So, here's an instance where the history 
is so compelling, that we have to follow 
it. 
So, the image here is of course the great 
spiral Andromeda. 
Over the course of the centuries 
astronomers had classified stars and 
they'd realized found planetary nebulae, 
and they knew about gaseous nebulae like 
the Orion Nebula. 
And then, there were these spiral nebulae 
of which Andromeda is a spectacular 
example. 
This thing is almost 3 degrees across in 
the sky. 
Remember, the moon is a 1/2 degree 
across, so this is huge, but very, very 
faint. 
You need a big telescope and to get an 
image like this, 
lots of light collection and processing. 
But, spectacular and beautiful though it 
were, though it is, it was not at all 
clear to anybody what it is and the, what 
this comes down to is the question that 
has been hounding us throughout this 
class, 
how far? If you know how far, you can use 
the small angle, its approximation to 
figure out how big. 
But how far is this thing? How do you 
measure the distance? And this proved to 
be a big question in early days of the 
twentieth century. 
So in 1920 in fact, there was a public 
debate conducted between two of the 
leading astronomers of the day, Harlow 
Shapley and Curtis. 
And Shapley made the, the, the argument 
was over the following question. 
These spiral nebulae, like Andromeda, are 
they gaseous nebulae within the Milky Way 
or are they Kant's original island 
universes? Kant had this reasoning that 
these spiral nebulae should be worlds, 
universes on their own just like the 
Milky Way, because there should be a 
hierarchy of structure as I understand 
it. 
so Shapley, in fact, argued that there is 
no way, this is a scientific argument, 
and Shapley was arguing that these spiral 
nebulae are gas clouds in the Milky Way. 
And his arguments were basically this if 
you take M31 to be a 100 kiloparsecs in 
radius, because that was the radius that 
Shapley had found for the radius of of 
the Milky Way, and he knew one galaxy he 
said, okay, if you're going to make this 
another galaxy, then it's probably going 
to be like the Milky Way. 
If you give Andromeda a radius of 100 
kiloparsecs, that puts it two mega 
parsecs away, six and, more than 6 
million light years away. 
If Andromeda were to be that far we've 
already seen that there are stars 
embedded in these nubulae and they had 
tracked most interestingly novae. 
So there were, presumably, we now know 
white dwarfs and white dwarfs with binary 
partners, there were novae. 
Going on in these stars and the 
luminosity of a nova is not really 
constant enough to make it a standard 
candle, 
but the maximum luminosity, the order of 
magnitude of luminosity of a novae is 
known. 
And what Shapley noted is that if you 
take M31 and put it 2 megaparsec away, 
then you find that its novae must be much 
more luminous than those in the Milky 
Way. 
This is unlikely, it's much more 
reasonable to put it 100 kiloparsec away 
on the other side of the Milky Way where 
it can safely reside. 
And he also thought that there were 
measurements of the rate of rotation of 
another spiral and 101. And, again, if 
your input, assume that in 101 has the 
size of of the Milky Way, then you find 
that it is rotating too fast to be bound. 
Curtis had reasonable arguments on the 
other side. 
His argument was that these spiral 
nebulae are indeed island universes far 
away and outside the Milky Way. 
And, again he was referring to scientific 
evidence. 
He was saying, let us assume that the 
novae M31 are the same novae we find in 
the Milky Way. 
We know the average luminosity of a nova. 
This puts M31 at least a 150 kiloparsec 
away. 
if you put M31 100 kiloparsec, 150 
kiloparsec away, notice a lot closer, 
almost by a factor of ten, than Shapley 
did then, its size is about 7.5 
kiloparsec, which is quite reasonable. 
This is about the size of Kapteyn's 
measurement for the Milky Way. 
Remember Shapley's measurement of the 100 
kiloparsec Milky Way had not yet been 
accepted. 
It has never been accepted, it was wrong 
by a factor of two. 
And there was this alternative small 
Milky Way, so it basically comes down to 
what is the size of the Milky Way will 
tell us whether Andromeda is in it or out 
of it. 
also, he noted, that we measure radial 
velocities for stars in these spirals. 
but we measure very little proper motion 
that suggests that they're very far away, 
unless they're, these objects are 
preferentially moving radially. 
