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| {{confused|proper velocity}}
| | Nice to meet you, my name is Refugia. I am a meter reader. The favorite hobby for my kids and me is to perform baseball and I'm trying to make it a profession. Years ago he moved to North Dakota and his family members loves it.<br><br>Also visit my blog [http://www.btpnadzor.ru/ru/consults/solid-advice-relation-candidiasis http://www.btpnadzor.ru/ru/consults/solid-advice-relation-candidiasis] |
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| The '''proper motion''' of a [[star]] is its angular change in position over time as seen from the [[center of mass]] of the Solar System.<ref name=Koupelis>{{cite book |title=In Quest of the Universe |author=Theo Koupelis, Karl F. Kuhn |page= 369 |url=http://books.google.com/?id=6rTttN4ZdyoC&pg=PA369 |isbn=0-7637-4387-9 |publisher=Jones & Bartlett Publishers |year=2007}}</ref> It is measured in [[arcsecond|seconds of arc]] per year, arcsec/yr, where 3600 arcseconds equal one [[Degree (angle)|degree]].<ref name= Green>{{cite book |title=An Introduction to the Sun and Stars |author=Simon F. Green, Mark H. Jones |page= 87 |url=http://books.google.com/?id=lb5owLGIQGsC&pg=PA87 |isbn=0-521-54622-2 |publisher=Cambridge University Press |year=2004}}</ref> This contrasts with [[radial velocity]], which is the time rate of change in distance toward or away from the viewer, usually measured by [[Doppler shift]] of received radiation. The proper motion is not entirely "proper" (that is, intrinsic to the star) because it includes a component due to the motion of the solar system itself.<ref name=Birney>{{cite book |title=Observational astronomy |author= D. Scott Birney, Guillermo Gonzalez, David Oesper |page= 73 |url=http://books.google.com/?id=cc9L8QWcZWsC&pg=RA1-PA73 |isbn=0-521-85370-2 |year=2007 |publisher=Cambridge University Press}}</ref> Due to the constant, and unvarying speed of light (that is also constant; without regard to whatever is the velocity of the eminating or reflecting source), the true (i.e., instantaneous) velocities of distant stars cannot be observed; the observed proper motion reflects the motion (velocity) of a star at the time the light was emitted from that source. [[File:Proper motion.JPG|thumb |250px |Relation between proper motion and velocity components of an object. At emission, the object was at distance ''d'' from the Sun, and moved at angular rate ''μ'' radian/s, that is, ''μ = v<sub>t</sub> / d'' with ''v<sub>t</sub>'' = velocity transverse to line of sight from the Sun. (The diagram illustrates an angle ''μ'' swept out in unit time at tangential velocity ''v<sub>t</sub>''.)]]
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| == Introduction ==
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| Over the course of centuries, stars appear to maintain nearly fixed positions with respect to each other, so that they form the same [[constellation]]s over historical time. [[Ursa Major]], for example, looks nearly the same now as it did hundreds of years ago. However, precise long-term observations show that the constellations change shape, albeit very slowly, and that each star has an independent [[motion (physics)|motion]].
