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# Hubble's law

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.