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

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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.

WookiemasterPost authorfirst

CrossfaceXPost authorgreat video

zbe8Post authorJust 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).

zbe8Post authorI guess thats the whole reason then that we see background radiation at that distance?

MelthornalPost authorSo 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?

MelthornalPost authorBy 60 times slower I mean 3600 times slower. o.0

zbe8Post author@Melthornal We would reach it. Although space is expanding, gravity is much stronger at "close" distances – galaxies are not expanding.

ShaheemA13Post author@zbe8 what unit did you use for D? km?

MarkusDDifyPost author@zbe8 haha that isnt calc.

MarkusDDifyPost 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.

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

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

TheisticThinkerPost 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.

globito42Post authorVery helpful for my exam.

Fuxy22Post authorwhat 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 CeccottiPost 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?! 🙂

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

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

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

Nathan MartinPost authorYes, 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.

ThorloarPost authorWell 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 JonesPost authorim gonna go and assume it's Dr. Khan…

ThorloarPost authorNo 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

E^2=(m0^2*c^4)+p^2*c^2)

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.

ThorloarPost authoralso 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 BlahPost authorIf 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?

shankyxyzPost authorin 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 DoolinPost authorHi 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

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

СергейPost authorHubble'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: //alemanow.narod.ru /hubbles.htm

xxxxxrandomPost authortypo at 8 mins

m = milli = 0.001

M = Mega = 1 000 000

Still very clearly explained.

vikrant pangamPost authorv=HoD

Julian EspinosaPost authorpoiNT

my name is my namePost authori thought it as draw to scale alllll along :p

Farshid BesharatiPost authorThank you.

antonio casagrandePost authorThanks man! Very helpful!

MrWillybilllyPost authorgreat video, thanks

Nicole LiPost authorreally helpful! thanks a lot

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

SomeStevenPost authorWhat program is he using?

Mallu BadigerPost authoris it true ? i am wonder about astronomy

Antoine RaymondPost authorCan 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

MrAlec78ukPost authorif space is stretching outward are the particles in my body moving away from each other?

Drake DanosPost authorHubble’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 KanekiPost authorIt 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

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

carlos ortizPost authorthanks for saving me from my useless professor and his obese assistant rachel

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

Ozgur MoralPost authorTürkçe altyazi bir noktadan sonra bitiyor 🙁

Tanmay PaulPost authorWaste of time.. dont watch this video

New IdeasPost authorGood one

REED SMITHPost authoram 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 EgendorfPost authorthe 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 ToadsPost authoromg… 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 KellerPost authorEvery interstellar object in NOT moving away from Earth

Stevei SteveiPost authorHi K A

Thanks for the Nice and informative Video.

I have one major issue I am grabbling with ..ok here it is

Hubble's

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