Actually, two questions that are slightly related.

For starters, I understand the geometry behind measuring parallax, but I am curious what the margin of error is.

1. If a star is determined to be 100,000 light years away, what is the range that would fall in? Could the error allow for, say, 80-120K light years?

2. Secondly, what would the difference in angles be between a star...let's use an example...1,000 light years away and one 100,000 light years away?

It was suggested to me that due to the extremely small angles used the margin of error is just HUGE and a star we think is 100,000 light years away may only be 1,000 light years, or 10K. This seems silly, and I raised the above questions. I quickly realized I had no idea of the answers, and it would take a lot of work to determine them--even then I may not know if my answers are correct. This is particularly the case with question 1. Question 2 I could probably work out pretty easily, but once that is done, I have no way of knowing how those angles are measured and what the chances of mismeasuring would be. Thus I am taken back to question 1.

Does any one here know the answer to the first question, and if you are kind enough, the second as well?

Thanks, motm

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With current instruments we can't get meaningful parallax measurements for anything over about 500 light years from here (Using Hipparcos data). The Gaia probe will improve that dramatically, and distances to individual stars even further should be findable by other future missions, such as Terrestrial Planet Finder, but these parallax measurements are not the primary mission, and if found will be anecdotal.

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If I'm not misplacing a decimal, the parallax for a star 1000ly away is 3.26 milli-arcseconds; for 100000ly that would fall to 0.0326 milli-arcseconds. Because there's an inverse relationship between distance and parallax, you can see that a small error in measuring a large parallax results in a small distance error. But the same error when measuring a small parallax can result in a huge distance error. So large distances end up with wider error bars than small distances.

Edit: The Hipparcos catalogue gives standard errors for its parallax measurements. An example of the sort of problem we're talking about is Hip 46 (just the first that caught my eye), with a measured parallax of 1.19 mas, and a standard error of 1.2 mas. So the star is measured to be 2740 ly away, but with 95% confidence could be at anything between 908 ly and infinity. The parallax errors quoted for Hipparcos are rarely less than 0.5 mas, and occasionally as high as 3 mas.

Grant Hutchison

We will use parallax to determine distances within our own solar system but we do not use it to determine star or galaxy distances. We use redshift/blueshift.

We have used parallax to measure distance to nearby stars. From this we have modeled spectral types and luminosity, and used that for more distant stars in our galaxy (as well as other methods). Redshifts are used for relatively distant galaxies.

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It's used for star measurements, but not galaxies.
The first stellar distance measurements were carried out using parallax. Parallax's usefulness in this regard is embedded in the name of the parsec, which is derived from parallax-second (of arc).
The Hipparcos catalogue alone contains measured parallaxes for >100,000 stars.

Grant Hutchison

Antoniseb is correct, both posts. Parallax measurements on stars more than 2500 light years away only tell us that they are more than 2500 light years. Parallax is reasonably accurate at 500 light years or less. Neil

One of the difficulties with the analysis of parallax measurements is the inverse relationship between the measurement (an angle) and the result (a distance). Even though there may be a simple, symmetric description of the uncertainty in the angle, there is NO simple description of the uncertainty in the derived distance.

Long ago, I wrote a little document providing a mathematical example. See

http://stupendous.rit.edu/richmond/answers/parallax.txt

The best parallaxes these days are made with interferometers: most in the radio and mm range, but a few in the optical. Do some searching on NOFS and CHARA if you want to learn more.

Doesn't parallax depend on where you measure from?

If we assume measurements taken from earth 6 months apart, we use the earth's own orbit to create the distance.

However, can't we also use probes in Lagrange points and so forth? If we had a telescope on mars using the same earthbound technique, can't we then make parallax measurement up to 1k light years?

It depends on the length of the baseline. Earth based parallax using our own orbit around the sun gives a baseline 2 astronomical units long (the diameter of the orbit). Make the baseline longer, and you can measure smaller parallax, and larger distance, if you have the technology to take advantage of the longer baseline (like precision pointing capability and a point spread function small enough). The Thousand Astronomical Unit mission was a JPL proposal from the 80's to send a telescope out to a distance of 1000 AU, which takes ~50 years with appropriate propulsion. That would allow the parallax to be measured for any star bright enough in the Milky Way, by using the distance between Earth and the spacecraft as a baseline. But it was never funded (the Wiki article links to a couple of PDF reports on the mission).

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One thing I've wondered about is the 2 AU baseline we get by waiting 6 months between images. It's obvious that Earth has moved 2 AU relative to the Sun in this timespan. But the solar system is also moving at a rate of about 24 AU per 6 months in its journey around the galaxy. So why don't 2 images taken 6 months apart give us a baseline of ~24 AU instead?

Could it be that our target stars share our proper motion through space negating much of the baseline caused by the solar system's orbital velocity? Perhaps the 2 AU baseline serves as a cyclical deviation to the otherwise-smooth proper motions of the distant stars.

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Wow. A nice collection of answers, thank you. It's cool to know where parsec comes from!

