.
Whether you have
a very light object
or a very heavy satellite, they
have the same velocity in orbit
if they are
at the same distance,
and they have
the same orbital period.
I mentioned earlier,
notice that the orbital period
and the escape velocity vary
by a square root of two if you
are at a particular position.
For instance, you're
at a particular position
around the Earth,
here at a satellite.
If you want to escape from this,
you will need a speed
which is the square root
of two times larger
than that orbital velocity.
And so if you wanted
to escape from the Earth,
then you need your 11.2
kilometers-- we have it there.
If you are near Earth in orbit,
you are eight kilometers
per second,
and eight times the square root
of two is exactly that 11.2.
So you see
the connection is always
through this square root of two.
There is something remarkable
about these numbers.
The total mechanical energy--
and I will write that
once more here--
which is one-half m v squared
at a given radius
minus little m capital M G
over r;
whether M is the mass
of the sun or the Earth
is of no concern to me now.
This is the kinetic energy
for something in orbit
at this radius,
and this is
the potential energy.
But now notice, I can substitute
now for this v squared,
I can substitute
the square of this--
this is the... that is the orbital speed--
and then I get M G over R.
And so this one equals
one-half m MG over R.
And now compare the two.
They almost look like
carbon copies of each other,
except that there is a minus
sign here, which is crucial,
and there is a half here,
which is missing here.
And so the total energy E--
which I've called
the mechanical energy--
always for a circular orbit
is one-half U
and is the same
as minus the kinetic energy.
A remarkable coincidence,
you would think.
But it is not as much a coincidence
as you think, of course.
But if something is in orbit,
this is the orbital speed
at radius r,
then always
is its total energy...
is half the potential energy.
It's always negative.
Okay, later in the course
we will cover elliptical orbits.
I will not do that today,
and so I will march on
to a completely different topic,
and that is the topic of power.
So I will abandon for now
the orbits entirely.
What is power?
Power is work that is done
in a certain amount of time.
dw/dt, if w is the work, is the
instantaneous power at time t.
We also know power
in terms of political power.
That's very different.
Political power-- you can do
no work at all in a lot of time,
and you have a lot of power.
Here in physics,
life is not that easy.
The units of power are
the units of work,
which is joules per second,
for which we often write W,
which is named after
the physicist Watt.
Don't confuse this w for work
with the W for watt,
which is one joule per second.
Now, the work that I do,
that the force is doing,
is the dot product
between the force and a certain
displacement of that force.
We have dealt with that before.
That is a little bit of work
that I'm doing, right?
I have a force which is constant
during a short,
small displacement.
And so I can substitute that
in there, and so I get
that the power is the derivative
of this versus time.
And that is...
if I keep this force constant
for that short amount of time
is the dot product times
the velocity,
because dr/dt is simply
the velocity of that object.
So power is also force dotted
with the velocity.
If the force were perpendicular
at all times
to the velocity vector,
then the power is zero.
Let's take an example.
I am on a bicycle--
here is my bicycle--
and I'm sitting
on a bicycle here
and I'm trying to get going.
And I have a certain velocity,
and I keep
that velocity constant.
That's the way most people
would ride their bikes.
Now, there is air drag,
which is unavoidable.
We discussed that.
And the air drag acts
like a force on me, F drag,
and so somehow, I, Walter Lewin,
will have to come up
with the force in this direction
to overcome this drag
so that the speed
can be constant,
because if the net force
is zero on me,
then of course I will have
a constant velocity--
no acceleration,
no change in the velocity.
How do I do that?
Well, I push on the pedals.
But the pedals push back on me.
Action equals minus reaction.
So that causes no net force
on the bike at all.
I push on the pedal; 
the pedal pushes back on me;
those two forces cancel.
We call them internal forces.
Now, the pedals push
on the chain,
and the chain pushes
on the wheel,
and ultimately this wheel wants
to start rotating
in this direction
because of my pedaling.
And now here with the...
with the floor, with the road,
there is friction, and so now
the wheel pushes onto the road,
and the road pushes back.
Action equal minus reaction.
And it is that force,
which is really the friction--
that is the force that Walter
Lewin has to come up with
in order to make sure that
he can go with a constant speed.
It's the friction that does it.
You have to really think
about it.
