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## Cosmology and astronomy

### Course: Cosmology and astronomy > Unit 1

Lesson 4: Big bang and expansion of the universe- Big bang introduction
- Radius of observable universe
- Radius of observable universe (correction)
- Red shift
- Cosmic background radiation
- Cosmic background radiation 2
- Hubble's law
- A universe smaller than the observable
- How can the universe be infinite if it started expanding 13.8 billion years ago?

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# Hubble's law

Hubble's Law. Created by Sal Khan.

## Want to join the conversation?

- As the universe is expanding/stretching infinitely, why aren't stars and other cosmic bodies also being stretched. Going with the balloon analogy, when you draw points on a balloon, they get farther apart when it's inflated, but each individual point gets larger. Does this happen?(66 votes)
- It is hard to explain it using analogies, the best way is through the actual mathematical equations. Here's the real explanation: http://arxiv.org/abs/astro-ph/0310808

In the "raisin bread model" one imagines a loaf of raisin bread expanding in the oven. The loaf (space) expands as a whole, but the raisins (gravitationally bound objects) do not expand; they merely grow farther away from each other. That's the closest image we can give you as of now, all of the analogies have the conceptual problem of requiring an outside force acting on the "space" at all times to make it expand. Unlike real cosmological matter, sheets of rubber, ballons, and loaves of bread are bound together electromagnetically and will not continue to expand on their own after an initial tug.(86 votes)

- Isn't the Andromeda galaxy moving closer to us? So would that not mean that its velocity according to Hubble's law is slowing down?(23 votes)
- Andromeda is indeed moving closer to us (as evidenced by the fact that its spectrum exhibits a "blueshift"). Given this information, Hubble's Law would seemingly give a nonsense answer when applied to Andromeda - implying that Andromeda is at a "negative distance" away from us! So what's going on?

The issue is that Hubble's law is only applicable to galaxies far enough away* for the expansion of the Universe to be the dominant source of the apparent motion of that galaxy with respect to us.

Galaxies close to us (within our Local Group of about 50 galaxies, of which the Milky Way and Andromeda are the largest) are close enough to be gravitationally bound to one another, and are moving around within the local group with respect to one another, unaffected by the "Hubble flow" (apparent motion of galaxies due to the expansion of the Universe).

In short, Andromeda is too close to us for Hubble's Law to be applicable, and we are simply observing it's normal motion through space.

* "Far enough" is approximately 10 megaparsecs, or 30 million light years away.(52 votes)

- Fascinating stuff. the observable universe is 4.2 Gpc in radius. so the relative velocity of expansion at this distance would be 4200*70.6 = ~297000km/s, that's almost the speed of light!

If we were to observe the objects little further than that would they just blink out of existence when reaching the apparent speed of light? Or is that the reason that we cant observe anything further than that now?(29 votes)- Actually, according to wikipedia, the actual estimate for the radius of the observable universe is 14000 Mpc (or 14 Gpc), so the velocity of the expansion at this distance would be 14000 * 70.6 = 988,400 Km/s! Way beyond the light speed limit!

I've tried to do some math (but i'm not sure about it): if we wanted to know the distance that an object in space must have in order to move away at the speed of light (rounded at 300,000 km/s), we should do:

300,000 / 70.6 = 4,249,291,784 parsec (4.29 Gpc)-> approximately 14 billion light years

So the objects that are now 14 billion light years away from us are receding at the speed of light, and in time they will surpass that limit!

Anyway they won't "blink out of existence" because it's the space between us and them that is expanding at that velocity, not the object themselves (not that reaching the speed of light makes yourself disappear or something like that). What will happen is that the light that they will emit will never reaches us and so we will never be able to see them, anymore or at all.