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| This motion is caused by the true movement of the stars relative to the [[Sun]] and [[solar system]] through space. The Sun travels in a nearly circular orbit (the ''solar circle'') about the center of the [[Milky Way]] at a speed of about 220 km/s at a radius of 8 ± 0.65 k[[Parsec|pc]] from the center,<ref name=Smith>{{cite book |author=Horace A. Smith |isbn=0-521-54817-9 |year=2004 |publisher=Cambridge University Press |title=RR Lyrae Stars |url=http://books.google.com/?id=dMv_r82moCQC&pg=PA80&dq=Galactocentric+%22solar+circle%22 |page= 79 }}</ref><ref name=Combes>{{cite book |title=Mapping the Galaxy and Nearby Galaxies |author=M Reid, A Brunthaler, Xu Ye ''et al.'' |chapter=Mapping the Milky Way and the Local Group |editor=F. Combes, Keiichi Wada |isbn= 0-387-72767-1 |year=2008 |publisher=Springer |url=http://books.google.com/?id=bP9hZqoIfhMC&pg=PA24&dq=rotation+%22proper+motion%22+galaxy+OR+galactic}}</ref> which can be taken as the rate of rotation of the Milky Way itself at this radius.<ref name=Sofue>{{cite journal |arxiv=astro-ph/0010594 |author=Y Sofu & V Rubin |title=Rotation Curves of Spiral Galaxies |year=2001 |journal=Ann. Rev. Astron. Astrophys. |volume=39 |pages=137–174 |doi=10.1146/annurev.astro.39.1.137 |bibcode=2001ARA&A..39..137S}}</ref><ref name=Loeb>{{cite journal |title=Constraints on the proper motion of the Andromeda galaxy based on the survival of its satellite M33 |pages=894–898 |author=Abraham Loeb, Mark J. Reid, Andreas Brunthaler, Heino Falcke |journal=The Astrophysical Journal |volume=633 |year=2005 |url=http://www.mpifr-bonn.mpg.de/staff/abrunthaler/pub/loeb.pdf |doi=10.1086/491644 |bibcode=2005ApJ...633..894L|arxiv = astro-ph/0506609 |issue=2 }}</ref>
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| The proper motion is measured by two quantities: the '''[[position angle]]''' and the '''proper motion''' itself. The first quantity indicates the direction of the proper motion on the [[celestial sphere]] (with 0 degrees meaning the motion is due north, 90 degrees meaning the motion is due east, and so on), and the second quantity gives the motion's magnitude, in [[minute of arc|seconds of arc]] per year.
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| [[File:Components of proper motion.JPG|thumb |200px |Components of proper motion on the [[Celestial sphere]]. The celestial north pole is ''CNP'', the [[vernal equinox]] is ''V'', the star path on the celestial sphere is indicated by arrows. The proper motion vector is '''''μ''''', ''α'' = [[right ascension]], ''δ'' = [[declination]], ''θ'' = [[position angle]]. ]]
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| Proper motion may also be given by the angular changes per year in the [[right ascension]] (''μ<sub>α</sub>'') and [[declination]] (''μ<sub>δ</sub>''). On the [[celestial sphere]], positions are located by latitude and longitude. The coordinate δ corresponds to latitude. The coordinate α corresponds to longitude measured from the [[vernal equinox]] ''V'', the point on the sky where the Sun crosses the celestial equator on near March 21.<ref name=Birney>{{cite book |title=Observational Astronomy |author=D. Scott Birney, Guillermo Gonzalez, David Oesper |isbn=0-521-85370-2 |publisher=Cambridge University Press |year=2006 |page= 8 |url=http://books.google.com/?id=cc9L8QWcZWsC&pg=RA1-PA9}}</ref>
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| The components of proper motion by convention are arrived at as follows. Suppose in a year an object moves from coordinates (α, δ) to coordinates (α<sub>1</sub>, δ<sub>1</sub>), with angles measured in seconds of arc. Then the changes of angle in seconds of arc per year are:<ref name=Smart>{{cite book |title=Textbook on Spherical Astronomy |page= 252 |url=http://books.google.com/?id=W0f2vc2EePUC&pg=PA252 |author=[[William Marshall Smart]], Robin Michael Green |isbn=0-521-29180-1 |publisher=Cambridge University Press |year=1977}}</ref>
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| ::{|
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| |style="text-align: right;"|<math>\ \mu_{\alpha} = \alpha_1 - \alpha \ </math>
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| |-
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| |style="text-align: right;"|<math>\ \mu_{\delta}=\delta_1-\delta \ .</math>
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| |}
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| The magnitude of the proper motion ''μ'' is given by [[Vector_(spatial)#Length|vector addition]] of its components:<ref name=Doolittle>{{cite book |title=A Treatise on Practical Astronomy, as Applied to Geodesy and Navigation |page= 583 |author=Charles Leander Doolittle |url=http://books.google.com/?id=3HoAAAAAMAAJ&pg=RA1-PA583 |publisher=Wiley |year=1890}}</ref><ref name="majewski">{{cite web
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| | last = Majewski | first = Steven R. | year=2006
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| | url = http://www.astro.virginia.edu/class/majewski/astr551/lectures/VELOCITIES/velocities.html