It's remarkable.
If there were no friction of
that road, you couldn't cycle.
I could do this, and I would
just stay still, right?
There would never be
any force here
that would drive me in this
direction so you can go.
Of course, if you had a speed
that you were sliding,
then, of course, you would
always maintain that speed.
I want you to appreciate that
the power that I have to deliver
is an extremely strong
function of the speed.
If we are here
in the domain of what I called
earlier regime two,
which is the
pressure-dominated regime,
then the drag force is
proportional to v squared.
Let's say it is
a constant times v squared.
We spent a whole lecture
on this.
That's regime two.
Let's assume it's there.
Then if I have
ten miles per hour here,
I drive ten miles per hour,
and I tell you that the power...
this is a given, this is not
something that I show you,
that is just a given,
that that is about a power
of 0.02, 1/50, of a horsepower,
and one horsepower is some
crazy unit-- 400... 746 Watts.
So this is about 15 Watts.
So I'm pedaling, and I keep
my speed ten miles per hour,
and I have to generate
15 joules per second on average.
But now I want to go
to 25 miles per hour.
So here we get 25.
That is 2½ times higher.
But now the power
that I have to generate
is the dot product between
the force and the velocity.
Now, the force and the velocity
are in the same direction,
so the dot can disappear,
so I get that the power is
k times v to the third,
and so now if I want the speed
to go up by a factor of 2½,
the power that
I have to generate
is 2½ to the power three
times higher,
and that is
about 15 times higher,
so now you're talking
about 0.3 horsepowers,
and you're talking about
something like 230 Watts.
And that is quite a power,
let me tell you.
I wonder whether there are many
here in the audience
who could generate this
for more than even half hour.
Most of us could probably do it
for a few minutes,
but not for hours.
It depends entirely, of course,
on your condition.
There is also heat energy,
and heat energy is expressed
in a very different way.
We express that
in terms of calories.
And a calorie is defined
in a very special way
as the energy which is needed
to increase one gram of water
by one degree centigrade.
And so in general we can write
that Q, which is heat energy,
which is in calories,
is the mass of the object
times the specific heat,
which for water would be
one calorie per gram
per degree centigrade
times the temperature increase
that we apply.
So we increase
the temperature of an object.
The object has a mass m.
We increase the temperature
by this much,
so many degrees Kelvin
or degrees centigrade--
that's the same--
and then this is
the number of calories
that you have to put in there.
Um... I gave you
the specific heat for water
in calories per gram,
not per kilogram.
If I gave it per kilogram, which
may be nicer for this course,
then of course it would be
thousand instead of one.
Aluminum has
a specific heat of 0.2.
Lead is unusually low--
it's only .03.
It's very, very low.
Ice is only half
the specific heat of water.
Ice is only...
ice is only one-half calorie
per gram per degree centigrade.
The physicist James Joules,
after we...
we call after him
the unit of work--
was the first to demonstrate
that heat energy and mechanical
energy are really equivalent.
He did an ingenious experiment.
Of course once you hear it,
you said, "Well, I could have
thought of it myself."
He takes objects with masses
which hang from strings
and he lowers them
in a gravitational field
over a certain distance.
So he knows what mgh is.
And he uses this rope to rotate
scoops which are in water.
And these scoops are driven.
There is mechanical energy,
mgh comes out in the scoops,
and what does he notice?
That the temperature
of the water goes up.
And he measures
the increase in temperature,
and he knows
how the calorie was defined,
and so he found that one calorie
is approximately 4.2...
now it's called joules.
At that time
it wasn't called joules yet.
So there is a direct connection
between the two.
I would like to... I'm going
to throw several numbers at you
during this lecture,
and I prepared a view graph.
Don't copy the numbers,
because it's all on the Web.
But some of these numbers
I will return to,
and therefore I thought I might
as well compile them in one.
You see there on the top there
that one calorie is 4.2 joules.
And you also see the horsepower
and other units that will come
up very shortly
I all defined there.
When we burn something,
there is a chemical reaction
which produces heat,
in many cases.
Gasoline produces per gallon
something like close
to a hundred million joules.
Your body produces heat.
Your body is roughly
at a temperature
of 98 degrees Fahrenheit,
unless you happen to run
a high fever today.
