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(astronomy) The change in apparent position of a celestial body due to that body's velocity relative to the Sun.

Relation between proper motion and velocity components of an object. A year ago the object was d units of distance from the Sun, and its light moved in a year by angle μ radian/s. If there has been no distortion by gravitational lensing or otherwise then μ = ${\displaystyle {\frac {v_{t}}{d}}}$ where ${\displaystyle v_{t}}$ is the distance (usually expressed as annual velocity) transverse (tangential or perpendicular) to line of sight from the Sun. The angle is shaded light blue from the Sun to the object's start point and its year later position as if it had no radial velocity. In this diagram the radial velocity happens to be one of the Sun and object parting, so is positive.

(astronomy) The change in apparent position of a celestial body due to that body's velocity relative to the Sun.

The celestial north and south poles are above/below CNP, CSP; the origin of all 24 hours of Right Ascension (the measure of absolute celestial east–west position), the March equinox (center of the sun's position then) at the J2000 epoch, is vector V. In red the diagram adds the components of proper motion across the celestial sphere. An ideal time to measure exactly such a small annual shift is at culmination. The culmination of the star is daily reached when the observer (and Earth) passes as shown by the blue arrows "beneath" the star. The positive axes of the two components of its usually annually measured or published shift in proper motion are the exaggerated red arrows, note: the right arrows point to the east horizon. One red annotation is subtly shorter as the cosine of a star resting at 0° declination is 1, so such a star's east or west shift would not need to be multiplied by the cosine of its declination. The proper motion vector is μ, α = right ascension, δ = declination, θ = position angle.

(astronomy) The change in apparent position of a celestial body due to that body's velocity relative to the Sun.

Barnard's Star, showing position every 5 years 1985–2005.