I said that everything in some sense, 
that was done for centuries after Newton 
was filling in the details to F = MA. 
I don't want to give you the wrong 
impression. 
There are a lot of fascinating details. 
Newton's universe is rich and wonderful, 
and centuries of work by many, many, many 
brilliant people went into producing 
insights and understandings. 
And I wish I had the time to tell you 
about at least that part of it that I 
know. 
But, we're an astronomy class. 
What I'm going to do in the next two 
clips is give you sort of a highlight 
reel of those of the aspects of what has 
been learned in the 250 years since 
Newton and a little bit of the century 
since. 
that will impact what we do and that we 
will need. 
And, we will go through and try to 
develop, if not as deep an understanding 
as we did for gravity which will be 
central, some intuition and some 
understanding for some other important 
concepts in physics. 
And as I said, we'll organize it by the 
M, the structure of matter, and the F, 
the forces that act. [COUGH] And we will 
start. 
Well, let's start with the M side. 
We'll start with what we know the end of 
the 19th century about the structure of 
matter. By the end of the 19th century, 
there we have a pretty 
comprehensive understanding of the 
structure of matter. 
and its center is what is known as the 
atomic theory of matter. 
All known matter is made up of a 100 or 
so types of atoms, 
immutable units. 
they're indexed by an 
number called Z that runs from one to 
whatever a hundred, and roughly high 
elements with higher ZF, heavier atoms, 
more massive atoms. 
And these characterize the chemical 
elements. We understand some rules by 
which they bind together to form 
compounds and molecules and various kinds 
of objects. 
And bulk matter can appear in one of 
three common states. 
We have solids, we have liquids and 
gases. 
And in each, the bulk properties are 
understood as a consequence of the 
microscopic dynamics of the atoms and the 
molecules that form it. 
And, as a good and very helpful to us, 
example, 
one of the forms of energy we discussed 
when we talked about non-conservation of 
mechanical energy was heat. 
Friction, for example, converts kinetic 
energy to heat. 
And 
heat causes a object's temperature to 
rise, so we know what we mean when 
something is hot. 
We mean, it has a high temperature. 
in the context of an atomic theory, we 
have a good understanding of temperature. 
Temperature is simply a measure of the 
average random motions of atoms and 
molecules inside an object which explains 
why heat is sort of lowest common 
denominator of energy. 
Heat is the energy that something has, 
when it's doing its own thing. 
It's not moving in bulk, but its own 
internal degrees of freedom are randomly 
fluctuating. 
And for example, in an ideal gas, that's 
a gas that's made up of atoms or 
molecules, 
that have no internal degrees of freedom 
and are just non-interacting and bumping 
off each other in the walls. Then, you 
can show that temperature gives you the 
average kinetic energy of a molecule or 
an atom or whatever it is, is 
proportional to the temperature. 
And temperature, in this expression, is 
measured in Kelvin. 
Kelvin degrees are the same as centigrade 
degrees. 
That just determines the units in which 
we measure this con, constant here, K, 
which is called Boltzmann's constant. 
What is not arbitrary of course, is where 
you put the zero of T because doubling 
the temperature relative to that zero 
involves doubling the energy, and there 
is a temperature at which the average 
kinetic energy of molecules dissents to 
complete zero. 
This is absolute zero, or -273 or so 
degrees centigrade. 
And this is the origin of that. 
And using these equations, you can see 
that at higher temperatures the molecules 
bump around more. 
A gas exerts a pressure on any container 
in which you put it. 
The pressure is a force per unit area 
applied in, equally in all directions, 
and the pressure times the volume for an 
ideal guess is given by that same 
Boltzmann constant times the temperature 
times the number of atoms. 
In this guess, most guesses are not 
ideal. 
there are all kinds of subtleties here. 
But, the essence of what we see here is 
that temperature is a measure of the 
random motion of the atoms and that the 
pressure and the volume increase with he, 
rising temperature. 
if you take a gas and you cool it at 
sufficiently low temperatures and if the 
pressure if sufficiently high, we'll see 
that later. 
you form a liquid phase which is similar 
to a gas in that it doesn't have a fixed 
shape, the items are moving around, but 
they are weakly bound. And as a result, 
you form a phase called the liquid which 
is almost incompressible, which means 
under reasonable pressures it maintains a 
constant density. 
The volume of a chunk of a given amount 
of liquid is pretty much fixed. 
in both cases, in both phases, the 
density decreases with temperature. 
What that is especially useful to us for? 
Is it tells us that if you have a 
collection of fluid under gravity, then 
the worm fluid, which is expanded and is 
therefore less dense, 
will rise because it floats above the 
cooler liquid. 
And this brings us to the point that an 
equilibrium with gravity 
the pressure in a collection of fluid 
will not be constant and the same at all 
points on the container. 
This is the case in the absence of 
external forces. 
In the presence of an external force like 
gravity, pressure will, in fact, increase 
with depth at a rate proportional to the 
density of the fluid. 
And let's see a demonstration of this, 
and maybe it'll help us understand what's 
going on. 
In this image, 
what we see is very simply, me holding a 
slinky, 
a spring. 
And, what you see when you look at it is 
the following, not very surprising fact, 
which is that near the top of the spring, 
the spring is more stretched than it is 
near the bottom. 
And the way you understand that is quite 
simple. 
A slinky stretches more the more you pull 
it, and the top half of the slinky is 
holding up its own weight, as well as the 
entire half weight of the bottom half of 
the slinky. 
Whereas, the coils of the slinky very 
near the bottom are not holding up 
anything, and so they're relatively 
relaxed and unstretched. 
The higher up the slinky you go, the more 
of the weight the slinky is supporting. 
And therefore, if you look at it 
carefully, you'll see that the degree to 
which the slinky is stretched decreases 
uniformly from top to bottom. 
What wee see here is me holding a cup of 
water. 
this is to demonstrate the decreasing 
pressure with height or increase in 
pressure with depth. 
Now, this is true for the air. We know 
that at high altitude, air pressure 
decreases. But remember, the decrease in 
pressure is due to the extra weight of 
the air, and since air is not very dense. 
We're going to assume that air pressure 
is the same everywhere in this room. 
Not so for the cup because the density of 
water is much larger. 
The water at the bottom of the cup, just 
like the spring at the top of the slinky, 
is holding up all of the water above it, 
whereas the water at the top of the cup 
is not holding up anything. 
