Proper motion is the astronomical measure of the observed changes in the apparent places of stars or other celestial objects 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 for proper motion in the equatorial coordinate system (of a given epoch, often J2000.0) are given in the direction of right ascension (μα) and of declination (μδ). Their combined value is computed as the total proper motion (μ). It has dimensions of angle per time, typically arcseconds per year or milliarcseconds per year. Knowledge of the proper motion, distance, and radial velocity allows calculations of true stellar motion or velocity in space in respect to the Sun, and by coordinate transformation, the motion in respect to the Milky Way.
Proper motion is not entirely "proper" (that is, intrinsic to the celestial body or star), because it includes a component due to the motion of the Solar System itself.
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 8 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, typically expressed in arcseconds per year (symbol arcsec/yr, as/yr) or milliarcsecond per year (mas/yr).
where δ is the declination. The factor in cos2δ accounts for the fact that the radius from the axis of the sphere to its surface varies as cosδ, 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 μα, which must be multiplied by cosδ to become a component of the proper motion, is sometimes called the "proper motion in right ascension", and μδ the "proper motion in declination".
If the proper motion in right ascension has been converted by cosδ, the result is designated μα*. For example, the proper motion results in right ascension in the Hipparcos Catalogue (HIP) 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.
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 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.
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 × 106 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 billion 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 7.2±0.5 Mpc.
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.
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.
|μα · cos δ
|5||Gliese 1 (CD −37 15492) (GJ 1)||5634.68||−2337.71||+25.38||230.42|
|7||61 Cygni A & B||4133.05||3201.78||−65.74||286|
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:
23 Andromedae, abbreviated 23 And, is a presumed single star in the constellation Andromeda, although it has been a suspected spectroscopic binary. 23 Andromedae is the Flamsteed designation. Its apparent visual magnitude is 5.71, which indicates it is dimly visible to the naked eye under good viewing conditions. The distance to 23 And, as determined from its annual parallax shift of 26.8 mas, is 121.6 light years. The star is moving further from the Earth with a heliocentric radial velocity of −27 km/s. It has a relatively high proper motion, traversing the celestial sphere at the rate of 0.191″ per year.The stellar classification of 23 And is F0 IV, matching an F-type subgiant star that is in the process of evolving into a red giant. It displays a slight microvariability with a frequency of 0.85784 d−1 and an amplitude of 0.0062 magnitude. The star is around 759 million years old with a projected rotational velocity of 36 km/s. It has 1.43 times the mass of the Sun and is radiating 50 times the Sun's luminosity from its photosphere at an effective temperature of 7,089 K.25 Cancri
25 Cancri is a common proper motion star system in the zodiac constellation of Cancer, located around 348 light years away from the Sun. It has the Bayer designation d2 Cancri (d2 Cnc); 25 Cancri (25 Cnc) is the Flamsteed designation. It is near the lower limit of visibility to the naked eye in good viewing conditions, appearing as a dim, yellow-white hued star with a combined apparent visual magnitude of 6.11. The pair have a relatively high proper motion, traversing the celestial sphere at an angular rate of 0.245″ per year. It is moving further from the Earth with a heliocentric radial velocity of +37 km/s.Based upon a stellar classification of F6 V, the brighter component is an F-type main-sequence star that is generating energy through hydrogen fusion at its core. Cowley (1976) listed a class of F5 IIIm?, which suggests it may be an Am star. However, this has not been confirmed. It is about 2.5 billion years old with 1.51 times the mass of the Sun. The star is radiating 6.6 times the Sun's luminosity from its photosphere at an effective temperature of 6,487 K.The companion is 4.19 magnitudes fainter than the primary, and lies at an angular separation of 16.798″ along a position angle of 310°, as of 2013. If the pair are gravitationally bound, then they orbit each other with a period of around 4.05 million years.32 Boötis
32 Boötis is a single star in the northern constellation of Boötes, located 360 light years away from the Sun. It is visible to the naked eye as a faint, yellow-hued star with an apparent visual magnitude of 5.55. This object is moving closer to the Earth with a heliocentric radial velocity of −23 km/s. It has a relatively high proper motion, traversing the celestial sphere at the rate of 0.195 arc seconds per annum.This is an aging giant star with a stellar classification of G8 III. It is most likely on the horizontal branch and is a candidate red clump giant. The star is an estimated 1.46 billion years old with 2.15 times the mass of the Sun. With the hydrogen at its core exhausted, it has expanded to 12 times the Sun's radius. 32 Boötis is radiating 79 times the luminosity of the Sun from its swollen photosphere at an effective temperature of 4958 K.38 Aurigae
