|
|
| Line 1: |
Line 1: |
| {{Infobox unit
| | Too long starting paragraph also serves essay writing as a template. Essay writing is all that experience and evidence are important in the United States have increased in number since 2000. It helps the reader not only simple for the client to place marks to acquire a meticulous subject are extremely well-liked. The scholarship essays that are not the writer should categorise their ideas and points which are impacted by failing to proofread your essay.<br><br>Stop by my web-site; [http://essaydragons.wordpress.com/ professional essay writing] |
| | image = [[Image:ParallaxeV2.png|200px]]
| |
| | caption = stellar parallax motion from annual parallax
| |
| | standard = astronomical units
| |
| | quantity = length
| |
| | symbol = pc
| |
| | units1 = [[International System of Units|SI units]]
| |
| | inunits1 = {{val|3.0857|e=16|ul=m}}
| |
| | units2 = [[Imperial units|imperial]] & [[United States customary units|US]] units
| |
| | inunits2 = {{val|1.9174|e=13|ul=mi}}
| |
| | units3 = other astronomical
| |
| | inunits3 = {{val|2.0626|e=5|ul=AU}}
| |
| | units4 = units
| |
| | inunits4 = {{val|3.26156}} [[light-year|ly]]
| |
| }}
| |
| {{other uses}}
| |
| | |
| A '''parsec''' (symbol: '''pc''') is an astronomical [[units of measurement|unit]] of [[astronomical units of length|distance]] derived by the theoretical annual [[stellar parallax|parallax]] (or heliocentric parallax) of one [[arcsecond|arc second]], and is found as the inverse of that measured [[parallax]]. In astronomical terms, parallaxes are the apparent measured difference in the position of a star as seen from Earth and another hypothetical observer at the Sun. As the distance is the inverse of the parallax, the smaller the measured parallax the larger the celestial object's distance.
| |
| | |
| One parsec equals about 3.26 [[light-year]]s (30.9 [[orders of magnitude (numbers)#1012|trillion]] [[kilometre]]s or 19.2 trillion [[miles]]). All known stars lie more than one parsec away, with [[Proxima Centauri]] showing the largest parallax of 0.7687 arcsec, making the distance 1.3009 parsecs (4.243 light years).<ref>{{cite conference
| |
| | author=Benedict, G. F. ''et al''
| |
| | title =Astrometric Stability and Precision of Fine Guidance Sensor #3: The Parallax and Proper Motion of Proxima Centauri
| |
| | booktitle =Proceedings of the HST Calibration Workshop
| |
| | pages =380–384
| |
| | url =http://clyde.as.utexas.edu/SpAstNEW/Papers_in_pdf/%7BBen93%7DEarlyProx.pdf
| |
| |format=PDF| accessdate = 2007-07-11 }}</ref> Most of the visible stars in the nighttime sky lie within 500 parsecs of the Sun.
| |
| | |
| The parsec was introduced to make quick calculations of astronomical distances without the need for more complicated conversions, i.e. knowing the true speed of light to calculate [[light year]]s. ''Parsec'' is named from the abbreviation of the ''par''allax of one arc''sec''ond, and was likely first suggested by [[United Kingdom|British]] [[astronomer]] [[Herbert Hall Turner]] in 1913.<ref>[[Frank Watson Dyson|Dyson, F. W.]], ''Stars, Distribution and drift of, The distribution in space of the stars in Carrington's Circumpolar Catalogue''. In: Monthly Notices of the Royal Astronomical Society, Vol. 73, p. 334–342. March 1913. [http://adsabs.harvard.edu/abs/1913MNRAS..73..334D] <br />"There is a need for a name for this unit of distance. Mr. [[Carl Charlier|Charlier]] has suggested Siriometer ... Professor [[Herbert Hall Turner|Turner]] suggests PARSEC, which may be taken as an abbreviated form of 'a distance corresponding to a parallax of one second.'"</ref>
| |
| | |
| Usage of parsecs is preferred in astronomy and astrophysics, though popular science texts commonly use light-years, probably because it is much easier to understand the amount of time it takes light to travel from the source. Multiples of parsecs are commonly used for scales in the universe, including parsecs for the visible stars, kiloparsecs for galactic objects and megaparsecs for nearby and more distant galaxies.
| |
| | |
| == History and derivation ==
| |
| {{See also|Stellar parallax}}
| |
| | |
| [[Image:Stellarparallax parsec1.svg|thumb|right|A parsec is the distance from the [[Sun]] to an [[astronomical object]] which has a [[parallax]] angle of one [[arcsecond]]. (the diagram is not to scale (1 pc ≈ {{val|206264.81}} au)).]]