And your body is radiating
electromagnetic radiation.
You can't see it with your eyes,
because it's infrared.
But when it's dark and
you hold someone in your arms,
you can feel that heat.
That heat is a fantastic amount.
That is about 100 joules
per second that you radiate--
100 watts.
You radiate at the same level
as a 100-watt light bulb,
but it's, of course, distributed
over a much larger area,
so you're not that hot
as a 100-watt light bulb.
But it's a fantastic amount--
a hundred watts that you radiate
for the simple fact
that your body has to be kept
at that temperature.
It means that in one day
about ten to the seven joules
that you generate.
Ten to the seven joules--
that is what you generate
in terms of heat,
ten to the seven joules per day,
and that is about
two million calories per day.
Where does the body get it from?
Food.
You better eat two million
calories per day.
Now, I can see some of you turn
pale and green and purple,
and say, "Over my dead body!
"Two million calories per day?!
You must be out of your mind!"
Well, not quite.
You see, when you read
on the packages "calories,"
then it is called
a capital C-a-l
and that is really
a kilocalorie.
So you have to divide this
by a thousand
to compare it
with the packages that you buy,
how many calories
there is in the food.
So you have to eat roughly daily
about 2,000 kilocalories'
equivalent of food.
And if you eat
a lot more than that,
well, you pay a price for that
sooner or later.
How about mechanical work?
Don't we have to eat also
for all the mechanical work
that we do?
We work so hard, and I'm sure
there must be a lot of energy
going into that work.
Well, I have a surprise for you.
It's very disappointing.
The kind of work that
you and I do in one day
is so embarrassingly little
in terms of mechanical work
that you can
completely neglect it.
Suppose we go up three floors.
We walk up three floors,
which is about ten meters high.
And let's say we do that
three times per day.
And let's give you a mass
of about 70 kilograms.
It's about my mass.
How much work do I do
when I do that three times...?
Oh, let me do it
five times per day.
Boy, I really go out of my way.
Five times per day
I go three floors up.
Well, the amount of work
that I do is mgh.
mgh.
The ten meters have to be
multiplied by five,
because I do it five times,
and so I get 35,000 joules
of work that I do.
35,000 joules.
Compare that with the
ten to the seven joules per day
that your body generates
in terms of heat.
You think you have to eat
a little bit more
for these lousy 35,000 joules?
Forget it-- it's nothing.
In fact, your average power
if you did...
if you walked up these stairs
and you spread it out
over a day, and say you...
it took you ten hours.
You go once up in the morning
and then sometime the afternoon,
and you go up in the evening
and maybe twice in the evening.
It takes you ten hours
to go five times
up these three floors.
Then the average power
that you have done,
that you have generated,
is 35,000 joules
divided by 36,000 seconds.
That is embarrassingly little.
That's about one watt.
Compare that with your body,
which generates
a hundred joules per second
every second-- 100 watts.
So it is completely negligible.
However, if you climb
a mountain-- 5,000 feet--
and you do that,
then the work you have to do
is a million joules.
Now, a million is
no longer negligible
compared to the ten
to the seventh.
And so now you feel hungry,
and now you really need
more food.
And if you do that in two hours,
the power that you have
generated is substantial.
You will have generated
an average power of 160 watts--
more than the body heat--
during those two hours,
of course.
And so now the body says,
"I want to eat more.
I want to be compensated for the
work if I climb this mountain."
If I climb 5,000 feet
and I have to do an extra work,
which is ten to the six joules,
you got to eat more.
Now, you would think
that you have to eat
only ten percent more
than you normally eat,
because you say,
"Ten to the six is only ten
percent of ten to the seven."
But that's not true;
you have to eat a lot more,
because the conversion
from food to mechanical work
is very poor--
something like 20%.
So you may have to eat
40% or 50% more than
you normally do in one day.
Suppose I wanted to take a bath,
and I want to calculate
how much energy it takes
to heat the bath--
a wonderful thing to have.
Well, we now know
how to do that.
Q is the number of calories,
m times C times delta T--
that's the equation.
A bath would contain
about 100 kilograms of water.
That is about 28 gallons.
And let us assume
that the temperature increase is
about 50 degrees centigrade,
which is the same
as 50 degrees Kelvin.
