Editing Proper motion (section)

== Usefulness in astronomy ==

Stars with large proper motions tend to be nearby; most stars are far enough away that their proper motions are very small, on the order of a few thousandths of an arcsecond per year.  It is possible to construct nearly complete samples of high proper motion stars by comparing photographic sky survey images taken many years apart. The [[National Geographic Society – Palomar Observatory Sky Survey|Palomar Sky Survey]] is one source of such images. In the past, searches for high proper motion objects were undertaken using [[blink comparator]]s to examine the images by eye. More modern techniques such as [[image differencing]] can scan digitized images, or comparisons to star catalogs obtained by satellites.<ref>{{Cite journal |last1=Akhmetov |first1=V. S. |last2=Fedorov |first2=P. N. |last3=Velichko |first3=A. B. |last4=Shulga |first4=V. M. |date=2017-07-21 |title=The PMA Catalogue: 420 million positions and absolute proper motions |journal=Monthly Notices of the Royal Astronomical Society |volume=469 |issue=1 |pages=763–773 |doi=10.1093/mnras/stx812 |doi-access=free |issn=0035-8711}}</ref> As any [[selection bias]]es of these surveys are well understood and quantifiable, studies have confirmed more and inferred approximate quantities of unseen stars &ndash; revealing and confirming more by studying them further, regardless of brightness, for instance.  Studies of this kind show most of the nearest stars are intrinsically faint and angularly small, such as [[red dwarf]]s.

Measurement of the proper motions of a large sample of stars in a distant stellar system, like a globular cluster, can be used to compute the cluster's total mass via the [[Leonard-Merritt mass estimator]]. Coupled with measurements of the stars' [[radial velocities]], proper motions can be used to compute the distance to the cluster.

Stellar proper motions have been used to infer the presence of a super-massive black hole at the center of the Milky Way.<ref name=Ghez>{{cite journal |journal=Astrophysical Journal |title=The First Measurement of Spectral Lines in a Short-Period Star Bound to the Galaxy's Central Black Hole: A Paradox of Youth |first1=Andrea M. |last1=Ghez |display-authors=etal <!-- Gaspard Duchêne, Keith Matthews, Seth D. Hornstein, Angelle Tanner, James E. Larkin, Margaret Morris, Eric E. Becklin, Samir Salim, Ted Kremenek, David R. Thompson, Baruch T. Soifer, Gerry Neugebauer, Ian S. McLean -->|volume=586 |pages=L127–L131 |date=2003 |arxiv=astro-ph/0302299 |doi=10.1086/374804 |bibcode=2003ApJ...586L.127G |issue=2 |s2cid=11388341 }}</ref> This now confirmed to exist black hole is called [[Sgr A*]], and has a mass of 4.3 × {{Solar mass|10<sup>6</sup>|link=y}} (solar masses).

Proper motions of objects in galaxies in the [[Local Group]] can be used to estimate their distance. In 1999, the proper motion of [[Astrophysical maser|water masers]] moving very rapidly around the center of [[Messier 106|NGC 4258 (M106) galaxy]] was measured via [[Very Long Baseline Interferometry]]. In combination with their radial motion this yielded an accurate distance to the galaxy of {{val|7.2|0.5|u=Mpc}}.<ref name="Weinberg">{{cite book |author=Steven Weinberg |url=https://books.google.com/books?id=48C-ym2EmZkC&q=M33+%22proper+motion%22+date:2007-2010&pg=PA17 |title=Cosmology |date=2008 |publisher=Oxford University Press |isbn=978-0-19-852682-7 |page=17}}</ref><ref name="Hernnstein">{{cite journal |author=J. R. Herrnstein |display-authors=etal |date=1999 |title=A geometric distance to the galaxy NGC4258 from orbital motions in a nuclear gas disk |journal=Nature |volume=400 |issue=6744 |pages=539–541 |arxiv=astro-ph/9907013 |bibcode=1999Natur.400..539H |doi=10.1038/22972 |s2cid=204995005}}</ref> In 2005, the first measurement was made of the proper motion of the [[Triangulum Galaxy]] M33, the third largest and only ordinary spiral galaxy in the Local Group, located 0.860 ± 0.028 Mpc beyond the Milky Way.<ref name=Brunthaler>{{cite journal |journal=Science |volume=307 |pages= 1440–1443 |date=2005 |title=The Geometric Distance and Proper Motion of the Triangulum Galaxy (M33) |author=A. Brunthaler |author2=M.J. Reid |author3=H. Falcke |author4=L.J. Greenhill |author5=C. Henkel  |arxiv=astro-ph/0503058 |doi=10.1126/science.1108342 |pmid=15746420 |issue=5714 |bibcode=2005Sci...307.1440B|s2cid=28172780 }}</ref><ref name="Röser">{{cite book |author=Andreas Brunthaler |title=Reviews in Modern Astronomy: From Cosmological Structures to the Milky Way |date=2005 |publisher=Wiley |isbn=978-3-527-40608-1 |editor=Siegfried Röser |pages=179–194 |chapter=M33 – Distance and Motion |chapter-url=https://books.google.com/books?id=P3FAxGsJ_B8C&q=M33+%22proper+motion%22&pg=PA189}}</ref> The motion of the [[Andromeda Galaxy]] was measured in 2012, and an [[Andromeda–Milky Way collision]] is predicted in about 4.5 billion years.<ref name="Universe Today">{{cite web |last1=Gough |first1=Evan |title=Universe Today |date=12 February 2019 |url=https://www.universetoday.com/141471/thanks-to-gaia-we-now-know-exactly-when-well-be-colliding-with-andromeda/ |publisher=The Astrophysical Journal |access-date=12 February 2019 |ref=utgaia}}</ref>