Proper motion star

Proper motion is the astronomical measure of the observed changes in apparent positions of stars in the sky as seen from the center of mass of the Solar System compared to the imaginary fixed background of the more distant stars.

The components of proper motion in the equatorial coordinate system (of a given epoch, usually J2000.0) are measured in seconds of time for right ascension (RA or α) and seconds of arc in declination (Dec. or δ). Their combined value is computed as the total proper motion (μ), which is expressed in seconds of arc per year (arcsec/yr) or per century (arcsec/100yr), where 3600 arcseconds equal one degree. Because most proper motions are much less than one arcsec per year, most modern catalogues, like the Hipparcos Index Catalogue (HIP), now express proper motion in terms of milliarcseconds per year (mas/yr), where 1000 mas equals one arcsecond. This transverse sky motion is separate from the radial velocity, being the velocity moving toward or away from the observer in kilometres per second (km/s), as obtained from the Doppler shifts in starlight seen with a spectroscope. Knowledge of the proper motion, distance, and radial velocity allow approximate calculations of a star's true motion in space in respect to the Sun.

Proper motion is not entirely "proper" (that is, intrinsic to the star), because it includes a component due to the motion of the Solar System itself.

Over the course of centuries, stars appear to maintain nearly fixed positions with respect to each other, so that they form the same constellations over historical time. Ursa Major or Crux, for example, looks nearly the same now as they did hundreds of years ago. However, precise long-term observations show that the constellations change shape, albeit very slowly, and that each star has an independent motion.

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