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## Cosmology and astronomy

# Parsec definition

Parsec Definition. Created by Sal Khan.

## Want to join the conversation?

- Love the vids... One clarification perhaps... when you show the sky looking straight up, would west and east need to be switched? (looking away from earth rather than looking toward the earth)... may avoid some confusion lol. Sorry, not critical to your point.(30 votes)
- Yes, i felt that was the case. maybe this works at the poles... mathematically it is moot as the angle opposition is direction neutral(6 votes)

- Wait if 1 Parsec = tan(90deg-1arcs)
**1AU then 2 Parsec = tan(90deg-2arcs)*1AU.**1 Parsec or 2*3.26ly right?

But tan(2) isn't 2*tan(1) so 2 Parsec can't be simply 2(16 votes)- True. 2 parsec is NOT the distance of an object with a paralax of 2 arcseconds, it's twice the distance of an object with a paralax of 1 arcsec. Actually, it's even worse, an object with distance 2 parsec will have a paralax of about (but not precisely) 0,5 arcseconds. Think about it, an object that is further away, will move less in the sky relative to the vertical...(16 votes)

- is it possible that the sun is rotating on an axis? I mean how would we be able to tell(5 votes)
- yes, the sun does rotate on its axis. this can be observed by noticing solar flares. they tend to sway just like trees in a hurricane and the magnetosphere also shows signs of rotation.(8 votes)

- isn't the 'd' the distance from the sun to the star? do we measure distance of star relative to the earth or sun?(5 votes)
- It makes no difference because the sun-earth distance is rounding error on interstellar distances.

The earth is 8 light minutes from the sun. The nearest star is 4 light YEARS away. From the perspective of a distant star, the earth and sun are basically in the same location.(6 votes)

- at1:00what specifically makes an arc second(5 votes)
- Basically its 1/3600 of a degree.

Imagine yourself outside on a clear night. Extend your arm in front of you and hold out your pinky. That is about 1 degree. Now imagine dividing that space again into 60 equal parts. One of those parts is referred to as an arc minute. Take one of those 60 parts and divide it again into 60 equal parts. An arc second is the size of one of those parts.(4 votes)

- Is this the same thing as triangulation?(4 votes)
- It's similar, but not quite the same. Triangulation is where you take three known locations and measure how strong a force or signal is from each of those locations.(4 votes)

- I keep running into conflicting ideas about what a parsec is.

Drawing a right triangle as Sal does in the video (finished at2:45), he basically defines a parsec as being the distance of the cathetus adjacent to an angle of 1 arcsec, with the other cathetus being 1 AU. (One parsec would then represent the distance from the sun to the "star").

But I have also run into the the idea that 1 parsec is actually the lenght of the hypothenuse in that same triangle. (One parsec would then represent the distance from the earth, at either of the two positions, to the "star").

The difference in values are naturally quite small, but which one is correct?

Is 1 parsec the lenght of the cathode or the lenght of the hypothenuse?(3 votes)- It's the distance to the sun. It's not the hypotenuse.(5 votes)

- So if I'm not mistaken then, a parsec would still be the same even if it was calculated from a base on mars (for example) or from Centauri Prime even. That is to say that the distance to the sun or size of the orbit shouldn't matter?(3 votes)
- Well, 1 parsec is just a unit for length, like metre or mile, and 1 pc = 3.26 ly.

It's defined as being the length of the leg of a right-angled triangle, of which one leg equals 1 AU and one angle equals 1 ArcSec.

So, in this sense, 1 pc is always 3.26 ly no matter where you are.

HOWEVER, if you were on Mars, and you would construct an isosceles triangle following the method used in the previous videos on parallax (thus having one angle of 2 ArcSec), the altitude of that triangle would be more than 1 pc (because the base of that triangle would be more than 2 AU).(4 votes)

- Is there any specific reason for using second and minute for measuring parallax?(3 votes)
- Angles are measured in degrees, minutes, and seconds. There is an ancient relationship between measuring time and measuring angles that probably has to do with the fact that the earth's rotation has both physical and temporal significance, i.e. you can think of 1 day as a full circle of the earth or you can think of 1 day as 24 divisions of 60 minutes that are each divided into 60 seconds.(3 votes)

- According to wikipedia: A parsec is the distance from the SUN (not from the EARTH) to an astronomical object that has a parallax angle of one arcsecond.

Sal said in7:20, "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.

You could argue that it's approximately the same because 1 AU is miniscule compared to distance of a star from the earth. But still, the concept is different.(3 votes)- It's not just approximately the same, it's the same to an almost immeasurable degree. We are looking at objects that are light YEARS away. The distance between the sun and the earth is 8 light MINUTES. 8 minutes / 1 year = .0015%. The distance measurements themselves are nowhere near that precise.(2 votes)

## 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.