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Summary
Core Theme
This content transitions from discussing stellar end-states to exploring galaxies, specifically focusing on our Milky Way. It delves into the historical discovery of other galaxies, the structure and scale of the Milky Way, and methods used to determine its central mass.
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All
right, guys. Let's go ahead and get
started. So, we've been talking about
stars, of course, the end states of the
stars, the white dwarf, neutron star,
black hole. But we also remember this
course is stars and galaxies. So, it's
now time to start talking about galaxies.
system is
galaxy. And if you go out in a rural
setting away from city lights and at
night, uh, low humidity, if you look up
basically overhead, you know, say
midnight, 1:00 a.m., you'll see a filmy
band of light, very faint, filmy band of
light overhead, and that's the Milky
Way. So,
rural
area. Let's do away from city
lights. You have to be away from city
lights. You won't see
it. It's so
sky. So, our solar system is in the the
Milky Way galaxy. And
then you could ask, well, how many
galaxies are there? And so there are
approximately 100 billion that's 10
Now, I want to kind of put this in
perspective. You know, that's today. We
know that today, but long ago, we
didn't we didn't even understand that
there was these things, galaxies and
that. And so we want to kind of revisit
the history of how it came to be that we
uncovered what galaxies
galaxies
are. And so we'll do a new bullet here.
Hubble.
in
Way. Okay. And then
so then Hubble did some amazing work and
photographs
of what we call
And he noticed in those photographs
M31. And we remember the seafoods are
those variable stars that have a
luminosity pulsation period relation.
And if we time out the pulsation period,
we can get a very accurate uh number on
the absolute magnitude of the
luminosity. And then by measuring the
amount of light we get here, we can then
very accurately determine how far away
that seafood is. That was the important
thing of the seafoods. So I notice sephids
sephids um
um in
in
inside of
M31. And I'll just say here
here
seafoods
have a
period pulsation period luminosity relation.
And because of
that, we can very accurately
accurately
Oh gosh. To the
uh see if it and if the see if it's
embedded in the object M31 then we know
uh how far away M31 is. Fate. So just to
remind you
uh out of the uh period luminosity
relation we're going to get our absolute
magnitude that's our big m and then
we're going to measure the amount of
light that we get from that seit. So we
can also so comma we
we
also know the light that reaches earth
m you know the apparent magnitude
apparent brightness and then if you know
those two you can get the distance
because we have our our distance
Put the big M in there. Put the little M
in there. And then I'll know the
distance to the seafood and then by
therefore know the distance to the
object known as
M31. And so what Hubble found out was
M31 was
was
Thus,
M31 was another galaxy. So, we have the
Milky Way galaxy, our own galaxy, and
then this object known as M31. Well,
it's a galaxy, too. So, thus M31 was
So we now recognize then that the
visible universe is much larger than we
thought because we just thought
everything was inside the Milky Way. And
I'm going to give you the data on the
Milky Way this size. But roughly from
one edge of the Milky Way to the other
edge is about a 100,000 light years. And
and that's large, but now we're talking
an order of 2 million light years.
So huge increase in the size of the universe.
universe.
So by the end of
Um, by the way, this
though. And you're going to find out
later on that there's some interaction
happening between our galaxy, the Milky
Way, and Andromeda that gives us some
additional information about what's
happening in the universe. We'll we'll
save that for later. So M31 is also
known as Andromeda. Okay. So this is the
great work done by Hubble and we're
going to visit revisit this in later on
a bit here. But now let's step back and
then start to talk about the Milky Way
galaxy, our galaxy. So let's do a Milky
um the Milky Way
galaxy and
uh is
a rotating there's a lot of stuff here. disc
shape and of course I'm being very
general here. We'll get to the details
later on. Rotating disc shape
collection of
of
matter, stars and
planets, other things you know
interstellar medium and and so forth.
