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Why / why not?
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Yes,in fact they are constantly changing. The reason is precession of the eqinoxes, the slight wobble in the Earth’s axis over a 26,000 year period. RA and Dec must always be at a specified epoch, the one currently being used being 2000.0.
Plus they all have “proper motion”, so they wander… some hardly at all, some quite a bit, with Barnard’s Star being the big mover.
the sun changes ra/dec position all the time!
To obtain a system with horizontal and vertical coordinates of our spherical sky, we always take the movement of our star sky due to earth’s rotation. We first have to look what the celestial north pole is (the elongated direction of earth’s axis, and all stars seem to turn around it), then we can also draw a celestial equator (shall be parallel with earth’s equator)
But yes, like Geoff says, the direction of earth’s axis changes. So after a long time we have new celestial poles and a new celestial equator. That is why the position of stars also shall take other values for the Right Ascension and Declination in our invented coordinate system.