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## 宇宙学和天文学

### 课程: 宇宙学和天文学 > 单元 1

课程 4: 大爆炸与宇宙膨胀# 哈勃定律

哈勃定律. 由 Sal Khan 创建

## 视频字幕

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 a few 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 let me just pick nine points so that I have a proper grid so this is an early 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 and actually let me draw another row let me draw another row just to make it just actually 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 could 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 the velocity with which 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 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 rushing that infinite sheet out so it has no boundaries but we're still stretching it out another way to visualize it and that's what we did earlier on is you could imagine that this fear that the universe is the three-dimensional surface of a four-dimensional sphere or the three-dimensional surface of a hyper sphere sort of an early stage in the universe the sphere looked like this 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 had 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 they're all on the surface of the sphere obviously I'm only dealing with two dimensions right now it's nearly impossible or maybe impossible to imagine a three-dimensional surface of a four-dimensional sphere but then that analogy holds and this is the surface of a balloon or the surface of a bubble if the bubble were to expand so if the bubble were to expand over a few billion years and not 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 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 we're on the surface of an actual sphere now with that out of the way let's think about how fast or what is the apparent velocity with which things are moving away and remember we're gonna have to say not only how far things are moving away but we're gonna say how far they're moving it away from if the observer is us depending on how how far they already are so what we're going to do what we could say let me write this down all objects all objects moving away from each other away from each other and the velocity and the apparent velocity the apparent the apparent relative velocity relative velocity is proportional is proportional to distance 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 Hubble's 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 were they seemed 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 is going to be some constant times the distance 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 this H here is called Hubble's constant Hubble's 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-zero 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 proper distance now and this has to be very important because that proper distance is constantly changing as the universe expands so you know the now will actually change slightly from the beginning of this video to the end of this video but we can roughly say in 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 just to give a sense of or doing a little bit of math of how fast things are actually moving apart the current Hubble constant the current Hubble constant is let me actually write it where it's someplace where I have more space the current Hubble constant the current Hubble constant is seventy point six plus or minus plus or minus three point one so we have observed some variation here there is I guess some error to our actual measurements kilometres kilometres per second per per megaparsec per mega mega parsec 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 is if this object right over here if this distance right over here is one mega parsec so one million parsecs or 3.2 six million light years from Earth so this is roughly so just so we have a sense this is 3.2 6 roughly 3.2 6 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 70 it's look it looks like it's moving at 70 based on its redshift 70 point six millimeters per second away from us so this is a huge velocity 70 point 600 meters per second per second so this is a and this is a pretty this is a pretty fast velocity but you have to remember this is over one mega parsec the Andromeda galaxy is not even is not even a mega parsec away it was about 2.5 million light years so it's about 0.7 or point eight 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 seventy point six kilometers per second but what if you were to go twice that distance if you were to look at something that's um almost seven light-years away to mega parsecs away so if you look at if you were to look at this object over here 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 two mega parsecs away so it's going to be twice this you're just going to multiply its distance to mega parsecs times this the mega parsecs cancel out so seventy point six times two is so it's going to be moving it's going to look to be moving it's not moving in space remember space is just stretching so it's velocity it's apparent velocity will be seventy point six times two so that's 141 point two kilometres per second and this is you you know one question you say well how did Hubble know you know it's easy to you could 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 to look at the redshift of this object and say wow that's moving away at 70 point six kilometers per second and then you were look at the redshift of this and say wow that's moving away from us at 141 point two kilometers per second then you also know that these two objects are moving away from each other at 70 point six kilometers per second and we could keep doing this over different distances but this hopefully this gives you a little bit a more a little bit bigger sense of things and just remember even though I said this is a huge distance a mega parsec 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 largest galaxy 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 just the observable unit the universe so very quickly as you go near the edge of the observable universe these these velocities the the the apparent distance at which things move are moving away from us start to become pretty pretty significant