And so, I expect the pressure to increase 
from the top of the cup towards the 
bottom respectful of the density of the 
water in the cup and there's a way to see 
this. 
The way you see this is, we drilled holes 
at the edge of the cup. And when I open 
those holes, if the pressure of the fluid 
is identical to the pressure at the top, 
which is the pressure of the air around 
it, then the fluid will happily stay in 
the cup held in by air pressure. 
But, of course, it won't. 
When I remove my fingers, the fluid will 
come splashing out impelled by the excess 
pressure at the bottom of the cup, 
relative to the air pressure which is 
similar to the pressure at the top of the 
cup. 
And in case you're not certain that this 
is due to the weight of the water and to 
gravity, I will drop the cup. At which 
point, fluid becomes weightless, the 
pressure at the top of the cup and at the 
bottom of the cup are now the same, and 
indeed, the fountain ceases. 
So, I hope I've convinced you that, in a 
fluid and equilibrium under the influence 
of gravity, pressure increases with depth 
depending on the density of the fluid. 
This is going to be important in 
astronomical context in understanding the 
structure of things like planets and 
stars, which contain fluid and are 
certainly held together by gravity. 
we talked about gasses and liquids. 
matter comes in a solid state. 
In a solid, the positions of atoms are 
roughly fixed, they can oscillate about 
those positions. 
This allows a solid to maintain its shape 
under external force. 
You can apply pressures and stresses and 
a solid will react, but only a little 
bit. 
It will not, in fact, change its shape to 
suit a container. 
the slinky we had was a very good example 
of a solid object. 
It deformed in response to gravity, but 
it didn't completely stretch out. 
It gave some small proportionate response 
to the stresses that were placed upon it. 
And the larger those stresses the larger 
the response, but the response was 
limited. 
The slinky retained fundamentally its 
shape even under duress. 
In all of these phases, fundamentally the 
interaction is between each atom or 
molecule and those near to it. 
There is no long distance interaction 
or there's a weak interaction between 
atoms in one side, on one side of the 
slinky. 
And on the other, each side of the bit of 
a slinky knows about the bits around it. 
And the result is that if you, for 
example, compress the slinky at what one 
point or move it at one point, then the 
perturbation travels through the material 
as each piece communicates the 
information, if you wish, to the next bit 
over. And this mechanical deformations of 
a solid, of liquid or a gas are called 
sound wave, and they travel with a speed 
characteristic of the material. 
Now, the most familiar to us, of course, 
are the longitudinal sound waves in the 
air, that is what we hear with our ears. 
And let's use that slinky. 
There's a very nice demonstration of wave 
propagation. 
To do that, let's see what happens when I 
let go of the top of the slinky. 
Remember, the slinky was extended in such 
a way that it was in equilibrium. 
The net force on every bit of it vanished 
and this had to do with the fact that it 
was more extended at the top and less at 
the bottom so that this compensated for 
the pull of gravity on every individual 
piece. 
Now, when I release the top, the top of 
the slinky starts falling down. 
But near the bottom, everything is still 
in equilibrium. 
The bottom of the slinky is not falling. 
What we see is a density wave propagating 
at the appropriate speed, determined by 
the slinky, through the slinky. 
And it is only when this wave reaches the 
bottom of the slinky that the bottom 
begins actually to fall. 
Until that time, it is in equilibrium, 
and the information that something has 
happened at the top has not reached it. 
What we're seeing is a sound wave. You 
bang on something at one point and it 
takes time for that deformation to 
propagate through the material and reach 
the other end. 
In this simulation, 
we are going to be able to make some 
waves. 
So, if I grab the end of this rope, the 
dif, disturbance travels at the 
characteristic speed of sound down the 
rope. 
And frequently we deal not with 
random pertivations but with periodic 
oscillations,, usually in a sign wave 
pattern as is done here. 
Each point on the rope is oscillating 
periodically and they're all oscillating 
with the same frequency, which is the 
frequency that this motor is oscillating 
with. 
In this case, it's oscillating with a 
frequency of 50 something. 
And so, frequency F, is the number of 
oscillations per second. 
And so it's measured, since this is a 
number, in units of inverse second and 
once per second is called a hertz. 
Which is why the frequency of your radio 
signal is measured in megahertz if you're 
listening to FM radio. 
And so, I can restart this oscillation, 
and what we see is that because it takes 
longer amount of time for the wave to get 
farther down the string, this, 
the, the position of the string here 
reflects what happened here a longer time 
ago than the position of the string here. 
And so, the periodic oscillation of the 
driving force causes each point on the 
string to go up and down. 
Notice, the wave is moving. 
The string is not going anywhere. 
But, also what it causes is because 
distance translates to time. 
we get a periodic sinusoidal structure in 
space at any given instant, and that is 
characterized typically, by the distance 
between subsequent peaks. 
The distance along which the wave 
repeats, that's it's wavelength lambda. 
And if you think about it, sitting at 
some point for a second F peaks will come 
by. 
And so, 
F peaks will come by, 
that means the wave will have transferred 
a distance of F times the distance 
between peaks. 
In other words, F times lambda is how far 
the disturbance travels in a second. 
So, F times lambda is the speed of the 
wave which we characteristically call C. 
Now, the reason we're dealing with 
periodic oscillations is a complicated 
mathematical theory called free analysis 
that says, any deformation can be written 
as a sum of 
periodic ones. But, Fourier analysis is 
not some abstract mathematics, 
it's exactly what our ear does. 
When your ear hears sounds, it analyzes 
them into a sum of harmonics and you hear 
the pitch of a sound, you hear is given 
precisely by its frequency, and you can 
hear three different notes and 
distinguish that there are three notes 
there. 
this is biology and not physics, but it 
is definitely true. 
And I can increase the frequency. 
And what we see is that when I increase 
the frequency, the wavelength became 
correspondingly smaller, the frequency 
times the wavelength is a constant the 
speed of the wave. 
a wave is characterized therefore by it's 
frequency or it's wavelength, given the 
speed, those are related, but also by an 
amplitude. 
An amplitude is simply the magnitude of 
the largest deformation. So, an amplitude 
of seventeen is a very small deformation 
and an amplitude three times as large, is 
a very large deformation. 
