Video Transcript: Distance to Stars

And when you look at a picture like the first picture in our gallery, of just stars in the sky, in this case we have the Orion Nebula, maybe you go outside, and … I’m sorry, not the Orion Nebula but the Orion constellation… or maybe you go out and you are looking at the stars, and you're just giving yourself the chance to wonder about what you're looking at.  Do you ever wonder about that light that's coming from those stars, and how long it's maybe been traveling to get to you?

We learned in the last video that light takes eight minutes to get from the Sun, the closest star, to us.  What about the stars in the sky?  How long does light take to get from there to us?  Well, that's the question, and when we measure the distance to the stars, the unit we use, there's a couple different units we use, but the distance is so big, that we use a unit of distance called the light year. Now year sounds like a length of time; it is obviously a year.  But a light year is the distance.  It's the distance that light travels in one year, which is 6 trillion miles.  Enormous distance.  Enormous distance.  But when we're looking at stars, that's a relevant distance unit to us, because the stars are so far away.

One of the amazing things about the night sky is that the stars in any given constellation, they're not all the same distance away from us.  A constellation like Orion, which roughly looks like a person you know, like he's got shoulders and a belt and some legs… that constellation and those stars could be vastly different distances.  It's just our perspective that makes them look like they're in the same part of the sky.  So for example, the star Sirius, which is meant to be like the hunting dog of Orion, the hunter, that star is something like maybe eight light years away or it's in that neighborhood, it's relatively close, whereas a star like Betelgeuse which is the upper left shoulder there, a bright red star, that is like hundreds of light years away.

And it goes to one of the main problems that early astronomers had; those first scientists who tried to measure the distance to stars, and that is that they assumed that all stars were the same intrinsic brightness.  They assumed that Sirius and Betelgeuse must both basically be the same kind of star like our Sun and so Sirius must be a little bit closer and Betelgeuse must be just a little bit further because it's just a little bit fainter.  In reality, Betelgeuse is like 1000 times brighter than Sirius.  It's an incredibly huge, bright star.  And so it looks bright in our sky, even though it's incredibly far away.  And so we're going to explore this more is how we can ultimately learn about the intrinsic brightness of objects.  But if you know how bright something really is, and you compare it to how bright it looks in the sky, then you can figure something out about how far away it really is.  Okay.  But I'm getting ahead of myself.  

The first way to conclusively measure the distance to something, to stars in particular, is parallax. And parallax has been something that people tried to measure for stars since the time of Copernicus, really.  It's for hundreds of years.  It's just incredibly hard to make measure.  So let's talk about parallax in general.

Parallax as a principle is not an astronomical principle, it can be used to measure the distance to any object.  In fact, it's something that ancient people have used to locate the precise distance to something.  So here's kind of the idea; it’s that if you have two different perspectives on an object, and there's something in the far distance to compare it to, then you can tell roughly how far away it is; actually precisely how far away it is.  So the example that's always given is if you hold your finger out in front of you, and you use both your eyes, so you close one eye and look at it relative to maybe the wall in the distance or if there's some trees in the distance, you look at your finger and you see at one location, and then you switch eyes, you'll see that your finger kind of jumps back and forth.  And the amount that it jumps back and forth, depends on how far away it is.  So if you put your finger right at the edge of your nose, it's going to jump really, really far.  If you put it really far away, it only jumps a little bit. 

So measuring that change in the relative position or the apparent position of the object, you can measure how far away the object is.  And that's true of stars as well.  If there's a star that's closer to us and we can see its location relative to stars that are much more distant, then that star will appear to kind of move back and forth.  But how does this work for stars?  We only have one eye, I mean, we're here on the earth, and that was part of the trouble.  But here's what we can do.  As you'll see in the third picture of the gallery is, all you have to do is wait six months, because the earth, as it orbits the Sun, it's like you're getting a very different viewpoint on a star.  It's like you're blinking eyes, but your eyes are as far apart as the orbit of the Sun…I mean of the orbit of the Earth around the Sun.

So you can do this. And you'll see in that drawing, in that picture, that the equation to figure out the distance is very simple.  If you measure this angle, the angle that on the sky, this tiny little sliver of an angle that the star appears to change, you take one divided by that and that gives you the distance in a unit of distance called a parsec; a parsec. You maybe heard this in science fiction movies, like “Oh, it's 2000 parsecs away.”  And that's a unit of distance that astronomers use, just like the light year. In fact, the parsec and the light year are related to each other. One parsec is about three, a little over three light years.  Okay, so if you know how many parsecs away something is, multiply it by three, and that's how many light years away it is.  That's how they're connected.

Okay.  In fact, it's kind of an interesting point, you know.  As we were learning about the heliocentric versus a geocentric model, this is one of the things that people look to say, “Well, hey, if we can observe a parallax of a star, then we know that the earth must orbit the sun,” because then we know that the Earth has moved in space.  But they couldn't observe parallax because they didn't really have telescopes and equipment.  Like they didn't have the detectors. They didn't have the telescope big enough to be able to resolve this tiny shift in the position of the star.  So they say, well, we can't see parallax.  So either the stars are really far away, or the earth is sitting still.  So some people saw this as evidence for a geocentric model.  But now that we have observed stellar parallax, there's no question that the Earth is orbiting the Sun.

Okay, so parallax is the starting point, we can use that for the closest stars to us, the stars that are roughly within 100 parsecs or 300 light years.  Those stars are close enough that we can actually observe that little shift and we can measure the distance directly.  It's one of the best ways to measure distances in the sky.  In fact, there's a lot of stars that are within about 100 parsecs. There's something like 20,000 stars that are that close to us.  So we can directly measure the distance to those 20,000 stars. 

Now, what about stars that are further away?  We want to measure the distance to all sorts of things.  How can we do that?  Well, that brings us to the fourth picture in our gallery, which is a really important concept called the inverse square law of light. The idea here is that if you have a light bulb, and you're right up against it, it's going to look really bright to your eyes.  But as you get further and further away, it's going to look fainter and fainter.  It looks fainter, though according to a very precise mathematical relationship, which is it gets fainter by the distance that you are away from it, squared. So if you go twice as far away, it will be two squared – four – four times fainter.  If you were to go five times further away, it'll get 25 times fainter. 

Alright, so, depending now, here's the key.  We talked about how important astronomical detectors were, cameras and photographic film, because they can measure brightness, they can capture that information that photometry.  So if we can measure the brightness of stars in the sky,

and if we know how bright that star really is, like, we have some way of measuring its actual brightness… if I were standing right there, how bright would it be?  And we give that a word, we call that the luminosity of the star.

So if you know the luminosity of the star, and you know how bright it looks in your sky, well, then you can calculate, you say, “Well it looks like 1000 times fainter than its luminosity.  So it must be this distance away.”  You can calculate that.  So this allows us to calculate the distance to objects that are much further away.  And we'll see that this concept, the inverse square law of light, is going to come up again and again, as we talk about measuring distances out into space.

Okay, cool. So, if we take these distance measurements, and we look back at a constellation like Orion, then you get a diagram like the fifth picture in our gallery, which is from our perspective on Earth, you know, we see the sky as a flat dome above us.  And so the Orion constellation, for example, looks like this thing that's on the flat dome.  But in reality, the stars are all very different distances away.  In fact, they're totally unrelated to each other.  And so measuring distance allows us to get that third dimension in outer space, and allows us to start to build a bigger, better model of what outer space looks like, like truly.  And we can extend that further out, eventually to galaxies and our entire universe as you try to get a real clear picture of what this universe really looks like.  

All right, pretty cool.  We'll see you next time.