Proper motion - wikipedia Proper motion Not to be confused with proper velocity. 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 / d with v = the component of velocity transverse to line of sight from the Sun. ( The diagram illustrates an angle μ swept out in unit time at tangential velocity v. ) Proper motion is the astronomical measure of the observed changes in the apparent places of stars in the sky, as seen from the center of mass of the Solar System, compared to the abstract background of the more distant stars. The components of proper motion in the equatorial coordinate system ( of a given epoch, usually J2000. 0 ) are measured in seconds of time for right ascension ( RA or α ) and seconds of arc in declination ( dec. or δ ). Their combined value is computed as the total proper motion ( μ ), which is expressed in arcseconds per year ( arcsec / yr ) or per century ( arcsec / 100 yr ), where 3600 arcseconds equal one degree. Because most proper motions are much less than one arcsec per year, most modern catalogues, like the Hipparcos Index Catalogue ( HIP ), now express proper motion in terms of milliarcseconds per year ( mas / yr ), where 1000 mas equals one arcsecond. This transverse sky motion is separate from the radial velocity, being the velocity moving toward or away from the observer in kilometres per second ( km / s ), as obtained from the Doppler shifts in starlight seen with a spectroscope. Knowledge of the proper motion, distance, and radial velocity allow approximate calculations of a star 's true motion in space in respect to the Sun. 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. Contents 1 Introduction 2 Examples 3 Usefulness in astronomy 4 History 5 Stars with high proper motion 6 Software 7 See also 8 References 9 External links Introduction Proper motion is part of the intrinsic `` property '' of a star and involves its actual movement through space. By contrast, these photographic star trails are due to the Earth 's rotation while using a long exposure. This image of star trails at twilight was produced by combining 763 different 20 - second exposures. Over the course of centuries, stars appear to maintain nearly fixed positions with respect to each other, so that they form the same constellations over historical time. Ursa Major or Crux, for example, looks nearly the same now as they 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. This motion is caused by the movement of the stars relative to the Sun and Solar System. 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 7000800000000000000 ♠ 8 ± 0.65 kPc from the center, which can be taken as the rate of rotation of the Milky Way itself at this radius. The proper motion is a two - dimensional vector ( because it excludes the component in the direction of the line of sight ) and is thus defined by two quantities : its position angle and its magnitude. 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 is the motion 's magnitude, expressed in seconds of arc per year. 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. Proper motion may alternatively be defined by the angular changes per year in the star 's right ascension ( μ ) and declination ( μ ), using a constant epoch in defining these. 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, δ ), with angles measured in seconds of arc. Then the changes of angle in seconds of arc per year are : μ α = α 1 − α ( displaystyle mu _ ( alpha ) = alpha _ ( 1 ) - alpha ) μ δ = δ 1 − δ. ( displaystyle mu _ ( delta ) = delta _ ( 1 ) - delta . ) The magnitude of the proper motion μ is given by vector addition of its components : μ 2 ( displaystyle mu ^ ( 2 ) ) = μ δ 2 + μ α 2 ⋅ cos 2 ⁡ δ ( displaystyle = ( mu _ ( delta ) ) ^ ( 2 ) + ( mu _ ( alpha ) ) ^ ( 2 ) cdot cos ^ ( 2 ) delta ), μ 2 ( displaystyle mu ^ ( 2 ) ) = μ δ 2 + μ α ∗ 2 ( displaystyle = ( mu _ ( delta ) ) ^ ( 2 ) + ( mu _ ( alpha ast ) ) ^ ( 2 ) ) 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, 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 the `` proper motion in declination ''. If the proper motion in right ascension has been converted by cos δ into either arcsecond or milliarcsecond, the result is expressed as μ ( ' mu alpha asterisk ' ), i.e. the proper motion results in right ascension within the Hipparcos Catalogue ( HIP ) are expressed in the right ascension mas / yr, and therefore have already been converted. Hence, the individual proper motions in right ascension and declination are made equivalent for straightforward