38 Aurigae is a star located 236 light years away from the Sun in the northern constellation of Auriga. It is visible to the naked eye as a dim, orange-hued star with an apparent visual magnitude of 6.08. The star is moving further from the Earth with a heliocentric radial velocity of +34 km/s, and it has a relatively high proper motion, traversing the celestial sphere at the rate of 0.181 arc seconds per annum. It is a probable member of the Hercules stream.This object is an aging giant star with a stellar classification of K0 III. At the age of around 3.6 billion years it is a red clump giant, which indicates it is on the horizontal branch and is generating energy via helium fusion at its core. The star has 1.59 times the mass of the Sun and has expanded to 7 times the Sun's radius. It is radiating 18 times the Sun's luminosity from its swollen photosphere at an effective temperature of 4,834 K.38 Aurigae has a faint common proper motion companion at an angular separation of 152″, which is equivalent to a projected separation of 12,160 AU. This is a red dwarf star with a class of M5.3.39 Aurigae
39 Aurigae is a single star in the constellation of Auriga. The designation is from the star catalogue of English astronomer John Flamsteed, first published in 1712. The star is just barely visible to the naked eye, having an apparent visual magnitude of 5.90. Based upon an annual parallax shift of 20.11 mas as seen from Earth, it is located 112 light years away. 5 Andromedae is moving further from the Sun with a radial velocity of +34 km/s. It has a relatively high proper motion, advancing across the celestial sphere at the rate of 0.151 arc seconds per year.This is an F-type main-sequence star with a stellar classification of F1 V. It is an estimated 603 million years old with a relatively high rate of spin, showing a projected rotational velocity of around 88 km/s. The star has 1.45 times the mass of the Sun and it is radiating 9.36 times the Sun's luminosity from its photosphere at an effective temperature of around 7,161 K.3 Andromedae
3 Andromedae, abbreviated 3 And, is a single star in the northern constellation of Andromeda. 3 Andromedae is the Flamsteed designation. It is visible to the naked eye with an apparent visual magnitude of 4.64. The distance to this star, as determined from an annual parallax shift of 18 mas, is 181 light years. It is moving closer to the Earth with a heliocentric radial velocity of −35 km/s, and has a relatively large proper motion, traversing the celestial sphere at a rate of 0.236″·yr−1.This is an evolved giant star with a stellar classification of K0 IIIb, where the 'b' suffix indicated a lower luminosity giant. It is a red clump star, which means it is generating energy through helium fusion at its core. This star has an estimated 1.7 times the mass of the Sun, and, at the age of 2.3 billion years, has expanded to 10 times the Sun's radius. It is radiating 49 times the Sun's luminosity from its enlarged photosphere at an effective temperature of 4,668 K.41 Andromedae
41 Andromedae is a single star in the northern constellation of Andromeda. 41 Andromedae is the Flamsteed designation. It is bright enough to be faintly visible to the naked eye, having an apparent visual magnitude of 5.04. Based upon an annual parallax shift of 18.4 mas, it is located 178 light years away. The star is moving further from the Earth with a heliocentric radial velocity of +10 km/s and it has a relatively high rate of proper motion, traversing the celestial sphere at the rate of 0.171″ per year.The stellar classification for this star is A2IIIvs, matching an A-type giant star with narrow (sharp) absorption lines. Abt and Levy (1985) classed it as a kA2hA6mA6 star, which indicates the spectrum has the calcium K line of an A2 star, the hydrogen lines of an A6 star, and the metal lines of an A6 star. It is around 450 million years old and is spinning with a projected rotational velocity of 84 km/s. The star has 2.27 times the mass of the Sun and is radiating five times the Sun's luminosity from its photosphere at an effective temperature of 8,511 K.58 Andromedae
58 Andromedae, abbreviated 58 And, is a single star in the northern constellation Andromeda. 58 Andromedae is the Flamsteed designation. It is visible to the naked eye with an apparent visual magnitude of 4.78 The distance to this star, as determined from its annual parallax shift of 9.9 mas, is 330 light years. 58 And is moving further from the Earth with a heliocentric radial velocity of +8 km/s. It has a relatively high proper motion, traversing the celestial sphere at the rate of 0.159″ per year.This star is 425 million years old with a stellar classification of A5 IV-V, indicating the spectrum displays mixed traits of an A-type main-sequence star and an older subgiant star. It is spinning rapidly with a projected rotational velocity of 135 km/s, which is giving the star an oblate shape with an equatorial bulge that is 6% larger than the polar radius. The star has double the mass of the Sun and about 1.9 times the Sun's radius. It is radiating 36 times the Sun's luminosity from its photosphere at an effective temperature of 8,875 K.5 Andromedae
