Editing Proper motion (section)

{{Short description|Measure of observed changes in the apparent locations of stars}}
{{distinguish|proper velocity|stellar parallax}}
[[File:Proper motion.svg|thumb|250px|Relation between proper motion and velocity components of an object.<br>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 = <math>\frac{v_t}{d}</math> where <math>v_t</math> 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.<br>In this diagram the radial velocity happens to be one of the Sun and object parting, so is positive.]]

'''Proper motion''' is the [[astrometry|astrometric]] measure of changes in the [[apparent place]]s of [[star]]s or other [[celestial objects]] as they move relative to the [[center of mass]] of the [[Solar System]]. It is measured relative to the [[fixed stars|distant stars]] or a stable reference such as the [[International Celestial Reference Frame]] (ICRF).<ref name=Koupelis>{{cite book |title=In Quest of the Universe |author=Theo Koupelis |author2=Karl F. Kuhn |page= [https://archive.org/details/inquestofunivers00koup/page/369 369] |url=https://archive.org/details/inquestofunivers00koup |url-access=registration |isbn=978-0-7637-4387-1 |publisher=Jones & Bartlett Publishers |date=2007}}</ref> Patterns in proper motion reveal larger structures like [[Stellar stream|stellar streams]], the general rotation of the [[Milky Way]] disk, and the random motions of stars in the [[Galactic halo]].<ref>{{Cite journal |last=Leeuwen |first=F. van |date=2007-11-01 |title=Validation of the new Hipparcos reduction |url=https://www.aanda.org/articles/aa/abs/2007/41/aa8357-07/aa8357-07.html |journal=Astronomy & Astrophysics |language=en |volume=474 |issue=2 |pages=653–664 |doi=10.1051/0004-6361:20078357 |issn=0004-6361|arxiv=0708.1752 }}</ref>

The components for proper motion in the [[equatorial coordinate system]] (of a given [[epoch (astronomy)|epoch]], often [[J2000.0]]) are given in the direction of [[right ascension]] (''μ''<sub>α</sub>) and of [[declination]] (''μ''<sub>δ</sub>). Their combined value is computed as the ''total proper motion'' (''μ'').<ref name=Birney75>{{cite book |title=Observational Astronomy |author= D. Scott Birney |author2= Guillermo Gonzalez |author3= David Oesper |page= 75 |url=https://books.google.com/books?id=cc9L8QWcZWsC&q=celestial+sphere+%22right+ascension%22&pg=RA1-PA9 |date=2007 |publisher= Cambridge University Press |isbn=978-0-521-85370-5}}</ref><ref name= Green>{{cite book |title=An Introduction to the Sun and Stars |author=Simon F. Green |author2=Mark H. Jones |page= 87 |url=https://books.google.com/books?id=lb5owLGIQGsC&pg=PA87 |isbn=978-0-521-54622-5 |publisher=Cambridge University Press |date=2004}}</ref> It has [[dimension]]s of [[angle]] per [[time]], typically [[arcsecond]]s per [[year]] or milliarcseconds per year.

Knowledge of the proper motion, distance, and [[radial velocity]] allows calculations of an object's motion from the Solar System's [[frame of reference]] and its motion from the galactic frame of reference &ndash; that is motion in respect to the Sun, and by [[coordinate transformation]], that in respect to the [[Milky Way]].<ref name=Birney73>{{cite book |title=Observational Astronomy |author= D. Scott Birney |author2= Guillermo Gonzalez |author3= David Oesper |page= 73 |url=https://books.google.com/books?id=cc9L8QWcZWsC&pg=RA1-PA73 |isbn=978-0-521-85370-5 |date=2007 |publisher=Cambridge University Press}}</ref>