calculations of various other stellar motions. Position angle θ is related to these components by : μ δ ( displaystyle mu _ ( delta ) ) = μ cos ⁡ θ ( displaystyle = mu cos \theta ) μ α cos ⁡ δ ( displaystyle mu _ ( alpha ) cos delta ) = μ sin ⁡ θ ( displaystyle = mu sin \theta ) μ α ∗ ( displaystyle mu _ ( alpha ast ) ) = μ sin ⁡ θ ( displaystyle = mu sin \theta ) Motions in equatorial coordinates can be converted to motions in galactic coordinates. Examples For the majority of stars seen in the sky, the observed proper motions are usually small and unremarkable. Such stars are often either faint or are significantly distant, have changes of below 10 milliarcseconds per year, and do not appear to move appreciably over many millennia. A few do have significant motions, and are usually called high - proper motion stars. Motions can also be in almost seemingly random directions. Two or more stars, double stars or open star clusters, which are moving in similar directions, exhibit so - called shared or common proper motion ( or cpm. ), suggesting they may be gravitationally attached or share similar motion in space. Barnard 's Star, showing position every 5 years 1985 -- 2005. Barnard 's star has the largest proper motion of all stars, moving at 10.3 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, located at a distance of about 6 light - years. After the Sun and the Alpha Centauri system, it is the nearest known star to Earth. Because it is a red dwarf with an apparent magnitude of 9.54, it is too faint to see without a telescope or powerful binoculars. 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. Barnard 's star 's transverse speed is 90 km / s and its radial velocity is 111 km / s ( which is at right angles to the transverse velocity ), which gives a true motion of 142 km / s. True or absolute motion is more difficult to measure than the proper motion, because the true transverse velocity involves the product of the proper motion times the distance. As shown by this formula, 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. 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 constellation Delphinus. 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 Palomar Sky Survey is one source of such images. In the past, searches for high proper motion objects were undertaken using blink comparators 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 biases 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 dwarfs. 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. This black hole is suspected to be Sgr A *, with a mass of 4.2 × 10 M, where M is the solar mass. Proper motions of the galaxies in the Local Group are discussed in detail in Röser. 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. The motion of the Andromeda Galaxy was measured in 2012, and an Andromeda -- Milky Way collision is predicted in about 4 milliard years. Proper motion of the NGC 4258 ( M106 ) galaxy in the M106 group of galaxies was used in 1999 to find an accurate distance to this object. 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 7023222168785865637 ♠ 7.2 ± 0.5 Mpc. History Proper motion was suspected by early astronomers ( according to Macrobius, AD 400 ) but a proof was not provided until 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. 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 ). `` Improper motion '' would refer to `` motion '' common to all stars, such as due to axial precession. Stars with high proper motion The following are the stars with highest proper motion from the Hipparcos catalog. 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 the SIMBAD astronomical database. Proper motion of 61 Cygni in one year intervals. Highest proper motion stars # Star Proper motion Radial velocity ( km / s ) Parallax ( mas ) μ cos δ ( mas / yr ) μ ( mas / yr ) Barnard 's star − 798.58 10328.12 − 110.51 548.31 Kapteyn 's star 6505.08 − 5730.84 + 245.19 255.66 Groombridge 1830 4003.98 − 5813.62 − 98.35 109.99 Lacaille 9352 6768.20 1327.52 + 8.81 305.26 5 Gliese 1 ( CD − 37 15492 ) ( GJ 1 ) 5634.68 − 2337.71 + 25.38 230.42 6 HIP 67593 2118.73 5397.57 - 4.4 187.76 7 61 Cygni A & B 4133.05 3201.78 − 65.74 286 8 Lalande 21185 − 580.27 − 4765.85 − 84.69 392.64 9 Epsilon Indi 3960.93 − 2539.23 − 40.00 276.06 Software There are a number of software products that allow a person to view the proper motion of stars over differing time scales. Free ones include : HippLiner Windows, Moderately sophisticated, with some pretty