<p>The pedagogical answer is this.  You're confusing the</p>
<h1>width</h1>
<p>of something, with it's</p>
<h1>parallax!</h1>
<p>Here's the fixed background</p>
<p><a href="https://i.sstatic.net/sP8tT.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/sP8tT.png" alt="enter image description here" /></a></p>
<p>Here's something that happens to have width ...</p>
<p><a href="https://i.sstatic.net/rjaZc.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/rjaZc.png" alt="enter image description here" /></a></p>
<p>Here's something that has parallax ...</p>
<p><a href="https://i.sstatic.net/BXxqu.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/BXxqu.png" alt="enter image description here" /></a></p>
<p>That's the deal!</p>
<p>Note that width can just be measured, using one printout of the photo and a wooden ruler.</p>
<p>But parallax means <em>two</em> photos taken 180 days apart, and you measure how much the thing has <em>moved</em>.</p>
<p>(The mind-boggling <a href="http://sci.esa.int/gaia/" rel="nofollow noreferrer">GAIA</a> does <em>not actually use</em> wooden rulers!)</p>
<hr />
<p>One huge confusion with &quot;parsecs&quot; is this:</p>
<p>Parallax means the distance <strong>an object moves in two photos</strong> take six months apart. That technique can be used with objects <strong>from 1 to about 100 parsecs away</strong> from us.</p>
<p>However, astronomers (for convenience) still use the measure &quot;parsecs&quot; even when the distance <strong>is far more than 100 parsecs</strong>.  And, they even use the measure &quot;parsecs&quot; for things like &quot;size&quot;, which just have <strong>no connection at all</strong> to parallax photo measurements.</p>
<p>If you hear that something is &quot;<strong>5000</strong> parsecs away&quot;, it is inconceivable the distance was determined using parallax photo measurements!!  And, if you hear that something is &quot;1000 parsecs <strong>wide</strong>&quot;, that just has no connection at all to parallax photo measurements (it's a width - nothing to do with the distance from Earth!!)</p>
<p>In the question at hand here, the &quot;width&quot; of an object was <strong>quoted in parsecs</strong>. The OP was originally assuming that, since parsecs were mentioned in relation to the width, you could use something related to the <strong>technique of parallax photo measurement</strong>, in relation to the width.  In fact, parallax photo measurement just has <strong>no connection, whatsoever</strong> to width. You literally might as well use smell or taste - heh!  The confusion is that parsecs happen to be also used (very confusingly) to measure things like width: but remembering that the technique of parsecs (parallax photo measurement) has absolutely no connection at all to width, and no connection to anything more than 100 ps from us.</p>

CC BY-SA 3.0
2016-06-14T14:31:59.440Z
2016-06-21T22:26:00.007Z
2020-06-17T09:47:40.653Z
Fattie
<p>Only if it happens to be 206 kpc away, <em>i.e.</em> 1/4 of the distance from here to the Andromeda galaxy. A parsec is the distance at which 1 AU makes an angle of 1 arcsecond. If the nebula is 100 parsecs away and has an angular diameter of 250 arcseconds, then its diameter is
$$100 \ \mathrm{pc} \times 250 \ \mathrm{as} = 25000 \ \mathrm{AU} = 0.12\,\mathrm{pc}$$</p>

CC BY-SA 3.0
2016-06-22T01:08:57.757Z
2016-06-22T13:46:01.560Z
2016-06-22T13:46:01.560Z
Mike G
<p>I just wanted to double check I had something correct. If an object, say a nebula, is measured to roughly have a diameter or extent of, say, 250 arcseconds, would its diameter in parsec simply therefore be 250 parsecs?</p>