So, periodic disturbances, as we saw, are 
characterized by their frequency, F, in 
hertz the number of cycles per second. 
if a wave is traveling at a speed C, a 
periodic disturbance will produce a 
periodic wave in space at any given 
instant with a wavelength lambda that is 
related to the speed by this important 
relation. 
Lambda wavelength times frequency is 
equal to the speed of the wave. 
The wave was characterized also by the 
amplitude, which is the amount, the 
maximum amount of the pertubation. 
And one of the important things about 
waves is, the string didn't move. 
But clearly, waves carry energy from one 
place to the other. 
You could imagine hooking something at 
the other end of the string. 
I will vibrate this end, the wave will 
carry it and cause that object to vibrate 
giving it kinetic energy. 
That kinetic energy came from my hand, 
and therefore, a wave carries energy. 
in fact, it carries an energy if it's 
periodic per unit time that is constant. 
Over time, energy is flowing down the 
string. 
and so, you measure an energy flux in 
joule per second. 
A joule per second is known as a watt. 
This is the same unit of energy per unit 
time that you measure the intensity of 
your light bulbs in. 
How much energy does it take to operate 
that light bulb for a second. 
Now, this is a wave on a string. 
of course, a wave, 
like a sound wave that travels in three 
dimensions will carry an energy flux that 
is a density. 
Because if the wave is propagating over a 
wide front each bit of the wave carries 
an energy, 
so we measure the flux in watts per 
meter-squared of wavefront. 
And that energy flux, in watts per 
meter-squared, is proportional to the 
square of the amplitude. 
Clearly, the larger the amplitude, the 
more energy the wave is carrying. 
And the flux is going to be measured in 
watts per meter-squared. 
Now, what happens when two waves meet is 
a very important property of waves. 
Let's look at it in a demo and then we'll 
talk about it. 
In this demo, we have a loudspeaker. 
The loudspeaker will be creating a 
periodic wave. 
And we see the wave fronts are shown in 
this picture. They spread away from the 
loudspeaker. 
And what we see here is a measure of the 
pressure of the density that the 
perturbation that the wave represents at 
one given point. 
And we see the characteristic, periodic 
isolation that we're talking about. 
And, one thing you can see is that, 
unlike waves on a string, we'll talk 
about this. But, because these waves are 
spreading out, the amplitude of 
oscillation is larger near the source, 
then it is far, And anybody who stood 
very near a honking car horn is painfully 
aware of this fact. 
we'll talk about that aspect of things in 
a little bit. 
I just thought I'd just point it out 
while we're seeing it. 
But, the interesting thing to note is 
what happens when, instead of one loud 
speaker, we put two speakers. 
So now, the two speakers are both 
creating wavefronts. 
And we see here what happens as the 
wavefronts add, 
and you notice that I put my detect in a 
very interesting point. 
the two speakers together, 
each of which would've produced the noise 
with the amplitude we saw before, 
produces essentially zero noise at the 
position of this detector. 
But if I move the detector a little bit, 
I will see that it's is not because the 
two speakers are not producing noise at 
all, 
I see that indeed at this position, 
they're producing a far louder noise 
together than either one separately. And 
in fact, 
more than twice the sound that each would 
have produced separately, somehow the 
combination of the two speakers is 
focusing sound into these regions where 
the dark bands are and leaving these 
regions where the grey bands are, the 
nodes, where essentially no sound gets 
to. 
Now, the reason that this is possible is 
because waves can subtract from each 
other. When these two waves propagate, it 
turns they essentially don't interact 
with each other at all, that's the 
approximation that we're working in and 
it's valid one for sound waves. 
And what that means is that the total 
dis-perturbation at any point in space 
and time, is the sum of what it would be 
if there was one speaker, and what it 
would be if there was the other speaker. 
And, 
how does that, adding what one speaker 
would produce to what the other speaker 
would produce, lead to zero? 
Well, remember they're both oscillating 
at exactly the same frequency. So, there 
can be a point where because of the time 
delay from this speaker being different 
from the time delay from that speaker, 
due to the difference in distance. 
when a peak from this speaker reaches, it 
is always timed to arrive at the same 
time as a trough from this speaker, so 
that the two waves that these two create 
are always counteracting each other. 
Waves add, but that addition can amount 
to subtraction. 
And that phenomenon is known as 
interference and its characteristic of 
waves. 
So, let's summarize what we've learned 
here. 
A hallmark of wave behavior is that waves 
are deformations or perturbations to some 
equilibrium, and when two waves meet at 
the same point in space and time, the two 
disturbances add. 
In other words, each wave behaves as 
though the other were not there. 
We just add the disturbances. 
What this allows, if the waves are of the 
same frequency, is that if the time delay 
between 
one source and the other source relative 
to your position, is suitably adjusted. 
In other words the distance difference, 
which translates to the time delay, is 
suitably adjusted. 
You can adjust it so peak from one wave 
precisely meets a trough from the other. 
The two waves add in the sense that they 
subtract, and you can get nodes, you can 
get regions of quiet in the vicinity of 
two speakers producing the same 
frequency. 
this will be important to us. 
It's a hallmark of wave behavior. 
Now, another property of waves that is 
going to be useful to us is extremely 
useful in fact, is something called the 
Doper effect. 
It's the well known phenomenon that the 
sound from a moving source sounds 
different then the sound from a 
stationary source. 
If a source is the noise is approaching 
us, 
it sounds higher in pitch than where it's 
stationary. If it's receiving, if it's 
moving away from us the pitch sounds 
lower. 
the archetypal example of this is the 
sound of a race car driving past you. 
I'll play it in the speakers, perhaps you 
can hear it. 
[SOUND] That [SOUND] whine is the 
transition from an elevated pitch as the 
car approaches you to a decreased pitch, 
decreased frequency as the car recedes 
from you. 
And the mathematical formulation of this 
is due to Doppler in the 19th Century, 
and we can understand this rather 
straight forwardly. 
Here is a source producing regular, 
regularly spaced periodic waves, and an 
observer placed over here receives the 
waves with a time delay. 
It takes time for each wave to reach 
there. 
The time delay is the same for each wave 
so the time between subsequent floods is 
the same as the time between subsequent 
emissions. 
And this is a stationary source. 
The frequency with which his ear is 
oscillating is the same as the frequency 
with which this source is producing the 
sound. 
That is true. 
Now, let's move on to the case where the 
source is moving and let's again place an 
observer over here. 
