Thread: Quick calculations involving angular diameter + parsecs

1. Newbie
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Mar 2007
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Quick calculations involving angular diameter + parsecs

I'm not quite sure what formula to use to figure out the distance of some object (supernova remnant) given it's angular diameter (15" of arc in the year 2000). Thanks in advance!

2. Order of Kilopi
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Jul 2005
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9,761
Seems like we need more information, to nail the true diameter of the object so that we can do trig on it.
Is this an illumination wavefront? If so, we need to know how long before 2000 the supernova exploded, so we can figure how far the light has travelled.

Grant Hutchison

3. Originally Posted by ScottCP
I'm not quite sure what formula to use to figure out the distance of some object (supernova remnant) given it's angular diameter (15" of arc in the year 2000). Thanks in advance!
Welcome aboard, Scott.

If one can get a pretty good idea of how fast the sn ejecta is traveling then, after any given number of years, its actual diameter would be known. If you know the diameter and you know the angle then it is simple trig from there to get the distance.

These ejection rates are known to some reasonable degree of accuracy. I am not that knowledgeable in this, however.

You obviously have a sn picked out if it is 15 arcseconds. There are probably several references as to its distance based on the above which you can Google or we can help.

4. Established Member
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Oct 2006
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This should approximate it pretty well. The diameter will be given in the same units you used for the distance.

Distance from earth = True diameter of the object / Tan(angular diameter of the object)

Of course you need to know the supernova's true diameter somehow so you're going to need more information.

5. Newbie
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Mar 2007
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great, thanks for the info, I'll see if i can find the diameter

6. Order of Kilopi
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Dec 2004
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In most cases, the true diameter of a supernova remnant is the most
difficult thing to determine. If it is nearby, and there is a pulsar or
some other kind of star visible at the center which can be identified
as the source of the remnant, then it may be possible to measure the
distance, and thus calculate the true diameter. Or if there are other
stars near the supernova remnant which interact with the remnant,
and the distance to those stars can be measured, then again the
distance to the supernova remnant can be determined and the true
diameter calculated. But in most cases, the distance cannot be
measured, so the true diameter cannot be calculated. In such cases
the true diameter may be estimated from the general appearance of
the remnant. The appearance of a remnant will change as it grows.
If it looks dense, it will be small, and if it looks thin, it will be large.
There are various constraints that can be applied, depending on what
features can be seen. Spectra from both the near and far sides of a
remnant are most helpful in establishing the speed of expansion, which
can put strong limits on the true size. Usually, a lot of different lines
of evidence have to be brought together, and even then the result
typically has a fairly wide margin of error. But it is always possible to
put at least some limits on both the distance and size.

-- Jeff, in Minneapolis

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