| |
| | |
| The '''parsec''' is equal to the length of the [[adjacent side (right triangle)|adjacent]] side of an imaginary [[Special right triangles#Angle-based|right triangle]] in space. The two dimensions on which this triangle is based are the [[subtended]] [[angle]] of 1 [[arcsecond]], and the [[Triangle#Trigonometric ratios in right triangles|opposite]] side that is defined as 1 [[astronomical unit]], being the average Earth-Sun distance. From both values, along with the rules of trigonometry, the unit length of the [[adjacent side (right triangle)|adjacent]] side (the '''parsec''') can be derived.
| |
| | |
| One of the oldest methods for astronomers to calculate the distance to a [[star]] was to record the difference in angle between two measurements of the position of the star in the sky. The first measurement was taken from the Earth on one side of the Sun, and the second was taken half a year later when the Earth was on the opposite side of the Sun. The distance between the two positions of the Earth when the two measurements were taken was known to be twice the distance between the Earth and the Sun. The difference in angle between the two measurements was known to be twice the parallax angle, which is formed by lines from the Sun and Earth to the star at the [[Vertex (geometry)#Of an angle|vertex]]. Then the distance to the star could be calculated using trigonometry.<ref name='NASAparallax'>{{cite web | url = http://imagine.gsfc.nasa.gov/YBA/HTCas-size/parallax1-derive.html | title = Deriving the Parallax Formula | accessdate = 2011-11-26 | last = [[High Energy Astrophysics Science Archive Research Center]] (HEASARC) | work = NASA's Imagine the Universe! | publisher = Astrophysics Science Division (ASD) at [[NASA]]'s [[Goddard Space Flight Center]]}}</ref> The first successful direct measurements of an object at interstellar distances were undertaken by [[Germany|German]] astronomer [[Friedrich Wilhelm Bessel]] in 1838, who used this approach to calculate the three and a half parsec distance of [[61 Cygni]].<ref>Bessel, FW, "[http://www.ari.uni-heidelberg.de/gaia/documents/bessel-1838/index.html Bestimmung der Entfernung des 61sten Sterns des Schwans]" (1838) ''[[Astronomische Nachrichten]]'', vol. 16, pp. 65–96.</ref>
| |
| | |
| The ''parallax'' of a star is taken to be half of the [[angular distance]] that a star appears to move relative to the [[celestial sphere]] as Earth orbits the Sun. Equivalently, it is the [[subtended angle]], from that star's perspective, of the [[Semimajor axis|semi-major axis]] of Earth's orbit. The star, the Sun and the Earth form the corners of an imaginary [[right triangle]] in space: the right angle is the corner at the Sun, and the corner at the star is the parallax angle. The length of the opposite side to the parallax angle is the distance from the [[Earth]] to the [[Sun]] (defined as 1 [[astronomical unit]] (AU)), and the length of the [[Cathetus|adjacent]] side gives the distance from the sun to the star. Therefore, given a measurement of the parallax angle, along with the rules of [[trigonometry]], the distance from the Sun to the star can be found. A parsec is defined as the length of the [[Cathetus|adjacent]] side of this [[right triangle]] in space when the parallax angle is 1 [[arcsecond]].
| |
| | |
| The use of the parsec as a unit of distance follows naturally from Bessel's method, since distance in parsecs can be computed simply as the [[multiplicative inverse|reciprocal]] of the parallax angle in arcseconds (''i. e.'', if the parallax angle is 1 arcsecond, the object is 1 pc from the Sun; If the parallax angle is 0.5 arcsecond, the object is 2 pc away; ''etc.''). No [[trigonometric function]]s are required in this relationship because the very small angles involved mean that the approximate solution of the [[skinny triangle]] can be applied.
| |
| | |
| Though it may have been used before, the term ''parsec'' was first mentioned in an astronomical publication in 1913. [[Astronomer Royal]] [[Frank Watson Dyson]] expressed his concern for the need of a name for that unit of distance. He proposed the name ''astron'', but mentioned that [[Carl Charlier]] had suggested ''siriometer'' and [[Herbert Hall Turner]] had proposed ''parsec''.<ref>Dyson, F. W., "[http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1913MNRAS..73..334D The distribution in space of the stars in Carrington's Circumpolar Catalogue]" (1913) ''[[Monthly Notices of the Royal Astronomical Society]]'', vol. 73, pp. 334–42, [http://articles.adsabs.harvard.edu//full/seri/MNRAS/0073//0000342.000.html p. 342 fn.].</ref> It was Turner's proposal that stuck.