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| | title =Stellar Motions | publisher =University of Virginia
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| | accessdate = 2007-05-14
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| }}</ref>
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| ::{|
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| |style="text-align: right;"|<math>\ \mu^2</math>
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| |<math>={\mu_\delta}^2 + {\mu_\alpha}^2 \cdot \cos^2 \delta \ ,</math>
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| |-
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| |}
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| where ''δ'' is the declination. The factor in ''cos δ'' accounts for the fact that the radius from the axis of the sphere to its surface varies as ''cos δ'', becoming, for example, zero at the pole. Thus, the component of velocity parallel to the equator corresponding to a given angular change in ''α'' is smaller the further north the object's location. The change ''μ<sub>α</sub> '', which must be multiplied by ''cos δ'' to become a component of the proper motion, is sometimes called the "proper motion in right ascension", and ''μ<sub>δ</sub>'' the "proper motion in declination".<ref name=Newcomb>{{cite book |title=The Stars: A study of the Universe |author=Simon Newcomb |pages= 287–288 |url=http://books.google.com/?id=OG1AAAAAIAAJ&pg=PA287 | year=1904 |publisher=Putnam }}</ref>
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| The position angle ''θ'' is related to these components by:<ref name=Birney2>{{cite book |title=''op. cit.'' |author= D. Scott Birney, Guillermo Gonzalez, David Oesper |page= 75 |url=http://books.google.com/?id=cc9L8QWcZWsC&pg=RA1-PA9&dq=celestial+sphere+%22right+ascension%22 |year=2007 |isbn=978-0-521-85370-5}}</ref><ref name=MajewskiNotes>See {{cite web
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| | last = Majewski | first = Steven R. | year=2006
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| | url = http://www.astro.virginia.edu/class/majewski/astr551/lectures/VELOCITIES/velocities.html
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| | title =Stellar motions: parallax, proper motion, radial velocity and space velocity | publisher =University of Virginia
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| | accessdate = 2008-12-31
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| }}</ref>
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| ::{|
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| |-
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| |style="text-align: right;"|<math>\ \mu_\delta</math>
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| |<math>=\mu \cos \theta\ </math>
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| |-
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| |style="text-align: right;"|<math>\ \mu_\alpha \cos \delta</math>
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| |<math>=\mu \sin \theta\ .</math>
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| |}
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| [[Image:Barnard2005.gif|thumb|[[Barnard's Star]], showing position every 5 years 1985–2005.]]
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| [[Barnard's star]] has the largest proper motion of all stars, moving at 10.3 [[arcsecond|seconds of arc]] per year. Large proper motion is usually a strong indication that a star is relatively close to the Sun. This is indeed the case for Barnard's Star which, at a distance of about 6 [[light-year]]s, is, after the Sun and the [[Alpha Centauri]] system, the [[List of nearest stars|nearest]] known star to Earth (yet, being a [[red dwarf]], too faint to see without a [[telescope]] or powerful binoculars, with an [[apparent magnitude]] of 9.54).
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| In 1992, [[Rho Aquilae]] became the first star to have its [[Bayer designation]] invalidated by moving to a neighbouring constellation - it is now a star of the
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| constellation [[Delphinus]].<ref name="jrasc92">{{cite journal
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| | title = Book-Review - Sky Catalogue 2000.0 - V.1 - Stars to Magnitude 8.0 ED.2
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| | year = 1992
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| | bibcode = 1992JRASC..86..221H
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| | author1 = Hirshfeld
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| | first1 = A.
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| | last2 = Sinnott
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| | first2 = R. W.
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| | last3 = Ochsenbein
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| | first3 = F.
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| | last4 = Lemay
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| | first4 = D.