uh this say collection of matter uh with
a spiral structure but again I'm kind
of we'll get into these details here shortly
um and from one edge so it's disc shape
so you know mostly two dimensional
object you know circular spiral
structure from if you look from overhead
but I'm unloading all these details, but
from one edge to the other, it's about
across, you know, to put that in
perspective, you have a flashlight at
one edge of the Milky Way and you turn
it on and shine it towards the other
side, that light beam is going to take a
100,000 years to traverse, you know, the
diameter basically, if you will, of the
of the Milky Way. So, it gives you a
center
is darn it is
nucleus, galactic bulge, nuclear bulge. This
This
same. They're interchangeable depending
on what
textbook you're looking at or
reading. And then our solar system is about
about
uh 27 and a
half. I don't know. Let's see. page this
is was page
page
three and this will be page
four. So our solar system let
me let me draw a picture here.
uh 275
275
about from
me on edge. If we look at it again, you
do. Okay. So from here to here is
years and then there's the center and
then our solar system. So there's 50. So
a little beyond that. So there there's
our sun and the our planets in orbit
around this our solar system. So from
here to here is about 275 27,500
lis and then depending on how you
measure this the
thickness is on the order of uh 2,000 light
years. Okay. And then so this this part
here is the galactic nucleus, the
nuclear bulge,
it. Just going back to these three terms
we had here. Galactic nucleus, nuclear
bulge, galactic bulge.
Okay. So if we're there and then we
recognize that the Milky Way is filled
with uh interstellar gas, interstellar
dust, then it obscures our view. And so
then how are we able to determine, you
know, how far away we are from the center?
center?
So let's talk about that.
dust. fly
clusters and the the globular
clusters orbit well above the
plane of the Milky Way. And then we're
we're able So, let's draw a
picture just so you can see. Oh, wait.
Let me let me say this.
this.
these and then we'll draw I'll draw you
this sentence and then we'll draw the
orbit above the
Galaxy. Yes. Yes. Yes. So, if I go back
and kind of draw a picture again, the on edge
picture.
Okay. Why are we having trouble? Okay.
So, there's the center. There's us.
Okay. But then there's these globular
clusters that are well out
out above
above
the plane and see. So we're able to
pinpoint. We have a very narrow band of
of interstellar medium that are we have
to pass through to see these. And then
we just need to get a few data points as
they move. And then from just those few
data points up here, we can predict the
entire orbital path. And we'll do that
for multiple globular clusters. And then
we'll average out the centers of all
those uh or uh orbits. And then that
pins down the center of the of the Milky
Way. Okay. So these are the globular
clusters. And I've kind
of mucked up this drawing. We have a
nice picture on the web page.
my my hand drawing here. Okay. And so
those motions, those orbital
motions of these globular clusters,
maybe I should here, maybe I should draw
one just
this chicken scratch. Okay. So I'm going
one.
Okay. And there it is. And there we are.
Okay. So line of
sight. And what we
do is we'll do look this, you know, for
six, seven, eight months. And what we
see is we we get all these data points
here and we can map out. And then you
don't need to follow it the entire path.
If you just because of the laws of grav
gravity Newton either Newton's laws or
Einstein with just a few data points you
can then predict the entire orbital path
of that globular cluster. So we'll do it
for that one then there'll be another
one and we'll do it for that and another
one and then the centers of all those
will pinpoint the center of the Milky
Way galaxy and that's how we're able
then to know how far away we are from
the from the galactic center. Okay. So
that gives us one piece of information.
Then the other thing if you go back and
look I said in back on my page three
look see spiral structure. So let's talk
about how we know that because you know
if you think about that that's weird
because we're embedded in the Milky Way
and yet if we stand if we imagine we get
in a spaceship and hover above the Milky
Way and look down we'd see a spiral
structure. And you're thinking, well,
how how can you know that when when we
ourselves are embedded in the in the
plane of the Milky Way and it's full of
the interstellar particles, dust, what
have you. How how does that work? And so
some interesting physics that helps us
there. And again, it's always the
quantum physics that that gives us the
answer or the little trick that we can
use. So let's do a new bullet here. We
want to discuss the spiral structure of
So we recognize that the universe is
full of hydrogen. Hydrogen is the
simplest of the atoms. A single proton
in the nucleus then orbited by a single
electron. Now both the proton electron
have what's called spin. Uh you can
think of it as like if you have a top
and you wrap a string around the top and
pull the string the top spins. Okay. So
our subatomic particles have this same
uh uh physical
attribute spin. Uh the technical word is
angular momentum but we call it spin.
