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# Parsec Definition

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- You've probably heard the word "parsec" before
- in science fiction movies or maybe even in some things dealing with astronomy.
- And what I want to do with this video is really just tell you
- where this, 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... 3.26 light years.
- What I want to do is think about where did this weird distance come from,
- this distance that is roughly 3.26 light years?
- It comes from... it comes from the distance...
- the distance of something...
- 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 whose parallax, or let me say
- that has... that has... a parallax... parallax... angle
- of... one arc... one arc second, and the word
- comes from the "par" in parallax and the second is "arc second".
- So it's literally "par"... I'm going to do this in a different color...
- It's literally "parsec".
- You can think of this as a kind of a parallax... parallax arc second.
- How far would this thing be?
- It turns out it's 3.26 light years.
- So we can actually calculate that, that's essentially what I'm going to do with this video.
- So let's say there is something...
- let's say... 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're looking at some object, some distance away.
- We know that this distance right here is 1 astronmical unit,
- and what we want to do is to figure out the distance of this object.
- And all we know is that it has a parallax angle of 1 arc second.
- So let's remind ourselves of what this means.
- If we are looking right at, 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, if we look straight up,
- the angle, 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 1, this is going to be 1 arc, 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,
- we'll 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...
- 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 could 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 with 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 1 arc second.
- So, it's going to be right over here.
- So this, this angle right over here is going to be 1 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, we're going to be looking in the same... 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 of the night sky, we'll 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...
- the sun will be setting in the west.
- The sun will be setting in the west.
- And so this angle, this angle right here, which is also the same thing as a paralax angle,
- it'll be... this will also be 1 arc second.
- So this will also be 1 arc second.
- 1 arc second.
- So let's figure out how far this object is.
- What is... what is an actual parsec in terms of astronomical units or light years.
- So if this is 1 arc second, this is going to be...
- and remember, 1 arc second is equal to one-thirty-six-hundreth (1/3600) of a degree.
- 1/3600th of a degree.
- So this angle, right over here, is going to be 90-1/3600th.
- And we just use a little bit of trigonometry.
- The tangent of this angle.
- The tangent of 90-1/3600 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...
- the tangent of 90-1/3600, and we will get our distance in astronomical units.
- 206,264.
- We're going to say 265.
- So this is going to be equal to...
- 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 63,150 light years per astronomical unit...
- I'm sorry, astronomical units per light year.
- So this is... let me actually right it down.
- Just so you make it... 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,
- divided by 63,115, the number of astronomical units in a light year,
- 63,115... let me delete that right over there,
- we get 3.2 or the way, the way the math worked out here,
- round to 3.27 light years.
- So this is equal to... 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, you now you just realize it is just a distance.
- But even more, you understand where it comes from.
- It's the distance that an object needs to be from earth
- in order for it to have a paralax angle of 1 arc second.
- And that's where the word came from. Paralax. Arc second.

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