Something has a large radial velocity, we 
expect it to have a large tangential 
velocity, remembering that the tangential 
velocity is related to proper motion by v 
equals v tangential is 4.74 times mu 
times D. 
It measure a large v and a very small mu 
you conclude that you have a large D. 
This is how Curtis sought to reconcile 
these measurements. 
Both of them had valid arguments, near 
carried the day. 
All they did was illuminated the issue. 
the issue was actually resolved 
conclusively and beautifully by Hubble in 
1923. 
So we have here in fact, the plate on 
which Hubble made his discovery. 
So Hubble was investigating photographic 
plates taken of 
M31, the Andromeda spiral nebula, and in 
this region of M31, this is the region 
near the center is what he was taking 
plates of and he found a few novae. 
He was marking off novae, because 
measuring, as we said, the luminosity of 
novae was one way to estimate the 
distance. 
How do you know that a star is a nova? 
Well, it's a nova if it appears as a star 
in today's plate but was not there on the 
plate you took a week ago. 
So you compare new plates to old plates, 
and the new stars that have popped up are 
novae and there is a date on when he, he 
took the measurement in October of 1923. 
And then he went back and he realized 
that one of the novae he had marked, the 
one in the upper right-hand corner, 
actually was present in older plates and 
then was absent in yet older plates, but 
was present and he had found a variable 
star. 
And, this was a very exciting discovery, 
because unlike novae for which you only 
know the maximum luminosity. 
For variable stars, we have a period 
luminosity relationship, we can compute 
the luminosity of this star. 
Since we can measure its brightness, we 
can use that to find the distance and 
Hubble was clearly excited. You can see 
that he vigorously crossed out the n and 
with a big exclamation mark, marked on 
the plate, this is a variable, that's the 
VAR up there. 
He knew he was about to measure the size 
to Andromeda, he made the calculation and 
the period luminosity relations showed it 
that Andromeda was 285 kiloparsec away. 
That is too big to fit, even in Shapley's 
large hundred kiloparsec galaxy. 
Andromeda is a separate galaxy. 
Now, the distance measurement was wrong. 
We'll discuss that in a second, but you 
have this pause for a minute and 
appreciate the sort of Copernican 
magnitude of that varied why it was that 
Hubble was so excited. 
He had just realized that the universe is 
not one galaxy but two, and of course, 
once we have two, presumably millions, 
and as we know today, hundreds of 
billions of galaxies. 
And so he had increase the size of the 
universe exponentially with this one 
variable star. 
A very exciting discovery following its 
trail always gives me goosebumps. 
Just looking at that plate, I think. 
Imagine Hubble's excitement. 
So, I said his distance was wrong and 
this is a good exercise in following how 
creative and how exacting the astronomers 
had to be to figure out this 
three-dimensional structure that we take 
for granted because we read it in books. 
So remember, that the period-luminosity 
relation was discovered by Henrietta 
Leavitt, in Large Magellanic Cloud, 
Cepheids. 
there are Cepheid, these are Population I 
classical Cepheids in the Large 
Magellanic Cloud. 
Now, she did not know the distance of a 
Large Magellanic Cloud exactly, what she 
discovered was a period brightness 
relation. 
and she knew they were all about the same 
distance, because they're all in the 
Magellanic Cloud. 
So she knew she found a period luminosity 
relation, 
but she couldn't calibrate it. She 
couldn't know exactly what luminosity 
corresponded to what period only that 
twice the period corresponded to some 
factor times the luminosity. 
Now, Hertzsprung and Shapley both 
sequentially calibrated Leavitt's 
relationship using Cepheids in the solar 
neighborhood to which they knew the 
distance from parallax measurements. 
What they neglected was that these were 
Cepheids in the galactic plane and 
extinction had made them appear dimmer by 
a factor of four, so there was a 75% 
extinction to these Cepheids. 
They thought they were four times dimmer 
than they really were therefore, their 
period-luminosity relation was completely 
off. 
In, now, Hubble was applying this 
measurement to a Cepheid in Andromeda, 
where he's looking outside of the plane 
of the galaxy. 