And it turns out now in an
atom the spins are aligned either two
ways. So you have a spin axis for the
proton, you have a spin axis for the
electron. And in the atom, in the
hydrogen atom, they can line up two
ways. They can line up where both those
spin axises are parallel
or if we flip the electron the other way,
way,
antiparallel. So it's that's all that's
the only way it comes. Either the spin
axis will be
parallel or they'll be antiparallel.
Okay, parallel or antiparallel. Now,
there's an energy difference between the
two arrangements. The parallel structure
has slightly more energy when the spins
are aligned than the antiparallel. So if
you're in if the hydrogen atom is in the
parallel spin state and the electron
flips over to the antiparallel state,
it'll kick out a photon and the energy
of that photon is exactly the energy
difference between the parallel state
and the antiparallel state by so that we
satisfy conservation of energy and okay
so I'm going to write down what I said
just so you have it in your notes. So
tells
the
state for
for
state. Antip parallel
parallel spin
state. So the parallel has higher energy
than the antip parallel. So the
the reaction picture looks like this. So
we'll have I'll So we'll do here's the
proton and here's the electron. We're
going to put them in the parallel spin
state. So both the spin vectors are
pointing up and this I made this one
bigger. It's the
proton. It doesn't really matter. Technically
Technically
that's technically the electron is
bigger but oh I don't even want to go there
there
yet. From a mass standpoint no there's a
thousand factor a thousand between these
but from a size
perspective the electron is larger than
the proton guys that's a whole another
lecture. So okay so this is the parallel
spin state because both the spin
vectors are pointing up. So right here right
right
parallel and then what'll happen is on
occasion what'll happen that electron spin
spin
vector will flip.
So, and by virtue of conservation of
energy because this is a
electron and this is the antiparallel.
it's lower energy and so it a photon is kicked
out particle of
light and the energy of that photon
added to the energy of the antiparallel
state is exactly equal to the energy of
the parallel so right here below this
antiparallel guys remember this is
hydrogen the electron and so write
hydrogen up
hydrogen atom. This is a hydrogen atom.
Okay? And then that's a photon. Now,
because we know the energy of that
photon, we automatically know its
wavelength. So,
wavelength all this to just get to this
one important point. The wavelength of
is okay for our letters Greek letter
lambda 21 cm. So from one crest to the
frequency. It's not one you can see.
It's not infrared. It's in the radio
frequency. So we use radio telescopes
and with the radio
telescopes because there'll be some
motion involved then there'll be a
Doppler shift on that that
uh spin flip radiation. Okay. Yeah. So
this is called this this is called
and it's in the radio band. So, we use radio
telescopes. Those can detect radio
signals. And then what we'll see is
because of the spiral structure, we're
going to be able to we'll see Doppler
shifts at various locations. As we scan through
through
the plane of the um Milky Way, we'll see
Doppler shifts. And then we take all
that data, load it into computer, and
then it'll project the profile, the mass
distribution of the matter in the Milky
Way, and then we we see that spiral
structure. So we use radio telescopes And
the Doppler
shift of
of
cm
We can
determine these are drifting off on me.
determine
the Milky Way.