We have water,
and so you'll find
that Q then becomes
roughly 5,000 kilocalories--
that's how much heat energy
it takes--
which is two times
ten to the seven joules.
So that's the energy that
is needed to heat up a bath
and enjoy that pleasure.
I'll get back to this bath
very shortly.
There are many forms of energy.
As we're all familiar with,
there is electric energy,
there is chemical energy--
I mentioned that already,
gasoline burning--
there is mechanical energy,
when we move things
in a gravitational field,
and there is nuclear energy.
A waterfall is
mechanical energy-- mgh.
You can convert that
to electricity.
You can convert it to heat.
Electricity will power
your coffee machine.
It will power your TV,
your radio, your VCR,
your electric toothbrush--
everything.
It may power your electric
blanket, if you have one.
Electric blanket is
only 50 watts.
Compare that with
a human being-- 100 watts.
Much nicer to have a human being
with you in bed
than one electric blanket--
believe me.
(students chuckle )
LEWIN:
Nuclear energy can be
converted into heat,
and that can be converted
into mechanical energy
and again into electricity.
Chemical energy--
gasoline, fossil fuel can be
burned, converted to heat,
converted to electricity.
I have here a device
that allows me
to convert mechanical energy
to electric energy,
and I would like to invite
a student to come up here,
a volunteer, a he or a she,
who is going to show
how he or she can convert
mechanical energy
into electric energy.
We'll have the
special light conditions
so that we can see it well.
So, who wants to do that?
Yeah, please come.
There is a 20-watt
light bulb here.
You will see it very shortly.
And this man has a lot
of power, I can tell.
More than 100 watts.
Go ahead.
Power that 20-watt light bulb.
Put your foot on here.
Take it easy.
(apparatus trundling )
Quite impressive, eh?
Okay, now we'll tighten
the nuts a little on you.
Here we have six of them.
So now go ahead,
and now you are trying to
generate 120 watts of power.
You think you can do it?
STUDENT:
I'll try.
LEWIN:
Try it.
(apparatus trundling )
They look pretty dim to me.
Nowhere near.
(apparatus trundling )
Nowhere near--
keep going, man, keep going!
(students laugh )
LEWIN:
You're not even
at the level of 120 watts.
It's hopeless. It's hopeless.
(more laughter )
LEWIN:
You can't do it.
And even if you could do it,
you would have to do this
for 48 hours in a row
to heat up my bathtub.
Think about that.
For one bath, 48 hours.
But you can't even do it.
120 watts is too much.
I don't blame you--
I can't do it either.
(students applaud )
There are batteries.
Batteries convert chemical
energy to electricity directly.
We are all used
to these fancy dry cells,
but in the old days,
and still nowadays in your car,
there are acid batteries.
If I have here
a beaker with acid,
for which most commonly is used
sulfuric acid,
and I put here in a zinc wire
and here in a copper wire,
then this is a battery.
I believe this side
of the battery is positive
and this is negative.
Now, we have them here.
We have this sulfuric acid and
we have zinc and we have copper.
But if we use only one cell,
then I won't be able to light
a small light bulb.
Just like with your flashlight
that you have at home,
you sometimes have to put in
several cells in series
to get a higher voltage
so that you can power
a small light bulb.
The light bulb that we have here
is only a few watts.
It's almost nothing, and
I will still try to get it lit,
which is not so easy,
because this battery has
a self-destruct in it.
The moment that I put
this zinc in there,
I get very violent
chemical reactions.
The fumes are awful--
you may actually smell that
in the first row;
it's very awful--
and the battery works
only maybe for a few minutes.
So I have to do this very fast
since it has
a self-destruct built in,
and when I do it, I will make it
at the very last minute,
I will make it completely dark.
So the way I will do that is,
why don't we turn
everything off?
And now I leave
a few things on first.
I can put the copper in.
The copper is not the worst.
Let me first put the copper in.
That's pretty innocent.
So I'm going to build four cells
and put them in series,
and I have
the copper now in place.
So that's not the worst.
The moment I put the zinc in,
then things begin
to be very unpleasant,
but when I make it very dark,
I close the circuit,
and I hope you will be able to
see the light-- no pun implied.
So let's leave something on
and turn all the rest off.
