Hubble’s law | Scale of the universe | Cosmology & Astronomy | Khan Academy

Hubble’s law | Scale of the universe | Cosmology & Astronomy | Khan Academy

Articles, Blog , , 57 Comments

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.

57 thoughts on “Hubble’s law | Scale of the universe | Cosmology & Astronomy | Khan Academy

  • Wookiemaster Post author


  • CrossfaceX Post author

    great video

  • zbe8 Post author

    Just did little calc. Rougly at distance 13,85 billion light years space is stretching faster than the speed of light then. So i doubt we will see any further as we see now (which was stated in one of the previous videos).

  • zbe8 Post author

    I guess thats the whole reason then that we see background radiation at that distance?

  • Melthornal Post author

    So if we were to get in a spaceship and go 70.6 km/s, we would never be able to reach something that is a megaparsec from our initial point? Since Voyager is going about 60 times slower than this, does that mean Voyager has no hope of ever going any significant distance relative to the rest of the universe?

  • Melthornal Post author

    By 60 times slower I mean 3600 times slower. o.0

  • zbe8 Post author

    @Melthornal We would reach it. Although space is expanding, gravity is much stronger at "close" distances – galaxies are not expanding.

  • ShaheemA13 Post author

    @zbe8 what unit did you use for D? km?

  • MarkusDDify Post author

    @zbe8 haha that isnt calc.

  • MarkusDDify Post author

    @Melthornal Yes the escape velocity of our own galaxy ( the milky way) is greater than that of the velocity of voyager 1. It will never leave our galaxy.

  • picoParsec Post author

    @zbe8 We can see light from galaxies that are receding faster than light. There is just a time lag (this is because the expansion rate changes over time) the "Hubble distance" will grow and then encompass the photon. 🙂

  • Robert w Post author

    this with the andromeda galaxy is bullshit, that fat thing will collide with our galaxy in millions of years….

  • crorens Post author

    so if the space is stretching, that means we are stretching too… creepy

  • TheisticThinker Post author

    @runawaybg That's because the force caused by the gravitational attraction (acceleration) between the Milky Way and Andromeda is bigger than the stetching at this distance.

  • globito42 Post author

    Very helpful for my exam.

  • Fuxy22 Post author

    what would happen to a point in space that is moving away from earth at a speed greater then the speed of light? Would that determin the boundry of the observable universe?

  • Arthur Bicalho Ceccotti Post author

    @Fuxy22 Good question! The speed of light is theoretically a maximum. I dunno the answer :/ But I would guess once it gets to the speed of light it can't go any faster… Does anyone know?! 🙂

  • deejayphenom Post author

    What would be a good career field to get into for studying space ?

  • Nathan Martin Post author

    It can go faster than the speed of light because it's just an apparant velocity.

  • Thorloar Post author

    all velocities are apparent(relative) aren't they. So how would the expanding universe be any different?

  • Nathan Martin Post author

    Yes, good point, even relative velocities can't beat light speed. I don't know the answer I'm afraid but something tells me when it's a point in space relative to a point in space this might not apply, otherwise it would be space bending spacetime to preserve light speed. Not sure.

  • Thorloar Post author

    Well i think it might have something to do with space itself expanding? ie distance traveled over time would not change? but then why would we see the red shift? i don't know and it starts to hurt my head! I think i need to go to the library and get some good new physics books.

  • Nate Jones Post author

    im gonna go and assume it's Dr. Khan…

  • Thorloar Post author

    No no mater can move faster than light, and no mater with any mass can move as fast as light. this boils down to Einstines famous prof E=mc^2 for light or
    where E is energy m0 is the mass at rest c is speed of light(vacume) pis momentum
    from this pathagorean equation you can tell that nothing can reach the speed of light because the hypotenuse of the triangle is always longer than the longer leg.

  • Thorloar Post author

    also the expansion of the universe is tought to be an expansion of space/time itself so the speed of the exspansion distance/time does not change as it is the distance and the time that expand together so 1/2 light year becomes 2/4 light years, the same. Dark matter is thought to be nothing but matter that does not emmit el;ectromagnetic radeation, literaly dark matter. Some has actualy reacently been found by calculating galactic orbits. A good write up is on Discover Magaziens web page!

  • Blah Blah Blah Post author

    If the galaxies aren't moving in space, but rather moving away from eachother because of the expansion of the universe. Then why do scientiest say that the milkyway and the andromeda galaxy will collide in 2-3 billion years? Shouldn't they be moving away from eachother?

  • shankyxyz Post author

    in any local area of space anything can be happening. these laws/rules are valid at the large. For e.g. if a comet moves towards earth, it is not violating the idea that everything (in general and in the large) is moving away from everything else (in general and in the large).