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| | volume = 86
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| | pages = 221
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| | journal = Journal of the Royal Astronomical Society of Canada
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| }}</ref> This will next happen to [[Gamma Caeli]],{{dubious|date=April 2012}}
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| which is due to become a star of the constellation [[Columba (constellation)|Columba]] in the year 2400.<ref name="hamilton96">{{cite web
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| | url = http://amateurastronomy.org/EH/Jun96.txt
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| | title = Hamilton Amateur Astronomers
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| | year = 1996
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| | accessdate = 2008-05-16
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| }}</ref>
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| A proper motion of 1 arcsec per year at a distance of 1 light-year corresponds to a relative transverse speed of 1.45 km/s. For Barnard's star this works out to 90 km/s; including the radial velocity of 111 km/s (which is at right angles to the transverse velocity) gives a true motion of 142 km/s. True or absolute motion is more difficult to measure than the proper motion, as the true transverse velocity involves the product of the proper motion times the distance; that is, true velocity measurements depend on distance measurements, which are difficult in general. Currently, the nearby star with the largest true velocity (relative to the Sun) is [[Wolf 424]] which moves at 555 km/s (or 1/540 of the speed of light).
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| == Usefulness in astronomy ==
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| 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, but modern efforts use techniques such as [[image differencing]] to automatically search through digitized image data. Because the [[selection bias]]es of the resulting high proper motion samples are well-understood and well-quantified, it is possible to use them to construct an unbiased census of the nearby stellar population — how many stars exist of each true brightness, for example. Studies of this kind show that the local population of stars consists largely of intrinsically faint, inconspicuous stars such as [[red dwarf]]s.
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| 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.
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| 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 |author=AM Ghez ''et al.'' |volume=586 |pages=L127–L131 |year=2003 |arxiv=astro-ph/0302299 |doi=10.1086/374804 |bibcode=2003ApJ...586L.127G |issue=2}}</ref> This black hole is suspected to be [[Sgr A*]], with a mass of 2.6 × 10<sup>6</sup> M<sub>☉</sub>, where M<sub>☉</sub> is a [[solar mass]].
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| Proper motions of the galaxies in the [[Local Group]] are discussed in detail in Röser.<ref name= Röser>{{cite book |title=Reviews in Modern Astronomy: From Cosmological Structures to the Milky Way |author=Andreas Brunthaler |editor=Siegfried Röser |pages=179–194 |chapter= M33 – Distance and Motion|url=http://books.google.com/?id=P3FAxGsJ_B8C&pg=PA189&dq=M33+%22proper+motion%22 |isbn=3-527-40608-5 |publisher=Wiley |year=2005}}</ref> In 2005, the first measurement was made of the proper motion of the [[Triangulum Galaxy]] M-33, the third largest and only ordinary spiral galaxy in the Local Group, located 860 ± 28 kpcs beyond the Milky Way.<ref name=Brunthaler>{{cite journal |journal=Science |volume=307 |pages= 1440–1443 |year=2005 |title=The Geometric Distance and Proper Motion of the Triangulum Galaxy (M33) |author=A. Brunthaler, M.J. Reid, H. Falcke, L.J. Greenhill, C. Henkel |arxiv=astro-ph/0503058 |doi=10.1126/science.1108342 |pmid=15746420 |issue=5714 |bibcode=2005Sci...307.1440B}}</ref> Although the [[Andromeda Galaxy]] is known to move, and an [[Andromeda–Milky Way collision]] is predicted in about 5 – 10 billion years, the proper motion of the Andromeda galaxy, about 786 kpc distant, is still an uncertain matter, with an upper bound on its transverse velocity of ≈ 100 km/s.