5 Andromedae is a single, yellow-white hued star in the northern constellation of Andromeda. Its designation comes from a catalogue of stars by English astronomer John Flamsteed, published in 1712. The star is faintly visible to the naked eye, having an apparent visual magnitude of 5.68. Based upon an annual parallax shift of 29.12 mas as seen from Earth, it is located 112 light years away. 5 Andromedae is moving closer to the Sun with a radial velocity of −2.6 km/s. It has a relatively high proper motion, advancing across the celestial sphere at the rate of 0.201 arc seconds per year.This is an ordinary F-type main-sequence star with a stellar classification of F5 V. It is estimated to be 2.3 billion years old and is spinning with a projected rotational velocity of 9.7 km/s. The star has 1.39 times the mass of the Sun. It is radiating 5.6 times the Sun's luminosity from its photosphere at an effective temperature of about 6,605 K.68 Aquarii
68 Aquarii is a single star located 270 light years away from the Sun in the zodiac constellation of Aquarius. 68 Aquarii is its Flamsteed designation, though it also bears the Bayer designation of g2 Aquarii. It is visible to the naked eye as a dim, yellow-hued star with an apparent visual magnitude of 5.24. The object is moving further from the Earth with a heliocentric radial velocity of +24.5 km/s.This star is 3.79 billion years old with a stellar classification of G8 III, indicating the is a giant star that has exhausted the hydrogen at its core and expanded off the main sequence. It is a red clump giant, which means it is on the horizontal branch and is generating energy through helium fusion at its core. It has 1.39 times the mass of the Sun and 10 times the Sun's radius. The star is radiating 59 times the luminosity of the Sun from its enlarged photosphere at an effective temperature of 5,036 K.6 Andromedae
6 Andromedae is an astrometric binary star system in the northern constellation of Andromeda. The designation comes from the star catalogue of John Flamsteed, first published in 1712. Its apparent visual magnitude is 5.91, which is just bright enough to be visible to the naked eye under good seeing conditions. Based upon an annual parallax shift of 34.1 mas as seen from Earth, it is around 96 light years from the Sun. It is moving closer to the Sun with a radial velocity of −32.4 km/s. The system has a relatively high proper motion, advancing across the celestial sphere at the rate of 0.272 arc seconds per annum.This is a single-lined spectroscopic binary with an orbital period of 9.2 years and an eccentricity of 0.3. Some early observations of the star gave it a subgiant luminosity class and it was published in the Bright Star Catalogue as spectral class F5 IV. More modern measurements identify the visible component as an F-type main-sequence star with a stellar classification of F5 V. The star is an estimated 2.9 billion years old with 1.3 times the mass of the Sun and 1.5 times the Sun's radius. It is radiating 3.1 times the Sun's luminosity from its photosphere at an effective temperature of around 6,425 K. 6 Andromedae displays an infrared excess at a wavelength of 22 μm, which may indicate a circumstellar disk of warm dusty debris.The mass of the secondary component is roughly at or above that of the Sun. If it were a single, ordinary star, it should be readily visible as it would be just one magnitude fainter than the primary. The lack of conspicuous ultraviolet emission appears to rule out a white dwarf companion, so it may instead itself be a binary system consisting of two smaller stars having an orbital period between a week and a year.83 Cancri
83 Cancri (83 Cnc) is a star in the constellation Cancer. Its apparent magnitude is 6.61.Barnard's Star
Barnard's Star is a very-low-mass red dwarf about 6 light-years away from Earth in the constellation of Ophiuchus. It is the fourth nearest known individual star to the Sun (after the three components of the Alpha Centauri system) and the closest star in the Northern Celestial Hemisphere. Despite its proximity, the star has a dim apparent magnitude of +9.5 and is invisible to the unaided eye; it is much brighter in the infrared than in visible light.
The star is named after the American astronomer E. E. Barnard. He was not the first to observe the star (it appeared on Harvard University plates in 1888 and 1890), but in 1916 he measured its proper motion as 10.3 arcseconds per year relative to the Sun, the highest known for any star.Barnard's Star is among the most studied red dwarfs because of its proximity and favorable location for observation near the celestial equator. Historically, research on Barnard's Star has focused on measuring its stellar characteristics, its astrometry, and also refining the limits of possible extrasolar planets. Although Barnard's Star is an ancient star, it still experiences star flare events, one being observed in 1998.