| |
| | |
| === Calculating the value of a parsec ===
| |
| [[Image:Parsec (1).svg|400px|Diagram of parsec.]]
| |
| | |
| In the diagram above ''(not to scale)'', '''S''' represents the [[Sun]], and '''E''' the [[Earth]] at one point in its orbit. Thus the distance '''ES''' is one [[astronomical unit]] (AU). The angle '''SDE''' is one [[arcsecond]] ({{frac|3600}} of a degree) so by definition '''D''' is a point in space at a distance of one parsec from the Sun. By [[trigonometry]], the distance '''SD''' is
| |
| | |
| :<math>SD = \frac{\mathrm{ES}}{\tan 1^{\prime\prime}}</math>
| |
| | |
| Using the [[small-angle approximation]], by which the sine (and, hence, the tangent) of an extremely small angle is essentially equal to the angle itself (in radians),
| |
| | |
| :<math>SD \approx \frac{\mathrm{ES}}{1^{\prime\prime}} = \frac{1 \, \mbox{AU}}{(\tfrac{1}{60 \times 60} \times \tfrac{\pi}{180})} = \frac{648\,000}{\pi} \, \mbox{AU} \approx 206\,264.81 \mbox{ AU} .</math>
| |
| | |
| Since the astronomical unit is defined to be {{gaps|149|597|870|700}} metres,<ref>{{citation | contribution = RESOLUTION B2 on the re-definition of the astronomical unit of length | title = RESOLUTION B2 | editor-first = International Astronomical Union | publisher = [[International Astronomical Union]] | place = Beijing, Kina | date = 31 August 2012 | contribution-url = http://www.iau.org/static/resolutions/IAU2012_English.pdf | accessdate = 10 September 2012 | quote = The XXVIII General Assembly of International Astronomical Union recommends [adopted] that the astronomical unit be re-defined to be a conventional unit of length equal to exactly {{val|149597870700}} metres, in agreement with the value adopted in IAU 2009 Resolution B2}}</ref> the following can be calculated.
| |
| | |
| :{|
| |
| |-
| |
| |rowspan=5 valign=top|1 parsec
| |
| |≈ {{val|206264.81}} [[astronomical unit]]s
| |
| |-
| |
| |≈ {{val|3.0856776|e=16}} [[metre]]s<!--
| |
| |-
| |
| |≈ {{val|30.856776}} trillion [[kilometre]]s-->
| |
| |-
| |
| |≈ {{val|19.173512}} trillion [[mile]]s
| |
| |-
| |
| |≈ {{val|3.2615638}} [[light year]]s
| |
| |}
| |
| | |
| A corollary is that 1 parsec is also the distance from which a disc with a diameter of 1 AU must be viewed for it to have an [[angular diameter]] of 1 arcsecond (by placing the observer at '''D''' and a diameter of the disc on '''ES''').
| |
| | |
| == Usage and measurement ==
| |
| The parallax method is the fundamental calibration step for [[cosmic distance ladder|distance determination in astrophysics]]; however, the accuracy of ground-based [[telescope]] measurements of parallax angle is limited to about 0.01 arcsecond, and thus to stars no more than 100 pc distant.<ref>[http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit1/distances.html Richard Pogge, Astronomy 162, Ohio State.]</ref> This is because the Earth’s atmosphere limits the sharpness of a star's image.<ref>[http://science.jrank.org/pages/5021/Parallax-Parallax-measurements.html jrank.org, ''Parallax Measurements'']</ref> Space-based telescopes are not limited by this effect and can accurately measure distances to objects beyond the limit of ground-based observations. Between 1989 and 1993, the ''[[Hipparcos]]'' satellite, launched by the [[European Space Agency]] (ESA), measured parallaxes for about {{val|100000}} stars with an [[astrometry|astrometric]] precision of about 0.97 [[Minute of arc|milliarcsecond]], and obtained accurate measurements for stellar distances of stars up to {{val|1000}} pc away.<ref>{{cite web | title= The Hipparcos Space Astrometry Mission | url=http://www.rssd.esa.int/index.php?project=HIPPARCOS | accessdate=28 August 2007 }}</ref><ref>[http://wwwhip.obspm.fr/hipparcos/SandT/hip-SandT.html Catherine Turon, ''From Hipparchus to Hipparcos'']</ref>
| |
| | |
| <!-- [[NASA]]'s [[Full-sky Astrometric Mapping Explorer|''FAME'' satellite]] was to have been launched in 2004, to measure parallaxes for about 40 million stars with sufficient precision to measure stellar distances of up to 2,000 pc. However, the mission's funding was withdrawn by NASA in January 2002.<ref>[http://www.usno.navy.mil/FAME/news/ FAME news], 25 January 2002.</ref> -->
| |
| {{As of|2013|11}}, ESA's [[Gaia mission|''Gaia'' satellite]], which is scheduled to launch in December 2013, is intended to measure one billion stellar distances to within 20 microarcseconds, producing errors of 10% in measurements as far as the [[Galactic Center]], about {{val|8000|u=pc}} away in the [[constellation]] of [[Sagittarius (constellation)|Sagittarius]].<ref>[http://sci.esa.int/science-e/www/area/index.cfm?fareaid=26 GAIA] from [[ESA]].</ref>
| |
| | |
| == Distances in parsecs ==
| |
| | |
| === Distances less than a parsec ===
| |
| Distances expressed in fractions of a parsec usually involve objects within a single star system. So, for example:
| |
| * One [[astronomical unit]] (au), the distance from the Sun to the Earth, is just under {{val|5|e=-6}} parsecs.
