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I am not completely sure whether the Parallax is a "technique to measure the star distances" or a "tiny shift in star's position"?

The a book says two points about Parallax:

  • Astronomers have developed a variety of clever techniques for measuring the vast distances to stars, one is called Parallax.

  • Astronomers can measure a star's position once and then again 6 months later and calculate the apparent change in position. This tiny shift in stars position is called its parallax.

Apart from the book source, whatis.techtarget.com defines Parallax as the way an object’s position or direction seems to change depending on viewing angle.

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    $\begingroup$ You are presenting this as if it's one or the other, but not both. The answer is that both are true. Annual parallax is a tiny shift that varies inversely with distance. This means that the observed shift can be used as a way to measure distance. $\endgroup$ – David Hammen Nov 29 '18 at 8:11
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    $\begingroup$ Parallax is something you can see on earth. Eg, if you're traveling by vehicle and look out the window, the nearby trees appear to pass very quickly, the houses further away appear to pass slowly, and the distant mountains more slowly still. Parallax scrolling is used in video games to give the illusion of distance: en.wikipedia.org/wiki/Parallax_scrolling#/media/… I think the idea in astronomy is that as the earth moves, the things that appear most stationary must be farthest away, like the distant mountains on Earth. $\endgroup$ – Nathan Long Nov 29 '18 at 19:14
  • $\begingroup$ BTW, welcome to Astronomy.SE! $\endgroup$ – David Hammen Nov 30 '18 at 5:56
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It is both - a small shift of the position of a star on the sky as we see it, and a means of estimating the distance to the star.

The apparent position (with respect to very distant objects like quasars) changes because our viewing point changes as the Earth moves around the Sun in its orbit. The amount by which the position changes is inversely proportional to is distance.

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It's all of that! If you look at an object with just your left, and then with just your right eye, you'll see its position slightly differently. The angle that your lines of sight form (from one eye to the object, and from the other), divided by two, is called "parallax angle". With trigonometry, one can calculate the distance to the object by knowing this angle and the distance between your eyes. Instead of the eyes, astronomers typically use the distance from the Earth to the Sun, by observing when the Earth is at diametrically opposite points during its orbit (approximately). See: https://en.m.wikipedia.org/wiki/Parallax under "distance measurement" for more details.

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It is both

But, specifically, the small motion is what we observe of the star at opposing points of Earth's orbit around the Sun. Then, because we know the radius of that orbit (1 AU) we can use the parallax, the observed small angular change in the location of a star against a distant background between opposite sides of the Earth's orbit, to make a parallax estimate of the star's distance, which is the inverse of small angular change (in radians) in units of parsecs.

enter image description here

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It is really just imprecise language in the first example.

Parallax is the change in apparent position. To be formally correct, you measure or observe parallax and use it, with trigonometry, to determine the distance.

You can call this the parallax method of distance measurement. What you have found is that people often omit the word "method".

More precise language would be either:

Astronomers have developed a variety of clever techniques for measuring the vast distances to stars. One uses an effect called parallax.

Astronomers have developed a variety of clever techniques for measuring the vast distances to stars, one is by measuring parallax.

Astronomers have developed a variety of clever techniques for measuring the vast distances to stars. The parallax method is one of them.

A similar issue comes up with "Doppler".

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