So generically what if I take that data
and produce kind of a handdrawing an overhead
overhead
image basically we have the
uh galactic
nucleus nuclear bulge and then we have
these spiral like structures that come
off and
wrap and so from overhead this is the
sort of structure that we're talking
now I want to talk about so this is the
nuclear the
galactic nucleus nuclear bulge whatever
so let's I just want to say something
galactic nucleus. So, on
average, we can make a fairly accurate
statement on the number of stars that
are in the Milky Way. And that number is
also 10 the 11th. Now, 10 the 9th is a
billion. You get another factor too
that's 100. So, 100 billion. So there are
nucleus. Now remember, on average, if
you have a star, there'll be some
planets in orbit around that. That's
what a solar system is. So you're going
to have bunch of the stars here, planets
in orbit around them, bunch of solar
systems. So then if we kind of think
about if we if we're on a planet that's
in the galactic nucleus, what's the
situation? And it turns out that it's
kind of it's very different than what we
experience here. There's not a lot of
starlight in our nighttime sky. Uh but
that's not that would not be the case in
night. And the reason is is because you
have such a concentration of stars
there. You have so much starlight. Now
remember, night
is if you have a planet, it's an orbit
around a star. the planet itself
rotates. So when part of the planet is
on the back side away from the sun, then
the that surface of that planet that's
on the dark side, that's the nighttime.
That's what night is. Of course, then
the planet rotates and then oh, it's in
the morning and then noon and then
evening. Okay. But on the dark side of a
planet that's in the galactic um
nucleus, because there's so many stars
in the nighttime sky and they give off
so much light, you don't get that
experience of a dark night. And I can
just give you the numbers. Uh planet in
the galactic nucleus would never
experience a dark night. During
night,
about 200 full
So, you know, on a night you go out on a
full moon and a full moon kind of it
lights up the nighttime sky. Take that
number, multiply by 200, and that's the
darkest it's ever going to be for a
planet that's embedded in the in the uh
galactic nucleus. So, 200 full moons
worth of light.
Now, uh, now we want to, uh, kind of
we're still focusing on
the the galactic
nucleus, but we now want to kind of zero
in. There's a there's an issue. We'll
start that today and then the next
lecture we'll pick up and get into the
real details. So, we'll do a bullet
here that uh, we will call the
the [Applause]
[Applause] mass
mass in
the galactic
nucleus. So what we notice is there's a
very large concentration of matter i.e.
mass in the center, the exact center of
the Milky Way galaxy. And the way that
we do it is the following. Uh if we look
at the hydrogen gas
velocities that are in orbit around the
galactic center and using Kepler's third
law, we can fairly accurately make a
prediction on the amount of mass that's
in the center. So, we're going
the hydrogen
gas velocities. Remember, gravity pulls
things in. Any object that has some
tangential motion generates a
centrifugal force that repulses gravity
and that's what sets up a stable orbit.
Um, and if that object is not traveling
fast enough, then it'll get in closer.
If the object has no tangential
velocity, going to fall right into the
center. I mean, the moon, you think of
the Earth and the Moon system. The moon
is in circular orbit around the Earth.
If the moon's tangential velocity were
to go to zero, moon would come right in
and crash into the earth due to the
earth's gravity pulls on the moon. Okay.
near the
center using
using
K3L. You're gone. What's K3L? Kepler law.
We'll write it down. I'll explain
law.
We can um
estimate the amount of matter and that
you know the measuring of that is the
mass you know in kilograms the amount of
matter. So, I'll just put in here in parentheses
parentheses
center. Okay? And we're going to get to
that number. And then we get that
number, we'll end this. And then next
time we'll pick it up. There's another
important thing that comes out of that.
So, let me draw a picture
here to help you kind of we have uh two
bodies that are gravitationally bound
and one has more mass than the other.
So, it's mo that one that has more more
mass is basically located at the center
of mass point and then the other one
that doesn't have much mass basically is
in an orbit around the center. So, an
example would be and it's you know
applies to any two bodies that are
gravitational. Let's just look at the
moon. So here's the
earth and then here's the moon. Now
earth exerts a gravitational force on
that moon and it would pull the moon
into the earth but the moon also has a tangential
tangential
velocity and so by the uh laws of uh
Newton or the laws of Kepler or even
Einstein we can there's a relation here.
So the amount of gravity that earth
exerts on the moon is given well if I go
to Newton it's a very simple law. So the
gravitational pole that the earth exerts
on the moon looks like this. Let the
mass of the earth be big m. Let the mass
of the moon be little m. Okay. So it's
this the gravitational force that the
earth exerts on the moon. Big
g mass of the
earth mass of the
moon divided by the distance between
their center squared. So r squared. So r
That's Newton's law of gravity.