<ref name=Loeb>{{cite journal |journal=The Astrophysical Journal |title=Constraints on the proper motion of the Andromeda galaxy based on the survival of its satellite M33 |volume=633 |pages=894–898 |year=2005 |author=A Loeb ''et al.''|arxiv = astro-ph/0506609 |bibcode = 2005ApJ...633..894L |doi = 10.1086/491644 |issue=2 }}</ref><ref name=Marel>{{cite journal |title=M31 Transverse Velocity and Local Group Mass from Satellite Kinematics |author=Roeland P. van der Marel |journal=The Astrophysical Journal |volume=678 |pages=187–199 |year=2008 |doi=10.1086/533430 |bibcode=2008ApJ...678..187V|arxiv = 0709.3747 }}</ref><ref name=Metz>{{cite journal |title=The spatial distribution of the Milky Way and Andromeda satellite galaxies |author=Manuel Metz, Pavel Kroupa, Helmut Jerjen |year=2007 |arxiv=astro-ph/0610933 |journal=Mon. Not. Roy. Astron. Soc. |volume=374 |pages=1125–1145 |doi=10.1111/j.1365-2966.2006.11228.x |bibcode=2007MNRAS.374.1125M |issue=3}}</ref> Proper motion of the [[Messier 106|NGC 4258 (M106) galaxy]] in the M106 group of galaxies was used in 1999 to find an accurate distance to this object.<ref name=Weinberg>{{cite book |title=Cosmology |author= Steven Weinberg |page= 17 |url=http://books.google.com/?id=48C-ym2EmZkC&pg=PA17&dq=M33+%22proper+motion%22+date:2007-2010 |isbn=0-19-852682-2 |year=2008 |publisher=Oxford University Press}}</ref> Measurements were made of the radial motion of objects in that galaxy moving directly toward and away from us, and assuming this same motion to apply to objects with only a proper motion, the observed proper motion predicts a distance to the galaxy of 7.2 ± 0.5 Mpc.<ref name=Hernnstein>{{cite journal |journal=Nature |year= 1999 |volume=400 |pages=539–541 |title=A geometric distance to the galaxy NGC4258 from orbital motions in a nuclear gas disk |author=J. R. Herrnstein ''et al.'' |url=http://www.nature.com/nature/journal/v400/n6744/abs/400539a0.html| doi= 10.1038/22972|arxiv = astro-ph/9907013 |bibcode = 1999Natur.400..539H |issue=6744}}</ref>
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| == History ==
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| Proper motion was suspected by early astronomers (according to [[Macrobius]], AD 400) but proof was provided in 1718 by [[Edmund Halley]], who noticed that [[Sirius]], [[Arcturus]] and [[Aldebaran]] were over half a degree away from the positions charted by the ancient Greek astronomer [[Hipparchus]] roughly 1850 years earlier.<ref name=Neugebauer>{{cite book |title=A History of Ancient Mathematical Astronomy |author=Otto Neugebauer |url=http://books.google.com/?id=vO5FCVIxz2YC&pg=PA1085&dq=proper+motion+angle |page= 1084 |isbn=3-540-06995-X |publisher=Birkhäuser |year=1975}}</ref>
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| The term "proper motion" derives from the historical use of "proper" to mean "belonging to" (cf, ''propre'' in French and the common English word ''property''). There is no such thing as "improper motion" in astronomy.<ref name=Koupelis/>
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| == Stars with high proper motion ==
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| The following are the stars with highest proper motion from the ''[[Hipparcos]]'' catalog.<ref>{{cite web
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| | author=Staff
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| | date=September 15, 2003
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| | url=http://www.rssd.esa.int/SA-general/Projects/Hipparcos/table362.html
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| | title=The 150 Stars in the Hipparcos Catalogue with Largest Proper Motion
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| | publisher=ESA
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| | accessdate=2007-07-21 }}</ref>See [[List of stars in the Hipparcos Catalogue]]. It does not include stars such as [[Teegarden's star]] which are too faint for that catalog. A more complete list of stellar objects can be made by doing a Criteria query at http://simbad.u-strasbg.fr/simbad/ .
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| [[File:61 Cygni Proper Motion.gif|thumb|Proper motion of [[61 Cygni]] in about one year: 2012-11-19 - 2013-11-08.]]
