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Hubble's law

Hubble's Law. Created by Sal Khan.

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  • piceratops ultimate style avatar for user jordanlahn
    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)
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    • piceratops ultimate style avatar for user Adam Morgan
      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)
  • male robot johnny style avatar for user wilsonkouseph043
    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)
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    • ohnoes default style avatar for user shrikarsv2000
      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)
  • blobby green style avatar for user KaiChiu1947
    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)
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    • leaf green style avatar for user RAE 667648

      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)
  • hopper jumping style avatar for user shumway1312
    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)
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  • aqualine ultimate style avatar for user Divij Handa
    How did scientist found the value of hubble's constant?
    (3 votes)
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  • mr pants teal style avatar for user ericp
    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)
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    • blobby green style avatar for user Matthew Running
      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)
  • blobby green style avatar for user M M
    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)
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    • male robot hal style avatar for user Andrew M
      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)
  • female robot grace style avatar for user cranberry12345
    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)
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  • winston baby style avatar for user idoNOTeaTdumpLings
    According to hubbles law, everything moves AWAY from each other right? but does this include gravitational attraction? down here on earth, we're all attracted to each other but the force is so weak you wouldn't feel anything. So is gravitational attraction an excuse? This is all very interesting!
    (2 votes)
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    • boggle blue style avatar for user Davin V Jones
      Every cubic meter of space has a very small outward expansive pressure. This force is very negligible at close ranges, much less than even gravity. However, as gravity weakens with distance between two objects, expansion increases as you have more space.

      Thus, objects within our local galactic neighborhood are still close enough for gravity to overcome the expansive pressure of space and move objects closer. Once you go beyond the local neighborhood, expansion finally is able to tip the balance and overcome the attractive gravitational forces to push objects away.
      (3 votes)
  • aqualine tree style avatar for user Aly25 Ors
    If ALL objects moving away from each other then - the Sun moving away from The Earth, isn't it? Or is it valid only for galaxies?
    (1 vote)
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    • male robot hal style avatar for user Andrew M
      Space is expanding, but objects that are not very far apart (by astronomical standards) are still held together by gravity. The earth is too close to the sun for the expansion of space to overcome the gravitational attraction. The expansion of space only has a noticeable effect across intergalactic distances.
      (4 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.