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You've probably heard the word "parsec" before

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in science fiction movies or maybe even in some things dealing with astronomy.

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And what I want to do with this video is really just tell you

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where this, where the word and the definition of the word really come from

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and just to kind of cut to the chase.

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It's just a unit of distance.

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It's just about 3.26... 3.26 light years.

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What I want to do is think about where did this weird distance come from,

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this distance that is roughly 3.26 light years?

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It comes from... it comes from the distance...

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the distance of something...

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of something, probably a star, but let me say "something"

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because there are no stars exactly this far away from us.

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The distance of something whose parallax, or let me say

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that has... that has... a parallax... parallax... angle

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of... one arc... one arc second, and the word

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comes from the "par" in parallax and the second is "arc second".

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So it's literally "par"... I'm going to do this in a different color...

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It's literally "parsec".

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You can think of this as a kind of a parallax... parallax arc second.

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How far would this thing be?

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It turns out it's 3.26 light years.

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So we can actually calculate that, that's essentially what I'm going to do with this video.

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So let's say there is something...

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let's say... so this is the sun,

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this is the earth at some point in time,

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this is the earth six months later at the opposite end of the orbit.

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And we are looking at some distance,

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we're looking at some object, some distance away.

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We know that this distance right here is 1 astronmical unit,

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and what we want to do is to figure out the distance of this object.

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And all we know is that it has a parallax angle of 1 arc second.

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So let's remind ourselves of what this means.

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If we are looking right at, right at, remember we're looking from above the solar system,

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so the earth is rotating in this direction, in either case,

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and so in this point in the year, we don't know when this is,

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depends on what star that is,

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at this point in the year, right at sunrise,

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right when we first catch the first glimpses of the sun's light,

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if we look straight up, if we look straight up,

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the angle, the angle between that object in the night sky

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and straight up

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is going to be the parallax angle.

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So this is going to be 1, this is going to be 1 arc, arc second.

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And just to make it consistent with the last few videos we did on parallax,

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let's just visualize how that would look in the night sky.

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So let me draw the night sky over here,

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we'll do that in purple maybe

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Let me draw the night sky over here.

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This is looking straight up.

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This is north, south, west, and east.

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And so you can imagine in this situation, the sun is just rising on the east...

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The sun is just rising on the east.

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Let me make it the color of the sun.

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The sun is just rising on the east.

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And so this will be towards the direction of the sun.

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You could imagine that to some degree... well, this is north.

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North is the top of the earth right here, kind of pointed towards us, out of the screen.

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South is going into the screen.

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Hopefully, that helps with the visualization.

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Or another way to think about it, the sun is rising in the east.

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This is going to be towards the direction of the sun, of a certain angle from the center.

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In this case, it's 1 arc second.

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So, it's going to be right over here.

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So this, this angle right over here is going to be 1 arc second.

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And then if we were to see where that object is six months later, it'll be the opposite.

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We're going to be looking, we're going to be looking in the same... the center of the universe.

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Or I should say the center of the night sky at that point.

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The same direction of the universe.

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The universe actually has no center. We've talked about that many times.

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If we look at the same direction of the night sky, we'll be looking six months later,

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and instead of it being at dawn, it will now be at sunset.

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We'll be just getting the last glimpses of the sun.

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And so the sun will be setting...

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the sun will be setting in the west.

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The sun will be setting in the west.

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And so this angle, this angle right here, which is also the same thing as a paralax angle,

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it'll be... this will also be 1 arc second.

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So this will also be 1 arc second.

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1 arc second.

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So let's figure out how far this object is.

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What is... what is an actual parsec in terms of astronomical units or light years.

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So if this is 1 arc second, this is going to be...

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and remember, 1 arc second is equal to one-thirty-six-hundreth (1/3600) of a degree.

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1/3600th of a degree.

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So this angle, right over here, is going to be 90-1/3600th.

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And we just use a little bit of trigonometry.

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The tangent of this angle.

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The tangent of 90-1/3600 is going to be this distance in astronomical units divided by 1.

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Well, you divide anything by 1, it's just going to be that distance.

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So that's the distance right over there.

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So we get our calculator out, and we want to find the tangent...

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the tangent of 90-1/3600, and we will get our distance in astronomical units.

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206,264.

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We're going to say 265.

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So this is going to be equal to...

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This distance over here is going to be equal to 206,265. I'm just rounding, astronomical units.

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And if we want to convert that into light years, we just divide.

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So there are 63,150 light years per astronomical unit...

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I'm sorry, astronomical units per light year.

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So this is... let me actually right it down.

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Just so you make it... I don't want to confuse you with the unit cancellation.

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So we're dealing with 206,265 astronomical units,

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and we want to multiply that times 1 light year is equal to 63,115 astronomical units.

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And we want this in the numerator and the denominator to cancel out.

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And so if you divide 206,265, this number up here,

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divided by 63,115, the number of astronomical units in a light year,

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63,115... let me delete that right over there,

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we get 3.2 or the way, the way the math worked out here,

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round to 3.27 light years.

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So this is equal to... this is equal to roughly 3.27 light years.

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So I should just show it's approximate right over there.

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But that's where the parsec comes from.

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So hopefully, you now you just realize it is just a distance.

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But even more, you understand where it comes from.

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It's the distance that an object needs to be from earth

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in order for it to have a paralax angle of 1 arc second.

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And that's where the word came from. Paralax. Arc second.