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| {| class="wikitable"
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| |+ Highest proper motion stars<ref>{{cite web
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| | url = http://simbad.u-strasbg.fr/simbad/
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| | title=SIMBAD
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| | publisher = Centre de Données astronomiques de Strasbourg
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| | accessdate = 2007-07-21 }}</ref>
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| |-
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| !rowspan="2"| #
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| !rowspan="2"| Star
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| !colspan="2"| Proper motion
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| !rowspan="2"| Radial<br />velocity<br />(km/s)
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| !rowspan="2"| Parallax<br />(mas)
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| |-
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| ! μ<sub>α</sub> · cos δ<br />(mas/yr)
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| ! μ<sub>δ</sub><br />(mas/yr)
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| |-
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| | 1
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| | [[Barnard's star]]
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| |style="text-align: right;"| -798.71
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| |style="text-align: right;"| 10337.77
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| |style="text-align: center;"| -106.8
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| |style="text-align: right;"| 549.30
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| |-
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| | 2
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| | [[Kapteyn's star]]
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| |style="text-align: right;"| 6500.34
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| |style="text-align: right;"| -5723.17
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| |style="text-align: center;"| +245.5
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| |style="text-align: right;"| 255.12
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| |-
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| | 3
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| | [[Groombridge 1830]]
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| |style="text-align: right;"| 4003.69
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| |style="text-align: right;"| -5814.64
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| |style="text-align: center;"| -98.0
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| |style="text-align: right;"| 109.22
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| |-
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| | 4
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| | [[Lacaille 9352]]
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| |style="text-align: right;"| 6766.63
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| |style="text-align: right;"| 1327.99
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| |style="text-align: center;"| +9.7
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| |style="text-align: right;"| 303.89
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| |-
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| | 5
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| | [[Gliese 1]] (CD -37 15492) (GJ 1)
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| |style="text-align: right;"| 5633.95
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| |style="text-align: right;"| -2336.69
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| |style="text-align: center;"| +23.6
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| |style="text-align: right;"| 229.32
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| |-
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| | 6
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| | [[HIP 67593]]
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| |style="text-align: right;"| 2282.15
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| |style="text-align: right;"| 5369.33
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| |style="text-align: center;"| —
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| |style="text-align: right;"| 76.20
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| |-
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| | 7
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| | [[61 Cygni]] A & B
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| |style="text-align: right;"| 4133.05
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| |style="text-align: right;"| 3201.78
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| |style="text-align: center;"| -64.3
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| |style="text-align: right;"| 287.18
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| |-
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| | 8
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| | [[Lalande 21185]]
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| |style="text-align: right;"| -580.46
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| |style="text-align: right;"| -4769.95
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| |style="text-align: center;"| -85.0
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| |style="text-align: right;"| 392.52
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| |-
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| | 9
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| | [[Epsilon Indi]]
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| |style="text-align: right;"| 3961.41
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| |style="text-align: right;"| -2538.33
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| |style="text-align: center;"| -40.4
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| |style="text-align: right;"| 275.79
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| |}
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| ==Software==
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| There are a number of software products that allow a person to view the proper motion of stars over differing time scales. Two free ones are:
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| * [http://t.nomoto.org/HippLiner/index-e.html HippLiner] - Freeware - Windows, Moderately sophisticated, with some pretty displays. Still under development, needs some more navigation and configuration features.
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| * [http://www.xephem.com XEphem] - Freeware - Linux and Apple OS X - complete astrometry package, can view a region of the sky, set a time step, and watch stars move over time.
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| ==See also==
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| *[[Radial velocity]]
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| *[[Peculiar motion]]
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| *[[Solar apex]]
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| *[[Leonard-Merritt mass estimator]]
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| *[[Very Long Baseline Interferometry]]
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| *[[Galaxy rotation curve]]
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| *[[Celestial coordinates]]
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| *[[Milky Way]]
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| ==References==
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| {{reflist}}
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| == External links ==
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| * [http://www.rssd.esa.int/index.php?project=HIPPARCOS&page=high_p Hipparcos: High Proper Motion Stars]
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| * [http://www.leosondra.cz/en/halley-proper-motions/ Edmond Halley: Discovery of proper motions]
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| {{Star}}
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| {{DEFAULTSORT:Proper Motion}}
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| [[Category:Astrometry]]
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| [[Category:Stellar astronomy]]
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