  • Jonathan Doolin Post author

    Hi Mr. Khan. Your videos have inspired me to make my own. Not quite up to your level of quality yet, but they're getting better over time. Here's what I made about Hubble's Law a couple of months ago: watch?v=9ZpaBqiMwi8

  • therealjordiano Post author

    this would make for some nice homework excuses.. 'sir, all the letters on my essay just started drifting away from each other :|'

  • Сергей Post author

    Hubble's quantum law states that a photon's frequency decreases with each new wave oscillation by a quantum amount equal to the Hubble constant, which is being observed as a redshift. To determine by how much the frequency of the photon has decreased, the Hubble constant must be multiplied by the number of the committed oscillations that is completely consistent with the results obtained by the modern method of the "standard candles".
    A report in MSU: ht_tp: // /hubbles.htm

  • xxxxxrandom Post author

    typo at 8 mins
    m = milli = 0.001
    M = Mega = 1 000 000
    Still very clearly explained.

  • vikrant pangam Post author


  • Julian Espinosa Post author


  • my name is my name Post author

    i thought it as draw to scale alllll along :p

  • Farshid Besharati Post author

    Thank you.

  • antonio casagrande Post author

    Thanks man! Very helpful!

  • MrWillybillly Post author

    great video, thanks

  • Nicole Li Post author

    really helpful! thanks a lot

  • Joshy Post author

    doesn't he mean 7 milliion lightyears at 9:06 ?

  • SomeSteven Post author

    What program is he using?

  • Mallu Badiger Post author

    is it true ? i am wonder about astronomy

  • Antoine Raymond Post author

    Can someone clarify why according to Hubble's law everything is moving away, and the andromeda galaxy and the milky way are supposed to be crashing together in some couple of billions of years

  • MrAlec78uk Post author

    if space is stretching outward are the particles in my body moving away from each other?

  • Drake Danos Post author

    Hubble’s constant is changing at a constant rate. There is an acceleration of the expansion of space which is believed to be due to dark energy. We don’t know where dark energy comes from, though.

  • Ken Kaneki Post author

    It goes approximately 0.0000000000008 mph or something like that if it was in a race with a snail,bamboo, the snail would win and it’s a one meter race! And it would take 14MILLION YEARS to reach 1 meter

  • JHarrisDesigns Post author

    So how do we see new planets if they are all moving away from us?

  • carlos ortiz Post author

    thanks for saving me from my useless professor and his obese assistant rachel

  • Itzak Post author

    She asked me why I was blushing. I replied "I'm actually just moving away from you very, very quickly"

  • Ozgur Moral Post author

    Türkçe altyazi bir noktadan sonra bitiyor 🙁

  • Tanmay Paul Post author

    Waste of time.. dont watch this video

  • New Ideas Post author

    Good one

  • REED SMITH Post author

    am i the only who when faced with a problem like this and can't bring myself to understand it for a while but then i finally get it, some tears just run down my face?

  • Brian Egendorf Post author

    the way I picture it, is if the universe was a ball expanding and getting bigger and bigger from the beggining of time till the end of time, and we knew how often it expanded, we can think of each expansion as a concentric ring (similar to how you can tell how old a tree is by reading the rings). But here is the thing. If you assume that the same amount of material is created to expand the universe each expansion, something doesn't add up. Because each ring would be either smaller, or incomplete. Because as each ring expanded, it would take up a bigger area than the previous ring, and it would need more matter to stay uniform or grow homogoenously. So…if you thought that something was 70% into ring 1, and a new ring 1 appears, and the previous ring 1 would now be ring 2, and the object would still be relatively 70% into ring 2. But ring 2 is bigger now. And more matter had to be added to it, in order to maintain its size. So, if you STILL assume that the expansion happens at set regular intervals, ring 2 has to actually expand faster than when it was the original ring 1 in order to maintain its shape and be ready into time for the next expansion..So if you track the object that is at the 70% mark in ring one expanding…it will actually get to its new 70% positon in ring 2 FASTER than it got to its original 70% position in ring 1..

  • Horny Toads Post author

    omg… it is a moment of realization … i read Space is also expanding several times but never quiet registered how that affects two points upon the third… that is huge! Still im not quite following how Hubbles constants roughly 70.6km/sec//mega parsec? Anyone ?

  • Jim Keller Post author

    Every interstellar object in NOT moving away from Earth

  • Stevei Stevei Post author

    Hi K A
    Thanks for the Nice and informative Video.
    I have one major issue I am grabbling with ..ok here it is
    Constant is basically the Gradient of Reccession Velocities of Galaxies
    against their distance from the Observer in Megaparsec.
    OK What has
    the Inverse of the Gradient (1/Ho) got to do with the Age of the
    Universe. OK yes the inverse is a Unit of Time but no one has explained
    what this constant is and why it is the Age of the Universe. There are
    many Linear Relationships in Physics with known Constants, for example
    Plancks Constant, but I am not going to pin Plancks Constant on some
    Major Cosmology or other Physical datum. I dont see where you guys are
    getting the Inverse of Hubble's Constant to be the Age of the Universe..
    Where is the Maths.

  • Loavenus Lim Post author

    How to prove Hubble’s Constant like how did he come up with it

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