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Over many videos now, we've been talking about

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how every interstellar object is moving away from Earth.

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We've also been talking about how the further something is

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away from Earth, the faster it's moving.

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What I want to do in this video

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is to put a few numbers behind it,

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or even better conceptualize what we've been talking about.

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So, one way to think about it

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is that, if at an early stage in the Universe,

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I were to pick some points,

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so that's one point,

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another point, another point

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another point,

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let me just pick 9 points so that I have a proper grid.

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So this is an early stage in the Universe

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if we fast-forward a few billion years,

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and I'm clearly not drawing it to scale.

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All of these points

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have all moved away from each other.

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So this point is over here,

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and actually let me draw another row,

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actually another column,

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just to make it clear.

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So if you fast-forward a few billion years

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the Universe has expanded,

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and so everything has moved away from everything

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and let me color code a little bit,

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let me make this point magenta.

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So this point, the magenta point is now here.

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This green point

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has now moved away from the magenta point.

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And now this blue point

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has now moved away from the magenta point

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in that direction,

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and we can keep going,

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this yellow point is maybe

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over here now.

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I think you get the general idea.

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And I'll just draw the other yellow points,

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so they've all moved away from each other.

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So there's no center here

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everything is just expanding away

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from things next to it.

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And what you can see here,

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is not only did this thing expand away from this,

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but this thing expanded away from this

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even further,

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because it had this expansion plus this expansion.

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Or another way to think about it is

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the velocity with which,

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the apparent velocity with which something is expanding

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is going to proportional to how far it is.

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Because every point in between is also expanding away.

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And just to review a little bit of the visualiztion of this,

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one way to think of this, if you think of the Universe

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as an infinite flat sheet.

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You could imagine that we are just taking a sheet of

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I don't know

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some type of sheet of stretchy material and just stretching it out

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we're just stretching it out,

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that's if we kind of imagine a more infinite Universe,

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that just goes off in every direction.

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We're just stretching that infinite sheet out,

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so it has no boundaries, but we're still stretching it out.

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Another way to visualize it, and this is what we did earlier on,

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is you could imagine that this --, that the Universe is the

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three-dimensional surface of a four-dimensional sphere,

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or the three-dimensional surface of a hyper-sphere.

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Sort of an early stage in the Universe,

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the sphere looked like this, and these points here

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the magenta point is right over here

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the green point is right over there,

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then we had the blue point up here,

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and then let me just draw the rest of the yellow points.

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And the yellow points are here, they're all on the surface of this sphere.

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They're all on the surface of the sphere.

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Obviously, I'm only dealing with two-dimensions right now,

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and it's nearly impossible, or maybe impossible to imagine

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a three-dimensional surface of a four-dimensional sphere,

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but then the analogy holds.

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If is the surface of a balloon, or the surface of a bubble,

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if the bubble were to expand,

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so if the bubble were to expand over a few billion years,

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and once again - not drawn to scale.

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So now we have a bigger bubble here

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This part of the surface is all going to expand,

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so once again, you have your magenta

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you have your blue dot,

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you have your green dot,

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and then let me just draw the rest in yellow.

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So they will have all expanded away from each other on the surface of this sphere.

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Just to make it clear that this is a sphere, let me draw some contour lines.

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So this is a contour line,

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just to make it clear that we are on the surface,

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we are on the surface of an actual sphere.

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Now with that out of the way, let's think about

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how fast or what is the apparent velocity with which things are moving away.