In fact this is what will happen in the very distant future: if the earth were still around in some thousands of billions of years (and it will not), people on it would not be able to see any galaxies out there, the universe will just look as if our galaxy were the only thing in it

Hope i've been helpful : )(30 votes)

- Would the Universe continue expanding forever or will it stop some time in the future? Also, why is it expanding faster during some parts of it history and slower at other parts?(4 votes)
- We don't know whether the universe would keep expanding or not. But we do have a few theories to it. The first one would be where universe just keeps expanding and gravity wouldn't be able to stop it (the 'Big Freeze'). The second one is where the universe would stop expanding due to gravity restricting it, and the universe would end by collapsing on itself (we call this 'end' the 'Big Crunch'). The third is that the universe would accelerate while expanding (due to dark energy), so the universe will continue expanding faster and faster until atoms get torn apart, and the universe will end in a mightier explosion (as how we perceive relative to the big crunch) called the 'Big Rip'. As for your second question, I didn't understand it so well, what do you mean by 'why is it expanding in some places faster than others'?(15 votes)

- I tried to post this question yesterday.

Because a photon is traveling at the speed of light no matter from what object you are viewing it from and no matter which direction and how fast it is going it appears the same to everyone.

Therefore it seems that for the red shift to happen photons/energy must be imbedded in space to cause the photon to be stretched with the expansion of space.

How can I set up the equation to show the slowing down of the red shift over time and therefore determine the slowing down of the expansion of space over time.

How can I set up the equation to show the loss of energy in the photons over time as the longer wavelengths have less energy?

How can I set up the equation to correlate the loss of energy of the electromagnetic spectrum in space over time with the slowing down of the expansion of space over time.

If this has already been done, where can I find the equations.

If this has not been done can you help me do it or can you set up a work group in Khan Academy to help me do it.?

Thank you for your time.(8 votes)- KaiChiu1947

I realize that this question was asked over two years ago, but I may have found something to help you out. Firstly, you are right about light traveling the same speed regardless of which direction it is traveling in, or being perceived from. The photons themselves, however, do not "stretch" out with space. As I am sure you are aware, light itself can be thought of as a wave, as a luminescent object moves farther and farther from the point from which you are viewing it, the light continues to shine, the waves simply increase in length. This is exactly why more distant objects appear to inch closer to the "red" side of the electromagnetic spectrum over time. The actual waves are composed of photons that do not change in proportion, they simply grow farther and farther away from each other. It is important to note that despite the elongation of light waves, light itself continues to move at light speed.

Secondly, even if there was a certain energy "embedded" into the fabric of space, it wouldn't affect the actual movement of light through space. The expansion of space simply places more, (or less) distance between two or more bodies between which that light must travel to be visible from the others.

To properly set up an equation representing the speed at which light moves about in the electromagnetic spectrum, you would need to consider a particular object. Consider the deceleration or acceleration of the shift in light, and remember that the light itself does not slow down, the distance between a luminescent object and the observer changes.

If you are considering the loss of energy over time, you need to consider, once again, that there is very little change actually occurring regarding the photon as a singular particle, the distance it travels is really what determines such things as its detectability.

With regards to the actual rate of expansion, remember that the distance light must travel between two particles does not numerically determine the rate at which the volume of the Universe grows.

I hope this helps.(4 votes)

- Is there an observable center of the universe? If everything is expanding away from everything, is there a singularity origin from which it is expanding?(10 votes)
- We are at the center of the observable universe.(0 votes)

- How did scientist found the value of hubble's constant?(3 votes)
- So if I shined a flashlight today, the distance light would be away from me in a year is more than a light-year because of expansion. How much farther would the light be?(3 votes)
- Expansion is not uniform in speed or acceleration; what I mean is that the expansion between me and my computer is so infinitely small, while the expansion between our galaxy and one 15 billion light years away is tremendous. This is due to the fact that as you get farther away, you expand faster. In regards to you question, it would only be one light year away from where you're viewing, because the light has been traveling one year. This, actually, is not a very wide margin for expansion to take over, thus, it would be close to 1 light year.(2 votes)

- I have a question about the velocity of the expansion of the universe:

If the velocity of the expansion is getting higher and higher proportionally to the distance from earth, what happens if this velocity reaches speed of light? Becuase, being proportional to the distance from earth, in some place of the universe, the velocity would have to reach speed of ligth or - presumably - surpass it.(3 votes)- There is not a single velocity of expansion. The recession speed of one object from another depends on the distance between them, because space itself is expanding. If there is more space between two objects, then those objects move apart faster. The expansion rate is about 70 km/s per megaparsec of space between two objects. This means that very distant objects are indeed receding from one another at speeds far in excess of the speed of light. This is not a violation of the the theory of relativity because relativity does not place limits on the expansion of space itself, just on the speed at which objects might be measured to move through space.(3 votes)

- so, what is causing the expansion of the universe? is it the inertia from the Big Bang? If so, then why is it speeding up, wouldn't gravity slow it down?(3 votes)
- We don't know why it's speeding up. That's one of the biggest questions in cosmology at the moment. We've given the name "dark energy" to whatever it is, but we don't know anything about it. The discovery of the acceleration was a huge surprise(3 votes)

## Video transcript

Over many videos now,
we've been talking about how every interstellar
object is moving away from Earth. And we've also been talking
about how the further something is away from Earth,
the faster it's moving. What I want to do
in this video is to put a little bit
of numbers behind it, or even better conceptualize
what we've been talking about. So one way to think about it
is that, if at an early stage in the universe, I were
to pick some points. So that's one point, another
point, another point, another point. Let me just pick nine points
so that I have a proper grid. So this at an early
stage in the universe. If we fast forward a
few billion years-- and I'm clearly not drawing it
to scale-- all of these points have all moved away
from each other. So this point is over
here-- actually, let me draw another column,
just to make it clear. So if we fast forward
a few billion years, the universe has expanded. And so everything has
moved away from everything. And let me color
code it a little bit. Let me make this point magenta. So this point, the
magenta point is now here. This green point has now moved
away from the magenta point. And now this blue point
has now moved away from the magenta point
in that direction. And we could keep going. This yellow point is
maybe over here now. I think you get
the general idea. And I'll just draw the
other yellow points. So they've all moved
away from each other. So there's no center here. Everything is just expanding
away from things next to it. And what you can see here is not
only did this thing expand away from this, but this
thing expanded away from this even further. Because it had this expansion,
plus this expansion. Or another way to
think about it is, the apparent velocity with
which something is expanding is going to be proportional
to how far it is. Because every point in between
is also expanding away. And just to review a little
bit of the visualization of this-- one way
to think of this, if you think of the universe
as an infinite flat sheet. You can imagine that
we're just taking a sheet of, I don't
know, some type of sheet of stretchy material and
just stretching it out. We're just stretching it out. That's if we kind of imagine
a more infinite universe that just goes off in
every direction. We're just stretching
that infinite sheet out. So it has no boundaries, but
we're still stretching it out. Another way to visualize it--
and this what we did earlier on-- Is you can imagine that
the universe is the three dimensional surface of a
four dimensional sphere. Or the three dimensional
surface of a hyper-sphere. So at an early stage
in the universe, the sphere looked like this. And these points here--
that magenta point is right over here. The green point is
right over there. Then we add the
blue point up here. And then let me just draw the
rest of the yellow points. And the yellow points are here. They're all on the
surface of this sphere. Obviously I'm only dealing
with two dimensions right now and it's nearly impossible,
or maybe impossible, to imagine a three
dimensional surface of a four dimensional sphere. But the analogy holds. If this is a
surface the balloon, or the surface of a
bubble, if the bubble were to expand over a few
billion years-- and once again, not drawn to scale. So now we have a
bigger bubble here. This part of the surface
is all going to expand. So once again, you
have your magenta. You have your blue dot. You have your green
dot right over here. And then let me just
draw the rest in yellow. So they will have all
expanded away from each other on the surface of this sphere. And just to make it clear
that this is a sphere, let me draw some contour lines. So this is a contour line. Just to make it
clear that we are on the surface of
an actual sphere. Now with that out of
the way, let's think about what is the apparent
