Proper motion is the shift in the celestial position of a star or galaxy due to its intrinsic velocity in a direction perpendicular to our line of site, rather than any apparent shift in position caused by other effects, such as the Earth‘s rotation or parallax.

The proper motions of stars are usually quite small, due to their large distances from the Earth.

Barnard’s star, in the constellation of Ophiuchus, has the largest proper motion, at 10.3 seconds of arc per year. However, this is largely because it is relatively close to the Earth – around 6 light-years away. In contrast, Barnard’s Star has a parallax of around 0.55 arcsecond.

The further away a star is from the Earth, the lower its proper motion would appear to us, for a given intrinsic velocity. Barnard’s star is in fact moving at a velocity of around 142 km/s relative to us, although its transverse velocity (the component of its velocity perpendicular to our line of site, which is responsible for its proper motion) is around 90 km/s.