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Dustin wrote: "So most stars don't move much."
Yes and no.
While stellar parallax is rather small, less than 1 arcsec for all
known stars, each of aberration and nutation can reach up to 20 arcsec
or so. The latter pair are of no interest for solving to a specific
epoch such as 2000.0 as used in the astronomy.net tables. All these effects change the observed position cyclically over the course of the year.
The killer, though, is proper motion which is cumulative (positions
change in a specific direction and its magnitude always increases); a
motion of 1 arcsec per annum is not too unusual and > 0.3 arcsec per decade
is rather common. The extreme example is Barnard's star which moves by
about 9 arcsec every year. I have an animated GIF made from images I took each summer which shows it moving against
the background stars. It is really quite remarkable.
Now the above might sound rather theoretical and inconsequential, but I
have been badly bitten by proper motion. AAVSO provides positions of
variable and comparison stars. All their positions are precessed to J2000 but
the underlying astrometry often dates back to the 1950s. On numerous occasions, matching AAVSO data with Gaia-EDR3 values has required human intervention because
the stars have moved by several arcsec in the interim.
Paul