CC BY-SA 3.0
2016-06-14T13:49:16.007Z
How far away is the nebula?
Dean
CC BY-SA 3.0
2016-06-14T13:51:35.913Z
@Dean It is a H II region outside of our galaxy, with a distance of about 800kpc (but I'm pretty sure you don't need the distance...)
MichaelJRoberts
CC BY-SA 3.0
2016-06-14T13:55:51.680Z
Hint: If object A is twice the distance from us as object B, but they both span 250", are they equally large? :)
pela
CC BY-SA 3.0
2016-06-14T13:56:13.087Z
Hi @MichaelJRoberts, you do need distance, take the moon for example, its approximately 30 arcmin (1800 arcsec) in diameter, this doesn't mean that its physical size is 1800 parsecs across.
Dean
CC BY-SA 3.0
2016-06-14T13:56:22.803Z
@Pela No...apologies! :)
MichaelJRoberts
CC BY-SA 3.0
2016-06-14T13:57:22.563Z
@Dean Hi Dean, yes, I had thought of this and then pela and yourself commented. I apologise for this elementary oversight. How would I make the conversion then...would I divide the arcsecond by the distance to the object in parsecs?
MichaelJRoberts
CC BY-SA 3.0
2016-06-14T13:58:04.727Z
I can see where your coming from, but your trying to do the reverse of what parsecs were invented for. They allow us to measure the distances to things that have a small parallax in the sky, based on the orbit (1AU) of the Earth around the sun as the base measurement.
Dean
CC BY-SA 3.0
2016-06-14T13:58:24.690Z
No need to apologize  :)
pela
CC BY-SA 3.0
2016-06-14T13:59:54.383Z
@Dean Hi Dean, so is it possible to convert the two or should I leave the sky extent in arcseconds?
MichaelJRoberts
CC BY-SA 3.0
2016-06-14T14:00:31.180Z
If you know the distance and angular size then you can indeed calculate the diameter, although it would come out in AU (1pc = 206265AU). Use the equation d=r/tanP
Dean
CC BY-SA 3.0
2016-06-14T14:03:56.037Z
Thank you. I see it now. tan(P) I assume is the tan of the arcsecond value and since it is not small, we have to use tan rather than an approximation.
MichaelJRoberts
CC BY-SA 3.0
2016-06-14T14:04:52.583Z
Yes, make sure you have your calculator in deg, min, sec or convert arcsec into degrees before you apply tan. You should get an answer around 970 AU.
Dean
CC BY-SA 3.0
2016-06-14T14:06:33.043Z
@Dean I'll work through it now, thank you for giving me a rough guide too. Should be ok.
MichaelJRoberts
CC BY-SA 3.0
2016-06-14T14:07:25.670Z
@MichaelJRoberts No worries!  :)
Dean
CC BY-SA 3.0
2016-06-14T14:20:40.363Z
Did you mean 970 pc?
MichaelJRoberts
CC BY-SA 3.0
2016-06-14T14:37:10.750Z
Hey Michael, don't forget. **IF** we know the distance to something, we can figure the width. Often, we **have no clue** about the distance.  BUT we can GUESS the width from other factors. In that case we then base the DISTANCE, in fact *ON THE WIDTH!*  Makes sense?  If you KNOW one, you can FIGURE OUT the other.  If you GUESS one, that gives you a GUESS at the other. In your example: I'm concerned you think we "know" the distance. Indeed, we likely have (A) *no clue at all*, or (B) only a reasonable GUESS at the distance. (GIVEN the distance, it's then trivial to figure the width.)
Fattie
CC BY-SA 3.0
2016-06-14T15:04:17.147Z
@MichaelJRoberts no its not parsec because the parallax of 1 arcsecond it based on the orbit radius of the Earth (1AU). This diagram explains it better https://upload.wikimedia.org/wikipedia/commons/7/7d/Stellarparallax_parsec1.svg
Dean
CC BY-SA 3.0
2016-06-14T15:33:52.053Z
970 seems closer to the actual value of 760 light years tho for a region within my observation aperture.
MichaelJRoberts
CC BY-SA 3.0
2016-06-21T21:35:08.043Z
@JoeBlow I sometimes see kpc used to describe distances in this way...in the literature?
MichaelJRoberts
CC BY-SA 3.0
2016-06-21T22:12:19.077Z
Hi MJ - right, but it goes to the basic misunderstanding here.  Here's the thing: **WHY** do they use parsec to measure distance **FROM** us, **TO** a star? Because it's *defined that way*!!!  IF the parallax is 1 arcsecond, we DEFINE the distance as 1ps.  If it is 1/2 arcsecond, it is 2 ps away, if it is 1/3 arcsecond, it is 3 ps away, and so on.  Note that this ONLY APPLIES to measuring the DISTANCE TO an object when you measure it's PARALLAX.  Don't forget the parallax is the DIFFERENCE in TWO PHOTOS six months apart - see my diagram.
Fattie
CC BY-SA 3.0
2016-06-21T22:14:57.173Z
Be sure to understand that you can *not even measure parallax* more than about 100 ps.  That is the limit.  It's not possible to measure an angular change less than about 1/100th arcsecond.  Note that the distance the object in question is not 100, not 1000 but 800,000 parsecs away!!!  It is absolutely inconceivable that the parallax of an object that far away could be measured.  The furthest distance you can measure using parallax, is about 100 parsecs.
Fattie
CC BY-SA 3.0
2016-06-21T22:15:13.117Z
@JoeBlow Of course, I understand what you are saying but often I see distances between two galaxies in a merging situation quoted at distances between their central cores in kpc...
MichaelJRoberts
CC BY-SA 3.0
2016-06-21T22:15:44.083Z
Again: when you look at the object in question and say that it's WIDTH is "250 arcseconds". That has absolutely no connection to parallax.  Parallax is the *difference* in position in two photos, taken, 6 months apart.
Fattie
CC BY-SA 3.0
2016-06-21T22:16:27.947Z
But I've seen it used as a distance measurement between objects...
MichaelJRoberts
CC BY-SA 3.0
2016-06-21T22:17:45.363Z
For sure, you can use "parsec" to measure any HUGE distance.  But you must remember that parsecs are only DEFINED as the PARALLAX seen over six months, for objects which are LESS THAN about 100 ps away from us.  If you say "something is 1000 parsecs wide", that has *no connection at all* to the measurement technique of taking two parallax photos, 6 months apart.  You see?
Fattie
CC BY-SA 3.0
2016-06-21T22:29:23.353Z
Say @MichaelJRoberts, note that if you WERE MEASURING DISTANCE.  Parsces go the OTHER way!!!  As the arcseconds get bigger, the distance gets SMALLER.  1 arcsecond -> 1 parsec.  2 arcseconds -> .5 parsec.  And so on.
Fattie
<distances><parallax><parsec>
A quick (elementary) check on arsecond conversion to sky distance in parsecs
MichaelJRoberts
# A quick (elementary) check on arsecond conversion to sky distance in parsecs

