If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Cosmology and astronomy

### Course: Cosmology and astronomy>Unit 2

Lesson 3: Stellar parallax

# Parsec definition

Parsec Definition. Created by Sal Khan.

## Video transcript

You've probably heard the word parsec before in science fiction movies or maybe even some things dealing with astronomy. And what I want to do in this video is really just tell you where the word and the definition of the word really come from. And just to kind of cut to the chase, it's just a unit of distance. It's just about 3.26 light years. But what I want to do is just think about where did this weird distance come from, this distance that is roughly 3.26 light years? It comes from the distance of something, probably a star. But let me say "something" because there are no stars exactly this far away from us. The distance of something that has a parallax angle of one arc second. And the word comes from the "par" in parallax and the "second" in arc seconds. So it's literally par-- let me do this in a different color. It's literally parsec. You could think of it as kind of the parallax arc second. How far would this thing be? It turns out it's 3.26 light years. So we can actually calculate that. And that's actually what I'm going to do in this video. So let's say there is something. So this is the sun. This is the Earth at some point in time. This is the Earth six months later at the opposite end of the orbit. And we are looking at some distance. We are looking at some object some distance away. We know that this distance right here is one astronomical unit. And what we want to do is figure out the distance of this object. And all we know is that it has parallax angle of one arc second. So let's remind ourselves what this means. If we're looking right at-- remember, we're looking from above the solar system. So the Earth is rotating in this direction in either case. And so in this point in the year-- we don't know when this is. Depends on what star that is. At this point in the year right at sunrise, right when we first catch the first glimpses of the sun's light, if we look straight up, the angle between that object in the night sky and straight up is going to be the parallax angle. So this is going to be one arc second. And just to make it consistent with the last few videos we did on parallax, let's just visualize how that would look in the night sky. So let me draw the night sky over here. Let me do that in purple maybe. Let me draw the night sky over here. This is looking straight up. This is north, south, west, and east. And so you can imagine in this situation, the sun is just rising on the east. Let me make it the color of the sun. The sun is just rising on the east. And so this will be towards the direction of the sun. You can imagine that to some degree, well, this is north. North is the top of the Earth right here, kind of pointed towards us out of the screen. South is going into the screen. Hopefully that helps the visualization. Or another way to think about it, the sun is rising in the east. This is going to be towards the direction of the sun, of a certain angle from the center. In this case, it's on arc second. So it's going to be right over here. So this angle right over here is going to be one arc second. And then if we were to see where that object is six months later, it'll be the opposite. We're going to be looking in the center of the universe. Or I should say, the center of the night sky at that point, the same direction of the universe. The universe actually has no center. We've talked about that many times. If we look at the same direction in the night sky, we will be looking six months later. And instead of it being at dawn, it will now be at sunset. We'll be just getting the last glimpses of the sun. And so the sun will be setting in the west. And so this angle-- this angle right here, which is also the same thing as a parallax angle-- will also be one arc second. So let's figure out how far this object is. What is an actual parsec in terms of astronomical units or light years? So if this is one arc second, this is going to be-- and remember one arc second is equal to 1/3600 of a degree. So this angle right over here is going to be 90 minus 1/3600. And we just use a little bit of trigonometry. The tangent of this angle, the tangent of 90 minus 1/3600, is going to be this distance in astronomical units divided by 1. Well, you divide anything by 1, it's just going to be that distance. So that's the distance right over there. So we get our calculator out. And we want to find the tangent of 90 minus 1 divided by 3,600. And we will get our distance in astronomical units, 206,264. We're going to say 265. So this distance over here is going to be equal to 206,265-- I'm just rounding-- astronomical units. And if we want to convert that into light years, we just divide. So there are 63,115 astronomical units per light year. Let me actually write it down. I don't want to confuse you with the unit cancellation. So we're dealing with 206,265 astronomical units. And we want to multiply that times 1 light year is equal to 63,115 astronomical units. And we want this in the numerator and the denominator to cancel out. And so if you divide 206,265, this number up here, by 63,115, the number of astronomical units in a light year-- let me delete that right over there-- we get 3.2. Well, the way the math worked out here, it rounded to 3.27 light years. So this is equal to roughly 3.27 light years. So I should just show it's approximate right over there. But that's where the parsec comes from. So hopefully now you just realize it is just a distance. But even more, you actually understand where it comes from. It's the distance that an object needs to be from Earth in order for it to have a parallax angle of one arc second. And that's where the word came from. Parallax arc second.