And we see that what's going on is that 
the wavefronts appear compressed on this 
side, they're compressed, of course, 
because between the emission of one wave 
and the next the source moves. 
And so, the distance between the 
wavefronts, as seen by the observer here, 
is smaller than it would be were the 
source stationary. 
And we can easily compute the relation 
between the two because the distance 
between subsequent wavefronts as they 
arrive at this observer, 
lambda, which is the wavelength that this 
observer sees, is equal to the distance 
between the two wave fronts when they 
were omitted minus the distance which the 
source traveled. 
Because each subsequent wave front has a 
shorter distance to travel because in the 
interim between emitting one wave front 
and the following, the source traveled 
distance given by v times the time 
between wave fronts. 
What's the time between wave fronts? 
The time between emissions is one divided 
by the frequency because this is the 
number of seconds. 
And so, remembering that lambda times f 
is c, I can write f as c over lambda. 
And I get lambda is lambda zero minus, 
let me write this correctly. 
lambda is lambda zero minus v lambda zero 
over c, or Doppler's formula, lambda is 
lambda zero times one minus v over c. 
notice that this v was taken to be 
positive when the source was approaching 
the observer and observer on this side, 
of course, sees the wave dilated. 
The wavelength looks longer, the pitch is 
lower as the car is receding from you. 
Each subsequent wave front has a longer 
distance to go. 
That is compensated in this formula by 
considering v to be negative if the 
source is receding, and positive if the 
source is approaching you. 
We talked about heat energy and we need a 
few properties of heat because heat will 
be a dominant form of energy in some 
environments that we talk about. 
And so, it's a property of heat that if 
you have a hot object in a cooler 
environment, 
then the hot object will lose energy the 
environment and this process will 
continue indefinitely or until such time 
as the temperatures equilibrate. Because 
as the source looses heat, the 
environment gains heat and warms up. And 
eventually, if the temperatures are 
equal, then we have equilibrium, and heat 
flow stops. 
But so long as you have warm sun in cold 
space, the sun will continue to lose heat 
to space. 
And until such time as either space heats 
up or sun cools down, 
this process will continue. 
There will be a constant flux of energy 
out of the sun into space. 
And, there are several ways by which this 
transfer of heat from a hotter to a 
cooler body can occur. 
One is called conduction, this is where 
heat is transferred through continuous 
contact. 
And this is not an in, 
great importance. 
In astronomy, heat conduction on 
astronomical scales is rare. 
A second phenomenon is convection. 
This is basically like trucking. 
This is what happens when the physical 
motion of the fluid carries energy. 
this works very well if you have 
volume of fluid that is heated from 
below. 
That happens when you boil water on your 
stove, 
it also happens in stars, say, where a 
hot core is heating the atmosphere from 
the inside. 
What happens is that at the bottom of the 
pot or the bottom of the atmosphere the 
fluid is heated. 
The heated fluid expands. 
The expanded heated fluid is lighter, 
less dense then the surrounding fluid. 
And therefore, floats to the top and 
rises. 
Cooler fluid descends to take it's place. 
And what you have is a energy transfer 
from the bottom to the top by heated 
fluid physically moving from one part to 
the other. 
And this does occur in astronomical 
phenomenon. 
None of this, of course, is helpful to 
the sun in losing its energy to space 
because the sun is not in contact with 
anything nor is there any fluid around it 
to convect. 
The way the sun loses energy to space is 
radiation. 
It turns out that every object, unless 
its at zero temperature, glows and that 
phenom, that mechanism of energy loss is 
radiation heat transfer, and essentially 
the radiation question is sunlight. 
Sunlight is the way the sun attempts to 
heat up space, losing energy because it's 
warmer. 
And we'll come back to this calculation 
in a moment. 
But, 
let's understand something about this 
heat flux, 
energy flux problem. 
And so, the sun is hot and so it 
radiates. 
And we'll learn how to compute how hot it 
is and how much it radiates. 
But for now, let's assume that the sun is 
radiating energy at a constant rate. 
Why is the rate constant? 
Because the properties of the sun are 
unchanging, the properties of space are 
unchanging. So, the rate at which the sun 
loses energy to space is therefore 
unchanging. 
We call that rate the luminosity, and 
it's measured in joules per second, in 
watts. 
The sun like a light bulb produces a 
certain amount of energy or loses a 
certain amount of energy to space every 
second and we'll figure out this number, 
obviously. 
It's 
a great many light bulbs. 
Now, what interests us often is how 
bright the sunlight is at some given 
location in space. 
And what that implies is put some uniform 
detector, say, an eye with a fixed 
surface area. 
And as we saw or as this diagram shows, 
if this is something the size of your eye 
or of your detector, the farther it goes, 
the less sunlight it traps. 
Because essentially, the sun makes 
produces radiation in all directions. 
And so, at any distance, 
the sunlight is spread uniformly across 
the surface of a ball [SOUND] or a sphere 
of radius R. 
And, if you are at some distance and you 
place your detector, your detector takes 
up some fraction of that sphere. 
If you are twice as far, the sphere is 
larger and your detector now takes a 
smaller fraction of this larger sphere. 
And the result will be that your 
detector, since all of the suns rays pass 
through this sphere and all of the sun 
rays a little later pass through this 
sphere as well, 
the net total amount of energy passing 
through each sphere is the same. 
But the total amount passing through a 
fixed detector decreases because the 
spheres grow larger whereas the detector 
does not. 
Mathematically, the statement is that at 
a distance R, the radiation is 
distributed uniformly on the surface of a 
sphere. 
So, energy per second received by a 
square-meter of detector will be the 
luminosity divided by the surface of a 
sphere across which the radiation is 
spread uniformly. 
And so, the 
sun energy is diluted by a factor of R 
squared as it travels out into space. 
Light, of course, is going to be of 
incredible importance in our 
understanding of the universe. 
It's the main way we perceive our 
environment on Earth. 
It is certainly the main way that we 
receive information from distant places 
in the universe, so the properties of 
light will be extremely important to us. 
So, light 
light, of course, is the main way we as 
humans perceive the world around us. 
It's also the main way that we as 
astronomers learn about distant objects. 
The nature and the properties of light 
are going to be extremely important to 
us. 
And the first of these is the speed. 
So, light carries energy away from the 
sun to Earth to warm us. 
and the speed at which light propagates 
is huge. 