Gravitational constant. Mass of the
Earth, mass of the moon divided by the
distance between their two centers
squared. That's okay. So that's the
force of gravity. And that's the only
force that's acting on the
moon. So by the Newton's second law of
motion, some of the forces must equal
the mass times acceleration. We'll write
that one down.
So m * a. Now the m of course is the
thing that's the moving that's the moon.
So that's why I use little m and the a
then is the the acceleration. Now it
travels in a circular path. So the
acceleration is what we call the
centrial acceleration which is the velocity
squared divided by
the orbit radius.
So we can write this as m
v^2 over
r. Okay. So I'm going to relate the far
left to the far
right. Actually let's put some so this is
gravity and this is is equal to ma.
That's Newton's second law. So these two
are both Newton's second law. Sum of the
All right. Now, you see right away I
Okay, so next line. I don't want
to do all these cancellations in my
head. Then you'll say, "What's going on?
You're confusing us." All right, let's
write it down here. What we got? There's
what we
got. Okay. So, all right. So, that's the
mass of the moon. Mass the moon. So,
that goes away. And then I got an R
squared there and an R there. So we're
going to kill a power of that. Now what
I want is the mass of the Earth. We
already know the mass, but you'll see
where I'm going with
this. You we're going to generate the
formula and so that we can show what's
happening. All right. So I move this R
up there and then the big G I'll move
down. And so the mass of the
Earth is given by the following. So, r
r
v^2 / the gravitational constant.
constant.
Okay, so that's one
form of Kepler's third law, Newton's
laws of motion,
motion,
Einstein's general relativity,
Einstein's gravity. So m gives us the
earth. G is the gravitational
constant. I'll just say gravity
constant. You've had it before. 6.67 *
11. And r is the distance from the earth
to the moon. But it's measured not from
their surfaces but from their centers.
uh to the center of the [Music]
[Music]
moon. And then v is then the speed with
the moon. the orbital velocity of the
moon. So, I'll just say speed of the
moving? Now, here's the here's the
point. If you can look at a structure
and you notice that there's something
that's in circular orbit around the
center of the you know the structure
you're looking at, if you can measure
how far away that object is from the
center, that's the radius, the orbit
radius. distance from the center there
is the center mean also known as the orbit
orbit
radius but I wanted to spell it out so
confusion there it is r remember this
thing is in a circular
orbit around the earth the moon r is
orbit radius so if you can measure that
and then if you can also measure how
fast the moon is traveling with those
two pieces of information then you can
determine the mass of the earth. That's
how we weigh the earth. This is how we
weigh the earth. This is how we know the
mass of the earth. We examine the motion
of the moon or any for that matter any
satellite. All you need to know is how
far away is the satellite, the moon,
whatever that object is from the center
of the earth and then what's the
velocity of that object and put these
numbers in and then gives you the mass
of the earth. But this this formula has
universality in that it can be applied
to any system where you have a central
gravitating body and you have something
in orbit around that body. Using this
you can always get the mass of that
central gravitating
body. And see what we started out on
this was we wanted to find the amount of
matter the mass in the galactic nucleus.
So what we do is we
analyze the hydrogen gas velocities and
we know how far away they are from the
center and we can put those two numbers
in there. And
so using just about done here using m is
equal to r v^2 over g
both
the orbit [Music]
[Music] radius
radius
and speed technical word, you know, velocity
velocity for
the hydrogen
hydrogen
We can [Music]
galaxy. And here's the number. And I'm
going to quote it this way. So the M at the
center is or I'm going to write it this way
way
2.5* 10 6 multiplied by the mass of our
sun. So two and a half million times the
mass of our sun is
the mass at the exact center of the
Milky Way
galaxy. 2 and a half
million times the mass of our sun in the
center of the Milky Way galaxy. All
right. So folks, we'll end there and
then we'll next time we'll pick this up
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