| |
| * The most distant [[space probe]], ''[[Voyager 1]]'', was 0.0006 parsec (0.002 light-years) from Earth {{As of|May 2013|lc=on}}. It took ''Voyager'' {{age|1977|9|5|2013|5}} years to cover that distance.
| |
| * The [[Oort cloud]] is estimated to be approximately 0.6 parsec (2.0 light-years) in [[diameter]]
| |
| | |
| [[Image:M87 jet.jpg|right|thumb|225px|The jet erupting from the [[active galactic nucleus]] of [[Messier 87|M87]] is thought to be {{val|1.5|u=kiloparsecs}} ({{val|4890|ul=ly}}) long. (image from Hubble Space Telescope)]]
| |
| | |
| === Parsecs and kiloparsecs ===
| |
| Distances expressed in ''parsecs'' (pc) include distances between nearby [[star]]s, such as those in the same [[spiral arm]] or [[globular cluster]]. A distance of {{val|1000}} parsecs ({{val|3262}} light-years) is commonly denoted by the ''kiloparsec'' (kpc). Astronomers typically use kiloparsecs to express distances between parts of a [[galaxy]], or within [[galaxy group|groups of galaxies]]. So, for example:
| |
| * One parsec is approximately 3.26 light-years.
| |
| * The nearest known star to the Earth, other than the Sun, [[Proxima Centauri]], is 1.30 parsecs (4.24 light-years) away, by direct parallax measurement.
| |
| * The distance to the [[open cluster]] [[Pleiades]] is 130 ± 10 pc (420 ± 32.6 light-years) from us, per [[Hipparcos]] parallax measurement.
| |
| * The [[galactic center|center]] of the [[Milky Way]] is more than 8 kiloparsecs ({{val|26000|u=ly}}) from the Earth, and the Milky Way is roughly 34 kpc ({{val|110000|u=ly}}) across.
| |
| * The [[Andromeda Galaxy]] ([[Messier object|M31]]) is ~780 kpc (~2.5 million light-years) away from the Earth.
| |
| | |
| === Megaparsecs and gigaparsecs ===
| |
| <!-- Template:Convert/Mpc & Template:Convert/Gpc link here. -->
| |
| A distance of [[1000000 (number)|one million]] parsecs (3.26 million light-years or 3.26 [[Light-year|"Mly"]]) is commonly denoted by the ''megaparsec'' (Mpc). Astronomers typically express the distances between neighbouring [[galaxy|galaxies]] and [[galaxy cluster]]s in megaparsecs.
| |
| | |
| Galactic distances are sometimes given in units of Mpc/h (as in "50/h Mpc"). ''h'' is a parameter in the range [0.5,0.75] reflecting the uncertainty in the value of the [[Hubble constant]] ''H'' for the rate of expansion of the universe: ''h'' = ''H'' / (100 km/s/Mpc). The Hubble constant becomes relevant when converting an observed [[redshift]] ''z'' into a distance ''d'' using the formula ''d'' ≈ (''[[Speed of light|c]]'' / ''H'') × ''z''.<ref>{{cite web | title= Galaxy structures: the large scale structure of the nearby universe | url=http://pil.phys.uniroma1.it/twiki/bin/view/Pil/GalaxyStructures | accessdate=May 22, 2007 }}</ref>
| |
| | |
| One ''gigaparsec'' (Gpc) is [[1000000000 (number)|one billion]] parsecs — one of the largest [[Orders of magnitude (length)|units of length]] commonly used. One gigaparsec is about 3.26 billion light-years (3.26 [[Light-year|"Gly"]]), or roughly one fourteenth of the distance to the [[Cosmological_horizon#Practical_horizons|horizon]] of the [[observable universe]] (dictated by the [[cosmic background radiation]]). Astronomers typically use gigaparsecs to express the sizes of [[Large-scale structure of the cosmos|large-scale structures]] such as the size of, and distance to, the [[CfA2 Great Wall]]; the distances between galaxy clusters; and the distance to [[quasar]]s.
