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Course: Cosmology and astronomy>Unit 2

Lesson 3: Stellar parallax

Parsec definition

Parsec Definition. Created by Sal Khan.

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• Wait if 1 Parsec = tan(90deg-1arcs)1AU then 2 Parsec = tan(90deg-2arcs)*1AU.
But tan(2) isn't 2*tan(1) so 2 Parsec can't be simply 2
1 Parsec or 2*3.26ly right?
• 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...
• is it possible that the sun is rotating on an axis? I mean how would we be able to tell
• 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.
• isn't the 'd' the distance from the sun to the star? do we measure distance of star relative to the earth or sun?
• 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.
• I keep running into conflicting ideas about what a parsec is.

Drawing a right triangle as Sal does in the video (finished at ), 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?
• It's the distance to the sun. It's not the hypotenuse.
• at what specifically makes an arc second
• 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.
• Is this the same thing as triangulation?
• 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.
• 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?
• 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).
• This is fascinating. I am wondering which star has been observed that has the largest measurable parallax angle?
• It would be for the closest star (other than the sun) Proxima Centauri as 4.24 light years with a parallax angle of 0.76813 arc seconds.
• 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 in , "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.