displays. Still under development, needs some more navigation and configuration features. XEphem 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. Proper Motion Simulator Website - Runs in your browser. Watch the positions of the stars change with time. Fly through the constellations to get a sense of their volume. See also Radial velocity Peculiar motion Relative velocity Space velocity ( astronomy ) Solar apex Leonard - Merritt mass estimator Very Long Baseline Interferometry Galaxy rotation curve Celestial coordinates Milky Way References Jump up ^ Theo Koupelis ; Karl F. Kuhn ( 2007 ). In Quest of the Universe. Jones & Bartlett Publishers. p. 369. ISBN 0 - 7637 - 4387 - 9. ^ Jump up to : D. Scott Birney ; Guillermo Gonzalez ; David Oesper ( 2007 ). Observational Astronomy. p. 75. ISBN 978 - 0 - 521 - 85370 - 5. Jump up ^ Simon F. Green ; Mark H. Jones ( 2004 ). An Introduction to the Sun and Stars. Cambridge University Press. p. 87. ISBN 0 - 521 - 54622 - 2. Jump up ^ D. Scott Birney ; Guillermo Gonzalez ; David Oesper ( 2007 ). Observational Astronomy. Cambridge University Press. p. 73. ISBN 0 - 521 - 85370 - 2. Jump up ^ `` Twilight Rays at La Silla ''. www.eso.org. Retrieved 7 December 2016. Jump up ^ Horace A. Smith ( 2004 ). RR Lyrae Stars. Cambridge University Press. p. 79. ISBN 0 - 521 - 54817 - 9. Jump up ^ M Reid ; A Brunthaler ; Xu Ye ; et al. ( 2008 ). `` Mapping the Milky Way and the Local Group ''. In F Combes ; Keiichi Wada. Mapping the Galaxy and Nearby Galaxies. Springer. ISBN 0 - 387 - 72767 - 1. Jump up ^ Y Sofu & V Rubin ( 2001 ). `` Rotation Curves of Spiral Galaxies ''. Annual Review of Astronomy and Astrophysics. 39 : 137 -- 174. arXiv : astro - ph / 0010594. Bibcode : 2001ARA&A... 39... 137S. doi : 10.1146 / annurev. astro. 39.1. 137. Jump up ^ Abraham Loeb ; Mark J. Reid ; Andreas Brunthaler ; Heino Falcke ( 2005 ). `` Constraints on the proper motion of the Andromeda galaxy based on the survival of its satellite M33 '' ( PDF ). The Astrophysical Journal. 633 ( 2 ) : 894 -- 898. arXiv : astro - ph / 0506609. Bibcode : 2005ApJ... 633... 894L. doi : 10.1086 / 491644. Jump up ^ William Marshall Smart ; Robin Michael Green ( 1977 ). Textbook on Spherical Astronomy. Cambridge University Press. p. 252. ISBN 0 - 521 - 29180 - 1. Jump up ^ Charles Leander Doolittle ( 1890 ). A Treatise on Practical Astronomy, as Applied to Geodesy and Navigation. Wiley. p. 583. Jump up ^ Simon Newcomb ( 1904 ). The Stars : A study of the Universe. Putnam. pp. 287 -- 288. Jump up ^ Matra Marconi Space, Alenia Spazio ( September 15, 2003 ). `` The Hipparcos and Tycho Catalogues : Astrometric and Photometric Star Catalogues derived from the ESA Hipparcos Space Astrometry Mission '' ( PDF ). ESA. p. 25. Retrieved 2015 - 04 - 08. Jump up ^ See Majewski, Steven R. ( 2006 ). `` Stellar motions : parallax, proper motion, radial velocity and space velocity ''. University of Virginia. Retrieved 2008 - 12 - 31. Jump up ^ See lecture notes by Steven Majewski. Jump up ^ Hirshfeld, Alan ; Sinnott, Roger W. ; Ochsenbein, François ; Lemay, D. ( 1992 ). `` Book - Review -- Sky Catalogue 2000.0 -- V. 1 -- Stars to Magnitude 8.0 ED. 2 ''. Journal of the Royal Astronomical Society of Canada. 86 : 221. Bibcode : 1992JRASC... 86... 221H. Jump up ^ AM Ghez ; et al. ( 2003 ). `` The First Measurement of Spectral Lines in a Short - Period Star Bound to the Galaxy 's Central Black Hole : A Paradox of Youth ''. Astrophysical Journal. 586 ( 2 ) : L127 -- L131. arXiv : astro - ph / 0302299. Bibcode : 2003ApJ... 586L. 127G. doi : 10.1086 / 374804. Jump up ^ Andreas Brunthaler ( 2005 ). `` M33 -- Distance and Motion ''. In Siegfried Röser. Reviews in Modern Astronomy : From Cosmological Structures to the Milky Way. Wiley. pp. 179 -- 194. ISBN 3 - 527 - 40608 - 5. Jump up ^ A. Brunthaler ; M.J. Reid ; H. Falcke ; L.J. Greenhill ; C. Henkel ( 2005 ). `` The Geometric Distance and Proper Motion of the Triangulum Galaxy ( M33 ) ''. Science. 307 ( 5714 ) : 1440 -- 1443. arXiv : astro - ph / 0503058. Bibcode : 2005Sci... 307.1440 B. doi : 10.1126 / science. 1108342. PMID 15746420. Jump up ^ Sangmo Tony Sohn ; Jay Anderson ; Roeland van der Marel ( Jul 1, 2012 ). `` The M31 velocity vector. I. Hubble Space Telescope proper - motion measurements ''. The Astrophysical Journal. 753 : 7. arXiv : 1205.6863. Bibcode : 2012ApJ... 753... 7S. doi : 10.1088 / 0004 - 637X / 753 / 1 / 7. Jump up ^ Steven Weinberg ( 2008 ). Cosmology. Oxford University Press. p. 17. ISBN 0 - 19 - 852682 - 2. Jump up ^ J.R. Herrnstein ; et al. ( 1999 ). `` A geometric distance to the galaxy NGC4258 from orbital motions in a nuclear gas disk ''. Nature. 