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I understand the basics of how parallax is measured (i.e. two measurements 6 months apart), but I also understand that, in reality, it would have to be more complicated than that, because stellar parallax isn't the only thing that affects a star's position in the sky. Proper motion, stellar aberration, refraction (only an issue on the ground), and planetary nutation are all things that will affect a star's position in the sky.

So, how do astronomers filter out all those effects to actually measure the parallax?

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  • $\begingroup$ Not really sure what kind of answer you are expecting here. Basically, the effects that are important are modelled along with the parallax and proper motion and the model compared with a time-series of apparent positions on the sky. $\endgroup$
    – ProfRob
    Commented Jul 21, 2023 at 9:19
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    $\begingroup$ I almost wrote an answer based on ProfRob's comment but the details depend on where the data is from and how accurate you need it. You get a large set of images over as much of the year as you can for many years, and using nearby stars in the same field extract the apparent motion of the star. The stellar aberration and refraction effects relative to other stars a fraction of a degree away will be minimal, but if you need to account for it you can. As explained, you build a model that has all effects you worry about as parameters, then vary them to fit your data and estimate errors on each. $\endgroup$
    – uhoh
    Commented Jul 21, 2023 at 12:17
  • $\begingroup$ You also need to check for sensitivities and correlations to make sure you can't vary two or three parameters simultaneously and end up with similar fits from different combinations. $\endgroup$
    – uhoh
    Commented Jul 21, 2023 at 12:18
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    $\begingroup$ The ICRS has "defining sources", today that is the GAIA catalog for optical sources. So you would just compare objects in the image to those of known objects. Since the GAIA measurements were done in space, many of the variables were eliminated, and the stars were compared against the very distant stars that didn't move. $\endgroup$ Commented Jul 21, 2023 at 12:55
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    $\begingroup$ Put @uhoh and GregMiller's comments together with some references and you have an answer that covers to present practice. Key point is that it's done with respect to other stars, not based on the measurement of where in the sky the telescope is pointing. $\endgroup$
    – antlersoft
    Commented Jul 21, 2023 at 14:21

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Leaving aside the Gaia satellite, traditional measures of parallax are done with measurements of the location of stars on photographs.

The key fact here is that you measure the location of a star relative to other stars. This has the effect of stripping out refraction and nutation from the data, as these affect all stars (in a small part of the sky viewed through a telescope) equally.

You get, over several observations, multiple positions for the star relative to the background. To these you fit a "corkscrew" shape, which is a combination of the proper motion and the parallax (depending on the motion, the corkscrew might actually be a cycloid or a wave shape). Three observations are enough to find which combination of parallax and proper motion fit the observations of the star.

This still from an ESA video shows the principle:

enter image description here

But there are lots of practical difficulties. For relatively nearby stars (Barnards star, Proxima etc) the parallax and proper motion is much larger than that of the background stars, but for measurements of more distant stars, the "background" may actually be as close or closer than than the star of interest, and so will also show parallax. The video shows this well. You need to pick out the more distant stars to establish what "still" means in order to know what "moving" means. If there is a quasar in view, this can provide an excellent base point, since quasars are so distant that they show absolutely no motion. The positions of other stars can then be plotted or triangulated relative to quasars.

Moreover, the "blur" from the atmosphere may mean that each star actually appears as a relatively large "blob" in the image and not the crisp point, so identifying motion is practically difficult.

However the key points are "measure relative to background stars" and "take at least three measurements". And with this you can, in theory, find both parallax and proper motion.

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    $\begingroup$ Aren't there 5 parameters to be determined - position, parallax and proper motion? $\endgroup$
    – ProfRob
    Commented Jul 23, 2023 at 12:08
  • $\begingroup$ If this answer linked to and drew from an actual authoritative source, that source would provide the correct number of parameters. When we "wing it" and write off the top of our heads (because it's faster and "more efficient" (delta-reputation per minute) that way) answer quality inevitably suffers. $\endgroup$
    – uhoh
    Commented Jul 24, 2023 at 3:57
  • $\begingroup$ The ESA not authoritative enough? $\endgroup$
    – James K
    Commented Jul 24, 2023 at 7:42

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