I'm going to make it
very dark very shortly.
First you still have dim light.
Aah-- one thing goes in.
Ugh! I already smell it.
Two things go in.
And the third goes in,
and now I'm going to make it
completely dark.
And now I have to close the loop
with the last piece of zinc.
Look at that little light bulb
that is right there.
There it goes!
Men! I see the light!
Did you see it?
It doesn't last very long,
but it's there.
Boy, it was very bright,
wasn't it?
You saw it, right?
Unmistakable.
I have to get this out,
because otherwise we will all be
dead by the end of the lecture.
(students laugh )
Okay.
And let's cover these also up,
because this sulfuric acid--
ugh!
So your lead battery in your car
works with the same idea,
except this is lead oxide
and this is lead.
So it works
with lead oxide and lead,
and it's a very, very
powerful battery.
There are batteries which are
very fancy which can be charged.
Nickel-cadmium is a battery
that can be charged.
My electric shaver works
on these batteries.
It's wonderful.
If I forget to shave
in the morning,
I can still do it
before you come in here.
That's the great thing
about batteries.
This is probably...
this probably consumes 30 watts,
30 joules per second
is my rough guess.
And I can probably get
one hour of shaving out of that.
Probably shave six, seven times,
so that's a total
of 100,000 joules--
that's not bad--
out of a battery.
And you can even recharge it.
I'll give you back
your view graph,
because I'm going to talk
about a few more numbers,
and they're all here, so you
don't have to copy anything.
It'll all be on the Web.
The world energy consumption
of the entire world
of six billion people--
by the way, the six billionth
was born two days ago.
Have you heard about that
on the radio?
6.00000 billion people
now on Earth--
eh... is about four times
ten to the 20 joules per year.
That is the entire consumption.
The United States has only
1/30 of the world population
and consumes one-fifth of that.
We are really energy spoilers,
big energy spoilers.
The sun is a wonderful source
of energy.
The sun has a power of four
times ten to the 26 watts--
four times ten to the 26
joules per second--
mostly in the visible light
and some in the infrared.
If the sun is here
and the Earth is here,
and you can calculate how much
of that energy reaches the Earth
at the distance of the Earth--
so you have to know the
distance, but we know that;
that is 150 million kilometers.
And so that energy goes out
radially, symmetrically,
isotropically in all directions,
and so it's very easy.
You know that the surface area
of this sphere
is four pi r squared,
and so you can calculate
how much for every square meter
reaches the Earth.
And that is a classic number
that almost everyone knows,
certainly people
who are in solar energy.
That is 1,400 watts
per square meter.
That is what reaches the Earth.
That is about 100 million joules
per square meter every day.
It would be nice
if we could harvest that,
and it would be nice
if we could use that 100 million
joules per square meter per day
to provide the world
with this four times
ten to the 20 joules per year.
To do that, you would need
ten to the ten square meters
to absorb that solar energy.
That's trivial.
That's only the size of Holland.
No big deal.
If we lose Holland,
that's no big deal, so...
(students laugh )
However, there is a catch.
There is day and night, which
we haven't allowed for yet.
We just assumed that
the sun was always there.
There are clouds.
And then the sun rises
and the sun sets,
and of course
if the sun is at the horizon
and here is your plane
where you try to absorb the sun,
you get nothing, so you have
the cosine of the angle has
to be taken into account.
And then the efficiency
of the units that you're using,
with which you capture
the solar energy
could be solar cells.
It's a very low efficiency.
And if you take all that
into account,
you would need an area
more like 400 by 400 miles.
Now you're really talking.
That's something like
the whole of England
and the whole of France.
And so not only are the costs
staggering, but it is
simply beyond our present
technological capabilities.
So solar energy plays a very
small role in our world economy.
Nuclear energy, which is the
fission of uranium or plutonium,
was very popular in the '70s,
but it has become a little bit
less popular lately.
We had the Three Mile Island
accident in our own country,
And so people are,
understandably so,
emotionally strongly biased
against the use
of nuclear energy.
But nuclear energy is all
around me, at least every day.
I have a very special collection
of Fiestaware,
which is American tableware
which was designed and built
in the '30s, in 1937,
and it went on until the '50s.
And here I brought you
some of this.
