Proper Motion

Sometimes, a star does not move along your line of sight to give a radial velocity. Instead, it may move across your line of sight and the motion your perceive is called its proper motion.


Proper motion is measured in arcseconds per year and the largest determined is for Barnard's Star with a proper motion of 10.3"/year. This means for Barnard's Star, it would take about 18,540 years to move the apparent diameter of the Moon (0.5°).

By using parallax to determine the star's distance, we can calculate the transverse velocity of the star. By then combining the radial velocity of the star with transverse velocity, and using the Pythagorean theorem (c²=a²+b²), we can determine the space velocity.