# A quick (elementary) check on arsecond conversion to sky distance in parsecs

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?

• How far away is the nebula?
– Dean
Jun 14 '16 at 13:49
• Hint: If object A is twice the distance from us as object B, but they both span 250", are they equally large? :)
– pela
Jun 14 '16 at 13:55
• 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
Jun 14 '16 at 13:56
• @Dean I'll work through it now, thank you for giving me a rough guide too. Should be ok. Jun 14 '16 at 14:06
• 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.) Jun 14 '16 at 14:37

The pedagogical answer is this. You're confusing the

# width

of something, with it's

# parallax!

Here's the fixed background

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

Here's something that has parallax ...

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 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.

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 $$100 \ \mathrm{pc} \times 250 \ \mathrm{as} = 25000 \ \mathrm{AU} = 0.12\,\mathrm{pc}$$