(Asked by: username_0 on 2016-06-14)

I just wanted to double check I had something correct. If an object, say a nebula, is measured to roughly have a diameter or extent of, say, 250 arcseconds, would its diameter in parsec simply therefore be 250 parsecs?

**Tags:** distances, parallax, parsec
> **Comments:**
> **username_1**: How far away is the nebula?  
> **username_0**: @Dean It is a H II region outside of our galaxy, with a distance of about 800kpc (but I'm pretty sure you don't need the distance...)  
> **username_2**: Hint: If object A is twice the distance from us as object B, but they both span 250", are they equally large? :)  
> **username_1**: Hi @MichaelJRoberts, you do need distance, take the moon for example, its approximately 30 arcmin (1800 arcsec) in diameter, this doesn't mean that its physical size is 1800 parsecs across.  
> **username_0**: @Pela No...apologies! :)  
> **username_0**: @Dean Hi Dean, yes, I had thought of this and then pela and yourself commented. I apologise for this elementary oversight. How would I make the conversion then...would I divide the arcsecond by the distance to the object in parsecs?  
> **username_1**: I can see where your coming from, but your trying to do the reverse of what parsecs were invented for. They allow us to measure the distances to things that have a small parallax in the sky, based on the orbit (1AU) of the Earth around the sun as the base measurement.  
> **username_2**: No need to apologize  :)  
> **username_0**: @Dean Hi Dean, so is it possible to convert the two or should I leave the sky extent in arcseconds?  
> **username_1**: If you know the distance and angular size then you can indeed calculate the diameter, although it would come out in AU (1pc = 206265AU). Use the equation d=r/tanP  
> **username_0**: Thank you. I see it now. tan(P) I assume is the tan of the arcsecond value and since it is not small, we have to use tan rather than an approximation.  
> **username_1**: Yes, make sure you have your calculator in deg, min, sec or convert arcsec into degrees before you apply tan. You should get an answer around 970 AU.  
> **username_0**: @Dean I'll work through it now, thank you for giving me a rough guide too. Should be ok.  
> **username_1**: @MichaelJRoberts No worries!  :)  
> **username_0**: Did you mean 970 pc?  
> **username_3**: Hey Michael, don't forget. **IF** we know the distance to something, we can figure the width. Often, we **have no clue** about the distance.  BUT we can GUESS the width from other factors. In that case we then base the DISTANCE, in fact *ON THE WIDTH!*  Makes sense?  If you KNOW one, you can FIGURE OUT the other.  If you GUESS one, that gives you a GUESS at the other. In your example: I'm concerned you think we "know" the distance. Indeed, we likely have (A) *no clue at all*, or (B) only a reasonable GUESS at the distance. (GIVEN the distance, it's then trivial to figure the width.)  
> **username_1**: @MichaelJRoberts no its not parsec because the parallax of 1 arcsecond it based on the orbit radius of the Earth (1AU). This diagram explains it better https://upload.wikimedia.org/wikipedia/commons/7/7d/Stellarparallax_parsec1.svg  
> **username_0**: 970 seems closer to the actual value of 760 light years tho for a region within my observation aperture.  
> **username_0**: @JoeBlow I sometimes see kpc used to describe distances in this way...in the literature?  
> **username_3**: Hi MJ - right, but it goes to the basic misunderstanding here.  Here's the thing: **WHY** do they use parsec to measure distance **FROM** us, **TO** a star? Because it's *defined that way*!!!  IF the parallax is 1 arcsecond, we DEFINE the distance as 1ps.  If it is 1/2 arcsecond, it is 2 ps away, if it is 1/3 arcsecond, it is 3 ps away, and so on.  Note that this ONLY APPLIES to measuring the DISTANCE TO an object when you measure it's PARALLAX.  Don't forget the parallax is the DIFFERENCE in TWO PHOTOS six months apart - see my diagram.  
> **username_3**: Be sure to understand that you can *not even measure parallax* more than about 100 ps.  That is the limit.  It's not possible to measure an angular change less than about 1/100th arcsecond.  Note that the distance the object in question is not 100, not 1000 but 800,000 parsecs away!!!  It is absolutely inconceivable that the parallax of an object that far away could be measured.  The furthest distance you can measure using parallax, is about 100 parsecs.  
> **username_0**: @JoeBlow Of course, I understand what you are saying but often I see distances between two galaxies in a merging situation quoted at distances between their central cores in kpc...  
> **username_3**: Again: when you look at the object in question and say that it's WIDTH is "250 arcseconds". That has absolutely no connection to parallax.  Parallax is the *difference* in position in two photos, taken, 6 months apart.  
> **username_0**: But I've seen it used as a distance measurement between objects...  
> **username_3**: For sure, you can use "parsec" to measure any HUGE distance.  But you must remember that parsecs are only DEFINED as the PARALLAX seen over six months, for objects which are LESS THAN about 100 ps away from us.  If you say "something is 1000 parsecs wide", that has *no connection at all* to the measurement technique of taking two parallax photos, 6 months apart.  You see?  
> **username_3**: Say @MichaelJRoberts, note that if you WERE MEASURING DISTANCE.  Parsces go the OTHER way!!!  As the arcseconds get bigger, the distance gets SMALLER.  1 arcsecond -> 1 parsec.  2 arcseconds -> .5 parsec.  And so on.  