| |
| | |
| For example:
| |
| * The [[Andromeda Galaxy]] is about 0.78 Mpc (2.5 million light-years) from the Earth.
| |
| * The nearest large [[galaxy cluster]], the [[Virgo Cluster]], is about 16.5 Mpc (54 million light-years) from the Earth.<ref>[http://adsabs.harvard.edu/abs/2007ApJ...655..144M Mei, S. et al 2007, ApJ, 655, 144]</ref>
| |
| * The galaxy [[RXJ1242-11]], observed to have a [[supermassive black hole]] core similar to the [[Milky Way]]'s, is about 200 Mpc (650 million light-years) from the Earth.
| |
| * The [[particle horizon]] (the boundary of the [[observable universe]]) has a radius of about 14.0 Gpc (46 billion light-years).<ref>{{cite web | title= Misconceptions about the Big Bang | url=http://www.scientificamerican.com/article.cfm?id=misconceptions-about-the-2005-03&page=5 | accessdate=January 8, 2010 }}</ref>
| |
| | |
| == Volume units ==
| |
| To determine the number of stars in the Milky Way Galaxy, volumes in cubic kiloparsecs{{efn|name=vol|
| |
| {{{!}}
| |
| {{!}}-
| |
| {{!}}{{val{{!}}1{{!}}u=pc3}} {{!}}{{!}}[[Approximation|≈]] {{val{{!}}2.938{{!}}e=49{{!}}u=m3}}
| |
| {{!}}-
| |
| {{!}}{{val{{!}}1{{!}}u=kpc3}} {{!}}{{!}}≈ {{val{{!}}2.938{{!}}e=58{{!}}u=m3}}
| |
| {{!}}-
| |
| {{!}}{{val{{!}}1{{!}}u=Mpc3}}{{!}}{{!}}≈ {{val{{!}}2.938{{!}}e=67{{!}}u=m3}}
| |
| {{!}}-
| |
| {{!}}{{val{{!}}1{{!}}u=Gpc3}}{{!}}{{!}}≈ {{val{{!}}2.938{{!}}e=76{{!}}u=m3}}
| |
| {{!}}}
| |
| }} (kpc<sup>3</sup>) are selected in various directions. All the stars in these volumes are counted and the total number of stars statistically determined. The number of globular clusters, dust clouds, and interstellar gas is determined in a similar fashion. To determine the number of galaxies in [[supercluster]]s, volumes in cubic megaparsecs{{efn|name=vol}} (Mpc<sup>3</sup>) are selected. All the galaxies in these volumes are classified and tallied. The total number of galaxies can then be determined statistically. The huge [[Bootes void|void]] in [[Bootes (constellation)|Boötes]]<ref>[http://adsabs.harvard.edu/abs/1981ApJ...248L..57K Astrophysical Journal, Harvard]</ref> is measured in cubic megaparsecs.
| |
| | |
| In [[cosmology]], volumes of cubic gigaparsecs{{efn|name=vol}} (Gpc<sup>3</sup>) are selected to determine the distribution of matter in the visible universe and to determine the number of galaxies and quasars. The Sun is alone in its cubic parsec,{{efn|name=vol}} (pc<sup>3</sup>) but in globular clusters the stellar density per cubic parsec could be from 100 to {{val|1000}}.
| |
| | |
| == References ==
| |
| '''Explanatory notes'''
| |
| {{notes}}
| |
| | |
| '''Citations'''
| |
| {{Reflist|2}}
| |
| | |
| == External links ==
| |
| *{{cite web | author=Guidry, Michael | title=Astronomical Distance Scales | work=Astronomy 162: Stars, Galaxies, and Cosmology | publisher=University of Tennessee, Knoxville | url=http://csep10.phys.utk.edu/guidry/violence/distances.html | accessdate=2010-03-26}}
| |
| *{{cite web|last=Merrifield|first=Michael|title=pc Parsec|url=http://www.sixtysymbols.com/videos/parsec.htm|work=Sixty Symbols|publisher=[[Brady Haran]] for the [[University of Nottingham]]}}
| |
| | |
| {{Units of length used in Astronomy}}
| |
| | |
| [[Category:Units of measurement in astronomy]]
| |
| [[Category:Parallax]]
| |