400 ( 6744 ) : 539 -- 541. arXiv : astro - ph / 9907013. Bibcode : 1999Natur. 400... 539H. doi : 10.1038 / 22972. Jump up ^ Otto Neugebauer ( 1975 ). A History of Ancient Mathematical Astronomy. Birkhäuser. p. 1084. ISBN 3 - 540 - 06995 - X. Jump up ^ Staff ( September 15, 2003 ). `` The 150 Stars in the Hipparcos Catalogue with Largest Proper Motion ''. ESA. Retrieved 2007 - 07 - 21. Jump up ^ `` SIMBAD ''. Centre de Données astronomiques de Strasbourg. Retrieved 2016 - 04 - 13. ^ Jump up to : Fabricius, C. ; Makarov, V.V. ( May 2000 ). `` Hipparcos astrometry for 257 stars using Tycho - 2 data ''. Astronomy and Astrophysics Supplement. 144 : 45 -- 51. Bibcode : 2000A&AS... 144... 45F. doi : 10.1051 / aas : 2000198. Retrieved 2016 - 04 - 13. External links Hipparcos : High Proper Motion Stars Edmond Halley : Discovery of proper motions Star Formation Accretion Molecular cloud Bok globule Young stellar object Protostar Pre-main - sequence star Herbig Ae / Be Orion T Tauri FU Orionis Herbig -- Haro object Hayashi track Henyey track Evolution Main sequence Red giant branch Horizontal branch Red clump Asymptotic giant branch Protoplanetary nebula Planetary nebula PG1159 star Dredge - up Instability strip Luminous blue variable Blue straggler Stellar population Supernova Supernova impostor Hypernova Hertzsprung -- Russell diagram Color -- color diagram Luminosity class Subdwarf Dwarf Blue Red White Yellow Brown Subgiant Giant Blue Red Bright giant Supergiant Blue Red Yellow Hypergiant Yellow Spectral classification WR Be OB Subdwarf O Subdwarf B Late - type Chemically peculiar Am Ap / Bp Barium Carbon CH CN Extreme helium Lambda Boötis Lead HgMn Technetium Shell Remnants White dwarf Helium planet Neutron star Radio - quiet Pulsar Binary X-ray Magnetar Stellar black hole X-ray binary Burster Theoretical stars Black dwarf Exotic Quark Strange Preon Planck Electroweak star Dark - matter star Dark - energy star Black star Gravastar Frozen star Q star Quasi-star Thorne -- Żytkow object Iron star Blitzar Nucleosynthesis Deuterium burning Lithium burning Proton -- proton chain CNO cycle Helium flash Triple - alpha process Alpha process Carbon burning Neon burning Oxygen burning Silicon burning S - process R - process Fusor Nova Symbiotic Remnant Luminous red nova Structure Core Convection zone Microturbulence Oscillations Radiation zone Atmosphere Photosphere Starspot Chromosphere Corona Stellar wind Bubble Bipolar outflow Accretion disk Asteroseismology Helioseismology Eddington luminosity Kelvin -- Helmholtz mechanism Properties Designation Dynamics Effective temperature Kinematics Magnetic field Absolute magnitude Mass Metallicity Rotation UBV color Variable star Mira variable Star systems Binary Contact Common envelope Eclipsing Multiple Star cluster Open cluster Globular cluster Super star cluster Planetary system Earth 's Solar System Earth - centric observation of Pole star Circumpolar star Constellation Asterism Magnitude Apparent Extinction Photographic Radial velocity Proper motion Parallax Photometric - standard star Lists Star names Arabic Chinese Extremes Most massive Highest temperature Largest volume Smallest volume Brightest Historical Most luminous Nearest Nearest bright Stars with exoplanets Brown dwarfs White dwarfs Milky Way novae Notable supernovae Supernova candidates Supernova remnants Planetary nebulae Timeline of stellar astronomy Related articles Substellar object Brown dwarf Sub-brown dwarf Planet Galactic year Galaxy Supercluster Guest star Gravity Intergalactic star Infrared dark cloud Starfield Category : Stars Star portal Retrieved from `` https://en.wikipedia.org/w/index.php?title=Proper_motion&oldid=804696460 '' Categories : Astrometry Stellar astronomy Talk Contents About Wikipedia Afrikaans Беларуская ( тарашкевіца ) ‎ Bosanski Català Čeština Dansk Deutsch Ελληνικά Español Esperanto فارسی Français Gaeilge 한국어 Հայերեն हिन्दी Hrvatski Bahasa Indonesia Italiano עברית Қазақша Lëtzebuergesch Lietuvių Magyar Македонски Nederlands 日本 語 Norsk Norsk nynorsk Polski Português Română Русский Simple English Slovenčina Slovenščina Suomi Svenska Tagalog ไทย Türkçe Українська Tiếng Việt 粵語 中文 Edit links This page was last edited on 10 October 2017, at 15 : 51. 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Question: who discovered the first known instance of proper motion
Answer: Edmund Halley