---

## 2 answers

### Answer by username_3 on 2016-06-14. Score: 2

The pedagogical answer is this. You're confusing the

# width

of something, with it's

# parallax!

Here's the fixed background

[![enter image description here](https://i.sstatic.net/sP8tT.png)](https://i.sstatic.net/sP8tT.png)

Here's something that happens to have width ...

[![enter image description here](https://i.sstatic.net/rjaZc.png)](https://i.sstatic.net/rjaZc.png)

Here's something that has parallax ...

[![enter image description here](https://i.sstatic.net/BXxqu.png)](https://i.sstatic.net/BXxqu.png)

That's the deal!

Note that width can just be measured, using one printout of the photo and a wooden ruler.

But parallax means *two* photos taken 180 days apart, and you measure how much the thing has *moved*.

(The mind-boggling [GAIA](http://sci.esa.int/gaia/) does *not actually use* wooden rulers!)

---

One huge confusion with "parsecs" is this:

Parallax means the distance **an object moves in two photos** take six months apart. That technique can be used with objects **from 1 to about 100 parsecs away** from us.

However, astronomers (for convenience) still use the measure "parsecs" even when the distance **is far more than 100 parsecs**. And, they even use the measure "parsecs" for things like "size", which just have **no connection at all** to parallax photo measurements.

If you hear that something is "**5000** parsecs away", it is inconceivable the distance was determined using parallax photo measurements!! And, if you hear that something is "1000 parsecs **wide**", that just has no connection at all to parallax photo measurements (it's a width - nothing to do with the distance from Earth!!)

In the question at hand here, the "width" of an object was **quoted in parsecs**. The OP was originally assuming that, since parsecs were mentioned in relation to the width, you could use something related to the **technique of parallax photo measurement**, in relation to the width. In fact, parallax photo measurement just has **no connection, whatsoever** to width. You literally might as well use smell or taste - heh! The confusion is that parsecs happen to be also used (very confusingly) to measure things like width: but remembering that the technique of parsecs (parallax photo measurement) has absolutely no connection at all to width, and no connection to anything more than 100 ps from us.


---

### Answer by username_4 on 2016-06-22. Score: 0

Only if it happens to be 206 kpc away, *i.e.* 1/4 of the distance from here to the Andromeda galaxy. A parsec is the distance at which 1 AU makes an angle of 1 arcsecond. If the nebula is 100 parsecs away and has an angular diameter of 250 arcseconds, then its diameter is
$$100 \ \mathrm{pc} \times 250 \ \mathrm{as} = 25000 \ \mathrm{AU} = 0.12\,\mathrm{pc}$$


---