It's about three times ten to the eighth 
meters per second. 
this may, this large number makes 
accurate measurement difficult. 
First, really good measurement was in 
1850 by Foucault and Fizeau, though there 
were earlier less precise measurements. 
Now, 
in a classic experiment in 1670, our old 
friend Newton made the discovery that the 
sunlight, white colorless light from the 
sun, in fact contains all colors of 
light. 
he found a way to split a beam of white 
light into beams of various colors. 
He was using a prism, today we use a 
defraction grading. 
And he conjectured that the nature of 
light was that light was a stream of 
particles, of course, he had all the 
mechanics know how to understand the 
stream of particles, light moved in 
straight lines, light particles which 
upon no forces act. 
Moved at a constant velocity, it seemed a 
lot like mechanical particle model of 
light would be likely. 
This is one of the rare cases where 
Newton was wrong because in 1799, only 
120 years later, Young observes light 
waves interfering. 
So, he makes the observation that you can 
take 
light and you can construct these 
interference effects where light waves 
add and subtract, and you get nodes. 
This interference was a hallmark of wave 
phenomena, so Newton, for once, was 
actually wrong. 
Light is a wave. 
But never count Newton out. 
We'll come back to this point in the next 
clip. 
And that same Young, three years later, 
shows that 
our eyes while they are extremely 
accurate in giving directional 
perspective. 
So, they tell us very precisely which 
direction light is coming from, that's 
how we construct our image of the world, 
are in contrast relatively poor as fully 
analyzers. 
Unlike our ears, which can distinguish a 
great variety of sounds and hear several 
simultaneous tones and distinguish them, 
our eyes are very poor for an analysis 
machine. They only are sensitive to the 
relative intensity of three colors, red, 
green and blue, and we'll see in a minute 
what that leads to. 
What we're going to do is an experiment 
somewhat similar to what Newton did. 
So, we have here a beam of white light, 
and we're going to put a diffraction 
grating in front of it, and the 
diffraction grating splits the white beam 
so that the white stripe in the center is 
somewhat dimmed. 
And on both sides, we find the familiar 
rainbow structure. And so, we see a 
stripe of red flaring to orange and 
yellow and green, and into blue and 
violet. 
And, 
we can see what happens when we put a 
filter in front of the light, 
we get red light. 
And when we feed red light into the 
diffraction grating, what we see in the 
spectrum is that the green and the blue 
are missing. 
Similarly, when we feed green light into 
the defraction grating, the blue and the 
red are missing, and only green light 
comes in. 
So, the defraction grating is not 
coloring the light. 
It is deflecting whatever green light it 
gets to that region. 
Again, putting a blue filter in front of 
the beam, we see that only the blue 
remains in the spectrum. The blue filter 
absorbs the green and the red, the green 
filter absorbs blue and red, and the red 
filter absorbs green and blue. 
these are, it turns out, the primary 
colors it has to do with our eyes. 
here's what happens when you put a cyan 
filter in front. 
A cyan filter absorbs the red light, and 
so lets through the blue and the green. 
Similarly, if we use a magenta filter. 
A magenta filter absorbs the green, 
letting through the blue and the red. 
So, what we see as magenta is blue light 
and red light. 
There is also, 
we can put a yellow filter in, and this 
is important. 
We see that what we perceive as yellow 
light is, in fact, light that is missing 
its blue. 
The green and the red are present, 
the blue is absent, 
and we see yellow. 
And so, if we superpose the yellow and 
the magenta filters, the yellow filter 
absorbs the blue. 
The magenta absorbs the green, and what 
is left is red. 
And indeed, 
superimposing those two filters, we get 
red. 
If we superimpose yellow and cyan, the 
yellow absorbs the blue, the cyan the 
red, what's left is the green. 
And we see that very nicely in this 
picture, and we can keep playing. 
We can superimpose the cyan and the 
magenta, the cyan absorbs the red, the 
magenta absorbs the green. 
Putting them on top of each other, we're 
going to be left with blue. 
So, 
this has to do with the way our eyes see 
colors. 
the important thing for us to take away 
here is that a filter that absorbs the 
blue looks yellow. 
We cannot distinguish this yellow from 
the yellow in the spectrum there in 
between the red and the green that is 
pure yellow light. 
We saw that as Young showed us, light is 
a wave, and also as Young showed us, our 
eye, in fact, has three color detectors. 
One sensitive to red light, one sensitive 
to green light, and one sensitive to 
blue. 
And what we perceive as color is merely 
the relative intensity at which those 
three detectors are excited. 
So, yellow light that excites the red and 
the green approximately equally. 
Because in the spectrum, the other light 
is between red and green cannot be 
distinguished from a combination of 
actual red and green light. 
And so, our eye, unlike our ear, is not a 
very good free analyzer. 
so much for biology, but this will be 
important in understanding some phenomena 
later. 
And then, once we know that light is a 
wave, it's not too shocking that color is 
a property of the wave. 
Color turns out to be the frequency of 
light 
visible light has a frequency of order 
ten to the 12th hertz 
even at the rather high speed of light, 
we can compute the wavelength is pretty 
short. 
It's between 400 and 700 nanometers. 
A nanometer is a billionth of a meter, 
ten to the minus nine meter, and these 
are the units in which, typically we 
measure the wavelengths of visible light, 
at least in astronomy. 
And so, 400 nanometers, the shortest 
wavelengths visible light is the blue 
light as this indicates. 
And the red end of the spectrum is the 
longer wavelengths. 
And the order of the colors in the 
rainbow is according to their 
wavelengths. 
So, that violet light in fact, is at the 
short end of the spectrum, green is 
somewhere in the middle around 550 
nanometers is green light and so on. 
Now, for something completely different. 
we talked about gravitation as the force 
that dominates astronomy. 
But, in most of our lives, 
gravitation of the Earth is important. 
But, when we interact which each other or 
with objects around us, gravitation is 
completely unimportant. 
The gravitational force of a human being 
is negligible compared to the other 
forces we interact with. 
The force the tunes out turns out to 
dominate most of physics is 
electromagnetism. And so, we need to 
understand some things about this. 
And, the simplest version of 
electromagnetism is the force between two 
static charged objects. 
So, there is in the universe a thing 
called electric charge. 
some objects carry electric charge. 