His luminosity is off by a factor of 
four, because, you remember that our 
calculation of distance is proportional 
to the square root of the luminosity, 
because brightness decays looks like L / 
D^2. 
The fact that he was fourth, a factor of 
four off in the luminosity of this 
Cepheid, meant he was approximately a 
factor a two off. 
In, the distance in fact, the factor he 
was off by, was 2.7. 
Andromeda is farther then he measured by 
a factor of about 2.7. 
It's not it's, it's about 2.5 million 
light years away from here. 
Shapley on the other hand, had been 
measuring the size of the Milky Way, by 
measuring distances to globular cluster 
variables, but globular cluster variables 
are a population too. 
Those are W Virginis stars not Cepheids. 
And, at a given period, a W Virginis star 
is about four times less luminous than 
the Cepheid with the same period. 
Remember, we showed those two graphs of 
Population I and Population II Cepheids. 
And so Shapley, unknowingly, was actually 
using the right period luminosity 
relation, 
but, remember, he was missing extinction 
and so he overestimated the distances. 
And, this lead for awhile to a great 
puzzle, now that we had the distance to 
Andromeda, and we could therefore 
estimate its size by making a small angle 
approximation. 
You now know the distance, you have the 
angle, three degrees, figure out the size 
of Andromeda and figure out soon the 
sizes of other galaxies, the Milky Way 
was larger than all the galaxies they 
saw. 
This didn't seem reasonable. 
And 
the diffuse extinction that Trumpler 
discovered in 30s helped allay some of 
Shapley's correct, some of Shapley's 
errors, and the distinction between 
Population I and Population II Cepheids 
was not clear until 1952 when Bodey 
realized that there two populations of 
Cepheids and two different period 
luminosity relations. 
Now, today in the 90s we manage to 
calibrate Cepheid periods directly from 
parallax measurements to distant Cepheids 
parallax measurements give us a correct 
distance. 
we know enough about extinction in the 
Milky Way to correct them. 
And you can use Cepheid variables to 
measure distances out to as large as 30 
million, megaparsec. 
So that's 10 million light years sorry, 
that's almost a 100 million light years 
away that we can use Cepheids as distance 
markers, because we can still measure 
their periods, 
that's the distance record. 
Of course it's still you, that gives you 
a luminosity to compare to the brightness 
you see. 
You have to figure out something about 
extinction in the 100 million light years 
between you and the star, but we have a 
better understanding of extinction at 
least in the Milky Way then we had 
before. 
And so we have Cepheids more variable, 
relevant, we have a more reliable 
distance scale. 
However, this gives you again an 
appreciation for how difficult it is to 
actually build a three-dimensional 
universe out of that dark sky above us. 
Now, once Hubble discovers one galaxy is 
outside, 
he immediately goes on and measures the 
distances to many others, because you can 
find Cepheid variables now that you know 
what you're looking for and now you can 
just look at the nebulae. 
And Hubble comes up with a classification 
scheme, 
another contribution of, of Hubble's is 
the classification scheme for galaxies by 
their apparent shape and it has this 
tuning fork shape. 
So, to the left are elliptical galaxies 
in order of increasing electricity, 
so some galaxies are ellipsoids and 
Hubble is measuring how eccentric the 
ellipsoid looks to us. 
Of course, this is a crazy 
classification, because it tells you 
nothing about a galaxy because if you 
take a football and look at it head on, 
you can't distinguish it from a sphere. 
And so, this the E kind of classification 
tells you about the shape of the galaxy 
as it appears to us, but not much about 
the actual shape of galaxy. 
And then, there's this branching off into 
spirals with sort of increasingly 
intricate spiral arm structure on the one 
hand, 
and barred spirals on the other hand. And 
so, the Milky Way we now know recently is 
a barred spiral, the Milky Way is an SBb 
type barred spiral. 
Andromeda, which has no bar, is an Sb 
spiral galaxy, 
later other kinds of sort of less 
organized spirals were added by others 
and a class for the degree of coherence 
of the spiral arms was introduced, so, 
and give it, it can give a more precise 
classification. 
And we'll talk about the properties of 
various kinds of galaxies as we go on now 
that we know they exist.