velocity with which things are moving away? And remember, we're going have
to say, not only how far things are moving away, but we're going
to say how far they are moving away from-- if the
observer is us-- depending on how far
they already are. So what we're going
to do-- we could say is-- let me write this down. All objects moving
away from each other. And the apparent
relative velocity is proportional to distance. And what I've just
written down here-- and this is why
I wrote it down-- this is a rephrasing of,
essentially, Hubble's Law. And he came up with
this by just observing that when he looks-- especially
the further out he looks, the more redshifted objects are. And not only were they
moving faster and faster away from Earth, but they seem to
be moving faster and faster away from each other. So this is just a
restating of Hubble's Law. Or another way to say
it is, from any point, let's say from the
earth, the velocity that something
appears to be moving is going to be some
constant times the distance that it is away
from the observer. In this case, we
are the observer. And we put this little
zero-- so this H here is called Hubble's Constant. And it's a very
non-constant constant. Because this constant
will change depending on where we are in the
evolution of the universe. So we put this little zero
here, this little sub 0 right over here, to show that this
is Hubble's Constant right now. And when we talk
about distance, we're talking about the proper
distance right now. And this has to
be very important because that proper
distance is constantly changing as the
universe expands. So the now will
actually change slightly from the beginning of this
video to the end of this video. But we could roughly say in kind
of our current period of time. And when we say
proper distance, we're talking about if you
actually had rulers. And if you were to just lay
them down instantaneously-- obviously we can't do
something like that. But we can imagine doing
something like that. So that's what we're
talking about it. So just to give a sense of,
or do a little bit of math of how fast things are
actually moving apart-- let me actually write
it someplace where I have more space--
the current Hubble Constant is 70.6
plus or minus 3.1. So we have observed
some variation here. There is some error to
our actual measurements. Kilometers per second
per megaparsec. And remember, a parsec is
roughly 3.2, 3.3 light years. So another way to
think about it is, if this is where we are
in the universe right now. And if this object
right over here-- if this distance right over here
is one megaparsec, so 1 million parsecs. Or 3.26 million light
years from Earth. So just so we have
a sense, this is roughly 3.26 million
light years from Earth. Then this object will
appear to be moving away. Although it's not
moving in space, just the space that it's in
is stretching in such a way that it looks to be moving
at, based on its redshift, 70.6 kilometers per
second away from us. So this is a huge velocity. 70.6 kilometers per second. So this is a pretty
fast velocity. But you have to remember,
this is over one megaparsec. The Andromeda galaxy is
not even a megaparsec away. It is about 2.5
million light years. So it's about 0.7 or
0.8 of a megaparsec. So if you look at
a point in space a little bit further than
the Andromeda galaxy, it will look to be,
right now, receding at about 70.6
kilometers per second. But what if you were to
go twice that distance? If you were to look at something
that's almost 7 light years away? 2 megaparsecs away? So if you were to look
at this object over here, how fast would that be receding? Well, if you just
look at it over here, it's 2 megaparsecs away. So it's going to be twice this. You're just going to
multiply its distance-- 2 megaparsecs times this. The megaparsecs cancel out. So 70.6 times 2 is-- it's
going to look to be moving, It's not moving in space. Remember, space is
just stretching. So its velocity, It's apparent
velocity, will be 70.6 times 2. So that's 141.2
kilometers per second. And one question you
say, well how did Hubble know-- you can observe the
redshift of objects moving away from us. But how did he know that
they were moving away from each other? Well, if you were look at
the redshift of this object, and say, wow, that's moving away
is 70.6 kilometers per second. And then you were to look
at the redshift of this and say, wow, that's
moving away from us at 141.2 kilometers per second. Then you also know that these
two objects are moving away from each other at 70.6
kilometers per second. And we could keep doing this
over different distances. But hopefully this gives you
a little bit bigger sense of things. And just remember, even though
I said this is a huge distance-- a megaparsec is further than
it is to the Andromeda galaxy. The Andromeda galaxy is the
nearest large galaxy to us. There are some
smaller galaxies that are closer to us that
are kind of satellite galaxies around the Milky Way. But the Andromeda is the
nearest large galaxy to us. And we also know that we're
talking about hundreds of billions of galaxies in
just the observable universe. So very quickly, as
you go near the edge of the observable
universe, these velocities, the apparent distance at which
things move are moving away from us, start to become
pretty significant.