
The apparent angular shift of a star across the sky per unit time.Proper motion is the apparent angular shift of a star's position on the celestial sphere per unit time, caused by the star's actual motion through space relative to the Sun. It is measured in arcseconds per year and is a key component in understanding stellar kinematics, including the movement of stars within our galaxy. Proper motion, combined with radial velocity, gives the full three-dimensional velocity of a star.
The concept was first quantified by Edmond Halley in 1718, who noticed that Sirius, Arcturus, and Aldebaran had moved from their ancient Greek positions.
Astronomers measure a star's position at two different epochs, typically years apart, and calculate the angular difference. This shift is then divided by the time interval to obtain the proper motion. The motion is apparent because it is projected onto the sky, and it arises from the star's transverse velocity relative to the Sun. High proper motion often indicates a nearby star or one moving rapidly through the galaxy.
Proper motion is used to identify nearby stars, study the structure and dynamics of the Milky Way, and detect exoplanets via astrometric wobbles, as done by missions like Gaia.
Barnard's Star has the largest known proper motion of any star, moving across the sky by 10.3 arcseconds per year.