You can charge your hair by combing it on 
a dry day, and the knowing force that 
makes your hair stand on end on a dry day 
is this electrostatic or Coulomb force 
which has a formula that will appear 
familiar. 
The force between two objects of charges, 
q1 and q2, is given by a constant times 
the product of the charges, divided by 
the square of their distance. 
This might appear familiar, 
it's that square of the distance again. 
It's not exactly a coincidence. 
The big difference between electric 
charge and mass, or between a Coulomb's 
law and Newton's law is that Newton's 
law, remember had FGMM = GMm over R 
squared. 
And these numbers were positive, and the 
force was attractive. 
Always. 
Gravitation is a universally attractive 
force. 
Coulomb interactions can be attractive or 
repulsive. 
It turns out that the force is attractive 
when the two charges are of opposite 
sign, so positive and negative charges 
attract, and charges of like sign repel 
with an equal magnitude. 
But the sign, the direction of the force, 
depends on whether the charges are equal 
or opposite. 
This in turn explains why this force does 
not dominate the universe, and this force 
does. 
It's not because gravitation is stronger. 
In fact, we have an unvarying measure of 
strength in which gravitation will be a 
far weaker force than electromagnetism. 
But, 
because opposite charges attract, most 
objects are neutral. 
In the presence of charge, if you have 
something that's charged positively, it 
will attract negative charge until such 
time as it reaches equilibrium. 
In other words, as neutral. 
This is not possible for mass. 
There's no concept of negative mass. 
In fact, it's worse than that. 
We'll discuss the instability of gravity. 
This will have profound consequences so 
I'm not belaboring an obvious point. 
And charge, like mass, momentum, 
energy, etc., is conserved. 
You can neither create nor destroy 
charge. 
Though, of course, charge can be 
transferred from one object to the other. 
So, when you comb your hair, the comb is 
charged with one charge, your hair with 
the opposite charge. 
when atoms form an ionic bond, they 
exchange charges and so on. 
But, the total charge in the universe or 
in any enclosed region in the universe is 
conserved. 
And then, 
you see, 
in gravitation, I kept wanting to talk 
not about the gravitational force, 
but the gravitational acceleration. 
So, you talk about the Earth for example, 
generating around it a gravitational 
field. 
The gravitational field is the statement 
that were a mass to be placed there, it 
would experience a force. 
And, you can compute the force per unit 
mass without knowing what the size is of 
the mass that you would introduce. 
And in a similar way, you talk about an 
electric charge producing an electric 
field which is the force per unit charge 
that would act were a charge to be placed 
there. 
So, a charge create an electric field 
around it because another charge were it 
to be brought there, would be effected. 
And a charge is effected by electric 
field. 
A similar phenomenon of a field 
region around an object in which other 
objects might be impacted is encountered 
with magnets. 
A magnet creates around it, something 
that we can call a magnetic field. 
In the presence of such a field, any 
other magnet, like this little compass, 
will align itself in a particular 
direction at any given point in space. 
Of course, it will align itself so that 
its north pole faces the south pole and 
so on. 
And so, [SOUND] 
We can imagine that this region of space 
has some property called a magnetic field 
which is the statement that, were you, 
remember, there was a field here even 
before I brought the compass, that told 
you that were you to bring the compass, 
it would point in such and such a 
direction. 
Now, magnets and electricity initially 
appear completely unrelated. 
And it is known, however, that electric 
currents in fact produce magnetic fields 
in the vicinity of an electric current. 
Electric current flowing around the coil 
behaves very much like a magnet. 
We call this an electromagnet. 
And, we see that we have a magnetic field 
in the vicinity of an electric current 
moving charges create magnetic fields. 
So this is the first relation between 
electricity and magnetism, but there's 
another relation which is that you have a 
changing magnetic field, it will cause 
charges to move so that this magnet has 
absolutely no impact on the charges in 
this coil. 
But if I move the magnet so that the 
magnetic field in the coil changes, then 
while the change is on going, 
current will flow and current flows means 
there's a force on these charge carriers. 
This implies an electric field. 
A changing magnetic field causes an 
electric field and I can, of course, 
cause the change by moving either the 
magnet or the coil. 
And so, changing magnetic fields 
essentially can be thought of as 
generating electric fields. 
This has profound consequences. 
Let's see what they are. 
The fact that moving charges can create a 
magnetic field was discovered in 1820 by 
Orsted. 
And, it turns out that moving charges are 
also affected by magnetic fields. 
We saw that when we moved the coil in the 
presence of a magnetic field, 
Faraday realizes the phenomenon that we 
were discussing, which is that a changing 
magnetic field is tantamount to an 
electric field. 
30 years later, Maxwell writes down what 
are the collected set of equations 
describing electric and magnetic fields. 
And, in particular, the phenomenon he 
needs to add is that a changing electric 
field creates a magnetic field. 
In the presence of a changing electric 
field, there's a magnetic field. 
And the combination of these two 
phenomena leads in Maxwell's equations as 
part of the solutions to propagating 
waves. 
Propagating waves in which essentially an 
elec, you set up a changing electric 
field which creates a magnetic field 
which creates an electric field which 
creates a magnetic field. 
You solve the differential equation that 
this leads to, and you find that it 
describes a propagating wave. 
And Maxwell computes from the properties 
of magnets and currents and Coulomb's 
law, properties that have been measured 
in the lab, he can compute the velocity 
of these waves that he's discovered. 
And their velocity surprise, surprise, is 
precisely c. 
It co, he didn't get it this precisely, 
but it coincides with the speed of light 
that Fizeau and Foucault had measured 
eleven years previously. 
So, Maxwell has very good reasons to 
imagine that he has discovered that light 
is a wave, as Young said. 
In fact, we now know what it is a wave 
of, 
it's an electro-magnetic wave. 
The disturbance that propagates in space 
when a light beam travels through it is 
an electro-magnetic wave, is an elec, 
disturbance in the electric and magnetic 
fields which have come to take on sort of 
a life of their own. 
Remember, there were ways to calculate 
what would happen if you put a charge. 
And suddenly, they create each other an 
they propagate through space far away 
from the charges that might have created 
them in the dim distant past, they have 
essentially their own existence. 
And so, we do talk about these fields as 
important objects, the understanding that 
light is an electromagnetic wave also 
tells you that you can in principle 
imagine oscillating a charge or creating 
an oscillating electric field at any 
weave, wavelength or any frequency. So, 
we know that we see light from between 
400 and 700 nanometers in wavelength. 