This is a ten-inch plate,
and this is called "Fiesta red."
Even though it's orange,
we still call it Fiesta red.
It has uranium oxide in it.
That red is uranium oxide.
That is the same uranium
that powers nuclear reactors.
This is cobalt; 
it has no uranium in it.
And this, again, it's
my cup of tea-- radioactive.
Uranium oxide.
Okay.
You ready for this?
You hear this?
This is a Geiger tube.
It can measure the gamma rays
that the uranium emits
You'll hear a little beep.
I'll hold it close
to my microphone.
(rapid high-pitched beeping )
That's the plate
from which I eat.
(rapid high-pitched beeping )
(much slower beeping )
This cup has no uranium oxide.
But my cup of tea...
(rapid high-pitched beeping )
Radioactive.
So if you want
to come for dinner,
you're more than welcome
to do so...
(students laugh )
LEWIN:
But you know what you're in for.
We have fossil fuel on Earth.
We are consuming at this moment
the fossil fuel
at a rate which is
a million times faster
than nature could create it--
one million times faster.
And if we consume it
at the present rate,
or increase maybe
by only three percent per year,
then we won't have any left
in less than 100 years.
So we have an energy crisis--
a real energy crisis.
And we have
an environmental problem,
because all these power plants
and all the industries
cause pollution.
And so what are we going
to do about it?
My own energy consumption
is quite modest, I think,
although I am also
in your country,
so I'm sure I also consume
six times more than the
average person in the world.
I use electricity,
for which I get a bill.
I have gas heat; 
I heat with gas.
And I have also
cooking with gas.
I use my car-- gasoline.
And when I add that all up,
I think I consume roughly
400 million joules per day.
That 400 million joules per day
is the equivalent
of having 100 slaves working
for me like dogs 12 hours a day.
Think about that.
What a luxury, what
an incredible time we live in.
One hundred slaves are working
for every single person here
in my audience 12 hours a day,
working like dogs
to make you live comfortably.
For one kilowatt-hour
of electricity,
which is four million joules,
I pay only a lousy ten cents.
My entire energy bill
for those 100 slaves
is no more than $150 a month.
What a bargain
to have 100 slaves working
for you for $150 a month.
But now comes
the $64 million question:
How are we going
to continue this?
Because we are running out
of fossil fuel,
and nuclear energy has
its problems.
Well, the only way
that we might survive--
the quality of life is at stake
here-- is nuclear fusion.
Not fission, whereby uranium and
plutonium breaks up in pieces,
but fusion.
If you could merge deuterium
with deuterium, you gain energy.
Now, we have
one out of every 6,000 hydrogen
atoms on Earth is deuterium,
and we have a billion
cubic kilometers of water.
Now, it is unclear
whether we will ever succeed
in making a fusion reactor
working.
That is still
completely unclear.
People work hard on it.
But if we succeeded,
then simply the oceans
would provide the world,
if we consume it
at that same rate that
we are consuming today--
four times ten to the 20
joules per year--
we would have enough energy
for 25 billion years.
All the worries are over,
because the Earth is
not going to survive
for any more
than five billion years.
Five billion years from now,
the sun will become a hundred
times bigger than it is now,
and it will just swallow up
the world,
and it will be the end of MIT,
of everything.
(students chuckle )
LEWIN:
So all we have to think of
is in terms of energy
for about five billion years.
I want to leave you with
what I call a brain teaser.
I have here a very special ball.
And I'm going to bounce
this ball,
and I want you to look at it
and tell me what you think is
the source of that energy.
It's important that
we have little light,
because if there's
too much light,
then you won't see it well.
So, this is a ball.
See, I have another one here.
And I will bounce it here,
and then notice what you see.
Just keep looking.
It stops.
The other one.
And the other one.
Now, I want you
to think about...
you've seen now what happens.
I bounce it, it starts blinking.
Clearly, gravitational potantial energy, 
mgh is available when I bounce it.
Where does the energy come from
of the blinking light?
Think carefully
before you give an answer.
It took my graduate students
and me, embarrassingly,
at least ten minutes
before we had the answer.
Think about the fact
that they continue to blink
and then stop.
Talk about it among yourselves.
Think about it
when you have dinner, breakfast,
when you take your shower.
See you next Friday.