From the early 1960s to the early 1970s, Peter van de Kamp argued that there were one or more gas giants in orbit around it. His specific claims of large gas giants were refuted in the mid-1970s after much debate.
In November 2018 a candidate super-Earth planetary companion known as Barnard's Star b was reported to orbit Barnard's Star. It is believed to have a minimum of 3.2 M⊕ (Earth masses) and orbit at 0.4 AU.Double star
In observational astronomy, a double star or visual double is a pair of stars that appear close to each other as viewed from Earth, especially with the aid of optical telescopes.
This occurs because the pair either forms a binary star (i.e. a binary system of stars in mutual orbit, gravitationally bound to each other) or is an optical double, a chance line-of-sight alignment of two stars at different distances from the observer. Binary stars are important to stellar astronomers as knowledge of their motions allows direct calculation of stellar mass and other stellar parameters.
Since the beginning of the 1780s, both professional and amateur double star observers have telescopically measured the distances and angles between double stars to determine the relative motions of the pairs. If the relative motion of a pair determines a curved arc of an orbit, or if the relative motion is small compared to the common proper motion of both stars, it may be concluded that the pair is in mutual orbit as a binary star. Otherwise, the pair is optical. Multiple stars are also studied in this way, although the dynamics of multiple stellar systems are more complex than those of binary stars.
The following are three types of paired stars:
Optical doubles are unrelated stars that appear close together through chance alignment with Earth.
Visual binaries are gravitationally-bound stars that are separately visible with a telescope.
Non-visual binaries are stars whose binary status was deduced through more esoteric means, such as occultation (eclipsing binaries), spectroscopy (spectroscopic binaries), or anomalies in proper motion (astrometric binaries).Improvements in telescopes can shift previously non-visual binaries into visual binaries, as happened with Polaris A in 2006. It is only the inability to telescopically observe two separate stars that distinguish non-visual and visual binaries.Groombridge 1830
Groombridge 1830 (also known as 1830 Groombridge or Argelander's Star) is a star in the constellation Ursa Major.PPM Star Catalogue
The PPM Star Catalogue (Positions and Proper Motions Star Catalogue) is the successor of the SAO Catalogue. It contains precise positions and proper motions of 378,910 stars on the whole sky in the J2000/FK5 coordinate system.
It is designed to represent as closely as possible the IAU (1976) coordinate system on the sky, as defined by the FK5 star catalogue. Thus, the PPM is an extension of the FK5 system to higher star densities and fainter magnitudes.Q Scorpii
Q Scorpii (Q Sco) is an orange giant star in the constellation Scorpius. Its apparent magnitude is 4.27. It lies in the tail of Scorpius, between the stars λ Scorpii and μ Scorpii, 7′ from the faint globular cluster Tonantzintla 2.
Q Scorii is a suspected astrometric binary, a star whose position is seen to oscillate although no companion has been detected. From Hipparcos data, its proper motion is seen to be discrepant and accelerating, although there is insufficient data to determine any orbit.Q Scorpii is cooler than the sun, but more luminous. It is a red clump giant, at the cool end of the horizontal branch, fusing helium in its core. Like all red clump giants, it has an effective temperature near 5,000 K and a bolometric luminosity of around 75 L☉.Star catalogue
A star catalogue (Commonwealth English) or star catalog (American English), is an astronomical catalogue that lists stars. In astronomy, many stars are referred to simply by catalogue numbers. There are a great many different star catalogues which have been produced for different purposes over the years, and this article covers only some of the more frequently quoted ones. Star catalogues were compiled by many different ancient people, including the Babylonians, Greeks, Chinese, Persians, and Arabs. They were sometimes accompanied by a star chart for illustration. Most modern catalogues are available in electronic format and can be freely downloaded from space agencies data centres.
Completeness and accuracy is described by the weakest apparent magnitude V (largest number) and the accuracy of the positions.WISE 0855−0714
WISE 0855−0714 (full designation WISE J085510.83−071442.5) is a sub-brown dwarf 2.23±0.04 parsecs (7.27±0.13 light-years) from Earth, the discovery of which was announced in April 2014 by Kevin Luhman using data from the Wide-field Infrared Survey Explorer (WISE). As of 2014, WISE 0855−0714 has the third-highest proper motion (8118±8 mas/yr) after Barnard's Star (10300 mas/yr) and Kapteyn's Star (8600 mas/yr) and the fourth-largest parallax (449±8 mas) of any known star or brown dwarf, meaning it is the fourth-closest extrasolar system to the Sun. It is also the coldest object of its type found in interstellar space, having a temperature in the range 225 to 260 K (−48 to −13 °C; −55 to 8 °F).
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