What, what about the solutions to 
Maxwell's equation with wavelengths 
outside this region? 
And it turns out that there is an entire 
huge electromagnetic spectrum out there 
ranging from at very high frequency and 
very short wavelength gamma rays with 
wavelengths of down to ten to the 
fourteen, ten to the fifteen meters and 
below. 
Except though, below that are very hard 
to produce, 
through the x-ray spectrum. 
The drugs from wavelengths of about ten 
to the minus nine to ten to the minus 
twelve meters, and then the ultraviolet 
light which is the 
chunk of the spectrum, immediately beyond 
the deep violet light at 400 nanometers. 
that is the shortest wavelength our eyes 
can see. 
And then, on the other side, to the left 
of the red light we have infrared light 
and below that, microwaves and radio 
waves whose wavelengths can be hundreds 
of meters. 
and so there's this entire spectrum. 
And in fact, we're familiar with it, we 
use it. 
our eyes are sensitive only to this tiny 
little bit of the electromagnetic 
spectrum. 
Our eyes have all kinds of 
inefficiencies. 
But, in this case, our eyes are well 
adapted to where we live. 
if you look down here at the bottom of 
this plot, this is the transparency of 
the atmosphere. 
And you see that, for example, gamma rays 
and x-rays are not very useful despite 
Superman claim to the contrary, x-ray 
vision is not very useful because x-rays 
are very quickly absorbed in the 
atmosphere, they do not penetrate. 
Visible light penetrates the atmosphere. 
A little window in the infra red 
penetrates the atmosphere. 
And then, radio waves penetrate the 
atmosphere, well we know that, because 
that's how we watch TV. 
But the wavelengths of radio waves are 
too long you would need your eyes to be 
antenna. 
They would need to be on the order of 
meters in size. 
We do not have eyes meters in size. 
There would also be other limitations. 
It would be hard to see features of the 
universe smaller than a few meters 
across. 
So, given our need for fine resolution, 
our eyes are well adapted to the 
conditions under which we evolve. 
But the universe, on the other hand, 
produces light in, 
in the entire, across the entire spectrum 
from high energy gamma rays to radio 
waves. 
And it's important in order to collect 
information about the universe to be able 
to observe it in all possible frequency 
bands. 
And indeed, with technology, people have 
developed ways to observe the universe in 
all of these frequencies. 
And at every time that we've developed a 
new technology and a new way to look at 
the universe, there have been new and 
often surprising discoveries made. 
note that observations in many of these 
bands, in the ultraviolet and x-rays and 
in gamma rays for example, need to be 
made outside the atmosphere. 
Putting a very good gamma ray detector on 
the ground will not buy you anything, 
because gamma rays from space will not 
penetrate. 
So, these observatories including, 
actually, infrared observatories, tend to 
be space-born or at least high altitude 
balloon flights. 
radio telescopes can be placed on, are 
placed on the ground. 
Those are these very large dishes that 
receive radio waves. 
And over the course of the class, we will 
have occasion to use information 
collected by all of these bands. 
So, it's the richness of the spectrum 
corresponds to the richness of phenomenon 
out there. 
We're almost done with our discussion. 
One last statement now that we have our 
understanding of the spectrum. 
A hot object radiates, 
that's what we disussed. 
Everything radiates 
as long as it's warmer than the 
surroundings for a dense, dark object. 
So, for an object that essentially 
absorbs light that hits it, such as you, 
me, the Earth, and it turns out, the sun, 
the radiation is almost completely 
characterized, and it's precisely 
completely characterized for some 
idealized black body, an object that 
absorbs any light that falls upon it, by 
the temperature. 
It turns out that the nature of the 
radiation produced by a warm object, 
if it's dense, it's essentially a 
property of light and thermodynamics and 
has nothing to do with the object itself. 
And this is called black body radiation 
and it has two important properties. 
One is, that hotter objects are blue. 
This despite the fact that blue is a cold 
color and red a warm color. 
To our intuition it turns out that hotter 
objects radiate shorter wavelength. 
In other words, a blue glow is hotter 
then a red glow because a red glow has a 
longer wavelength. 
This is summarized in Wien's displacement 
law which says that the wavelength that 
which an object emits more radiation than 
any other wavelength, the wavelength of 
maximum emission, multiplied by the 
object's temperature, is actually a 
constant. So that if you double the 
temperature of an object, the wavelength 
at which it emits is halved. 
And Wien's constant is written over here. 
It's got units of meters times Kelvin, so 
wavelength times degree. 
The other and more familiar statement is 
that hotter objects produce more light. 
This is encoded in the Stefan-Boltzmann 
relation which tells us that the rate at 
which H meters squared of an object 
radiates. 
Of course, a big object radiates more 
than a little object if they're the same 
temperature. 
Two light bulbs make more light than one 
light bulb. So, we need to normalize to 
the rate at which an object produces 
radiation per meter squared, 
that's F in watts per meter squared. 
And the rate at which each meter squared 
of an object radiates is proportional to 
the fourth power of the temperature in 
degrees Kelvin. 
And so doubling the temperature leads to 
a sixteen fold increase in radiation and 
the constant, the Stefanu-Boltzmann 
constant, sigma has this numerical value 
in our units. 
And its units are watts per meter squared 
per degree Kelvin to the fourth. 
Let's take a look at what this black body 
radiation looks like. 
Here, we have a plot of the relative 
intensity in various wavelengths as a 
function of the wavelength from near zero 
to a few times ten to the minus six 
micrometers. 
And so, the visible band is located over 
here. 
And the 
black body curve has this characteristic 
shape. 
As I said, it's independent of the 
material. And the curve I have plotted 
here is the curve for an object that 
glows that has a temperature of about 
3,000 degrees Kelvin. 
3,000 degrees Kelvin is about the 
temperature at, of the filament in an 
incandescent light bulb. 
And what you will notice is that most of 
the light produced by an incandescent 
light bulb's black body radiation, 
is in fact not light. 
It is invisible to us. 
It is infrared radiation, which heats us, 
if you underst, if you talk about people 
not liking incandescent lamps as being 
very inefficient, this is because due to 
the limitations of the filament. 
Filaments melt if you heat them too hot. 
most of the light produced by an 
incandescent lamp is in fact not light, 
it is just heat. 