I thought at some point the angle would get too small to measure, but i didn't realize it wasn't that far. To make sure I'm clear, any stars beyond that point are measured by using radio waves, redshift, and/or standard candles among other methods? Also, am I safe to say the universe, measured solely by parallax is a minimum of 10,000 years; and the fact that measuring is difficult (suggesting great distance) beyond that is highly suggestive of an older age? Granted there are other measurement methods, but I'm looking for what is concrete right now.

I don't have a problem with an old universe, but I have the feeling I am going to be asked about it quite a bit sooner than I hope for. Think of this as a pre-emptive research question. :P

I found a page at talk origins that talks about it briefly at talk origins, but it leaves out some specifics for the sake of brevity. The answers you have given helps with that. Thanks! I put a question in the fourth and fifth sentences. I don't need deep answers, but if anyone has a few minutes I would be grateful!

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Ok, you'll probably laugh at me for posting twice, but first I wanted to respond to my OP and the posts relating to it. I also wanted to throw in two cents about a couple other posts. So I'm posting twice so as not to run them together.

Neverfly--parallax can be used on some stars, that much is true. The question in my mind was the limits on which stars.

Alainprice--I'm not sure simply putting a satellite at an L point would enlarge the baseline enough, but if there was one at each point of two points that could image the same star simultaneously...would that (anyone can answer) help with the issue tony mentioned? Is what tony mentioned (our traveling through the milky way) even an issue?

Just some food for thought/Q and A. I don't know the answers, but I also don't need them for the current issue at hand.

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You are on the track of a good idea. Yes, the main reason we talk about a 2 AU baseline rather than a 24 AU baseline is that the apparent motion of a star due to the Earth's revolution around the Sun makes a very clear signal with a known period; the cyclical nature of this apparent motion allows us to disentangle it from the relative motions of the star and the Sun through space.

But it certainly is true that if you track the apparent motion of a star over a 6-month period, you will in general see the back-and-forth cycle superimposed on straight-line motion. For example, take a look at figure near the bottom of this page:

http://spiff.rit.edu/classes/phys301.../parallax.html

It shows the apparent motion of the star Vega over a period of three years.

If you look at just a single star, you can't be sure what fraction of this straight-line motion is due to the space velocity of the star itself, and what fraction is due to the space velocity of the Sun. On the other hand, if you pick a large sample of stars distributed all over the sky, then you can separate to some extent the motion of the Sun from the motion of the stars. If you pick the sample of stars carefully, you may even be able to use the 24-AU baseline to perform a distance measurement. This idea is behind the methods known as "statistical" and "secular" parallax.

Here is an example of using the observed proper motion of a star to estimate, directly, to within ~5%, a distance that is considerably greater than that which can be determined by '2 au trig parallax' today.

Note that while this technique does not (directly) use the '24 au baseline', VLBI observations of SgrA* do, and when combined with an accurate estimate of the distance to SgrA*, produce some really cool results ...

Yes, they do, but you can still use that longer baseline, although it is difficult to do and not much value. The method is called secular parallax and is mentioned in Ned Wright's ABC's of Distances.

Cosmological redshifts are used to measure the cosmological distance to extremely distant objects outside our own galaxy, like galaxies in distant galaxy clusters or quasars. The distance to individual stars in our own galaxy is most reliably done by parallax. We can derive an estimated distance from the proper motion of a star. We can derive a distance by observing the color & brightness of a star, and using stellar atmosphere models to determine how bright the star really is from its spectral type, the difference between its true and apparent brightness giving the distance. The standard candle method, like Cepheid variables, works well, but only for special types of variable star. The more generic methods work for all stars. We can measure the distance to clusters of stars by main sequence fitting, where a color-magnitude diagram (or Hertzsprung-Russell diagram) is used to measure the main sequence of the cluster, which is then fit to stellar evolution models to derive a distance. If a cluster is near enough, the moving cluster method can be used, which makes use of the parallax of the proper motion of the cluster. If we can see a star, we can estimate its distance one way or the other. See ABC's of Distances.

Well, if we push Hipparcos to its limits, we can maybe measure the parallax of a group of stars or small cluster (but not individual stars) as far away as 1000 parsec (3260 light years, Lotkin & Beshenov, 2001). So if you use that light travel time as a basis for crudely estimating a minimum age of the universe, it would be 3260 years. But since we have written records back about 5,000 years, and reliable archeology of human settlements about twice that far back (i.e., Çatalhöyük), the "parallax age" seems not a very useful concept.

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Ok. Sorry it's taken me so long to get back and read this. Thanks for all the answers, I think this will be enough information to go off as I continue to research.

If I have more questions, or when the little bell in my head rings to say "tada" I'll check back and make sure I'm understanding. Thanks again!

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There is currently another telescope which is designed for astrometry which may yet equal Gaia in accuracy. VERA is looking to do 10 micro-arcsec astrometry with a dual beam radio telescope. There isn't much on the net about it in English though.

You can read some recent results from the VERA project by going to the astro-ph preprint server.

http://arxiv.org/archive/astro-ph

A search using the words "VERA" and "maser" pulls up several papers, including what I believe is their first published result.

http://arxiv.org/abs/0709.0820

Here's the abstract:

Note the size of the uncertainty: 8 micro-arcseconds! Yowza!

Thanks Stupendousman, they hadn't anything published last time I looked. It is a pretty amazing result.