And so, on the other hand, if we 
heat the object a little bit. 
This is an object with a temperature of 
say, 6,000 degrees. 
This is closer to the sun. 
And you see that much of the light 
produced by the sun is, in fact, in the 
visible spectrum. 
It's very nice of the sun to be adjusted 
to our atmosphere so that much of the sun 
light can, in fact, penetrate our 
atmosphere, and we can use it to see. 
And you also see that the factor of two 
in temperature leads to this huge 
increase. 
The previous light bulbs graph has been 
scaled down here, it looks very small. 
remember, doubling the temperature 
increases the total radiation by a factor 
of sixteen. 
And, it has also moved the maximum from, 
according to Wien's law, from the 
infrared in this case, down into the 
visible. 
And we can add another object say, with 
an even higher temperature. 
let's say, 12,000 degrees. 
So, another doubling in this case, 
the spectrum again increases to the point 
where the sun's spectrum is negligible 
and the peak is now in the ultraviolet. 
So, we're seeing Wien's displacement to 
the left, hotter temperatures mean bluer 
light. 
We're also seeing the Stefan-Boltzmann 
law in action, 
hotter temperatures mean way, way, way 
more light. 
These are all important observations. 
Let's see what we can do with them. 
[SOUND] That was a long, video clip. 
There was a lot going on there. 
We got to go through two and a one-half 
centuries of physics. 
Remember, what we're doing is we're 
packing our toolkit so that we know what 
it is we need to address understanding 
astronomy. 
So, don't despair. 
rather than trying to summarize all the 
disparate things we talked about, let me 
do an example of an application to actual 
astronomy of what we learned about that 
might clarify some things. 
So, lets talk about the sun. 
We said that the sun radiates its heat. 
Let's see what all our various results 
tell us about solar radiation. 
So, we can measure the brightness of 
sunlight on Earth in watts per meter 
squared. 
How do you do that? 
Not put our a meters squared of detector 
and measure how much sunlight hits it. 
Put out a meter squared of something very 
dark that absorbs all the sunlight, 
measure how much energy that thing 
receives. 
And you'll find, the number is called the 
solar constant, and it is 1,361 watts per 
meter squared. 
So, a meter squared of sunlight will run 
a very small hair dryer, or light ten 
incandescent light bulbs. 
So, we know the intensity of solar 
radiation, in the vicinity of Earth. 
Now, we know how far the sun is. 
The sun is one astronomical unit or 150 
million kilometers away. 
And so, if we know how bright it looks 
and we know how far it is, 
we know that we can compute its 
luminosity. 
Remember, we had that B, the brightness, 
is the luminosity divided by the area of 
the big ball whose radius in this case, 
is the distance to the sun or one 
astronomical unit. 
And so, we can com, solve this we know 
the brightness, we measured it, we know 
the distance. 
We can write an expression for the 
luminosity and it's four pi times the 
distance to the sun squared times the 
brightness of the sun. 
And so, we put in the numbers. 
This is 4 pi times 1.5. 
I'm rounding. 
Times ten to the eleven meter squared, 
times 1361. 
And we evaluate the calculation and you 
find that the sun is a very bright light 
bulb, indeed. 
It has a luminosity of 3.8 times ten to 
the 26 watts. 
That's a lot of energy lost by the sun. 
Now, 
we can measure the radius of the sun 
since we know the distance. 
we can make a small angle calculation. 
We measure the angular size of the sun in 
the sky, and we find that the radius of 
the sun is 6.96 times ten to the eighth 
meter, 
that's about 700,000 kilometers. And from 
this, 
we can figure out something else. 
Because what we know now is that, think 
of the sun as a ball. 
Every square meter of the ball is 
radiating light to the outside, you count 
how many square meters there are on the 
surface of a ball. 
That would be 4 pi times the radius of 
the sun squared. 
If I multiply that by the flux, the 
amount of power in watts emitted by each 
square meter, this should equal L. Since 
I know the radius of the sun and the 
luminosity, the total amount of energy 
that's being emitted, I can figure out 
the flux that each 
square meter emits. 
Now, the lumina, the luminosity, as I 
said, is the area of the sun times the 
flux. 
And so, I could compute the flux. 
the nicest way to do this is to use a 
scaling relation, as usual. 
So, the scaling relation is going to be 
that 
I have that F, which is L over 4 pi times 
the radius of the sun squared. and I have 
that b is L over four pi times the 
distance to the sun squared. 
I can cancel everything around. 
Find that L is b times the distance to 
the sun divided by the radius of the sun 
squared. 
And this relates again, a flux to a flux 
through a dimensionless quantity. 
I recommend this method of computing and 
this is 150 million, this is 700,000. 
That's a big factor. 
Every square meter of the sun produces 
6.3 times ten to the seven watts, a 
square meter of sun produces 63 megawatts 
of light emitted out towards the 
universe. 
That's a large number, but we can go 
further. 
We have the flux and we know the 
Stefan-Boltzmann law, we know that the 
flux is also equal to sigma, T to the 
fourth. 
Since the sun emits approximately as a 
black body, it's dense enough. 
And so, since we know the flux, we can 
compute the temperature, 
and we can actually find the temperature 
of the part of the sun that we see. 
It's called the photosphere. 
It's somewhere outside on the surface of 
the sun. 
And, we find that the temperature is the 
fourth root of F divided by sigma, the 
temperature of the radiating surface of 
the sun of the photosphere is about 5800 
Kelvin. 
I can use Wien's Law because I know the 
temperature to figure out the wavelength 
of maximum emission for the sun. 
The wavelength at which the sun emits 
more light than anything else. 
I take Wien's constant, 0.0029 meters is 
the value of Wien's constant. 
I divide by the temperature of the sun, 
and I find that the sun produces more 
light than any other frequency at a 
wavelength of 503 nanometers. 
And if you look up the table, this is 
somewhere between the red and the blue, 
and indeed it is green. 
But Ronin, you tell me every 
kindergartner knows the sun is yellow. 
Yes, but not really. 
Every kindergartner knows the sun appears 
yellow. 
Why that is consistent with the maximum 
emission being green, we'll see in the 
next clip. 
In the meantime, go and catch your 
breath. 
We have gone through many, many different 
topics here. 
We have a whole grocery list of new ideas 
and new concepts to digest and to learn 
how to use. 
And we'll start applying those very soon.