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{{short description|Unit of length used in astronomy}}{{Other uses}}{{Use dmy dates|date=May 2020}}

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   ~31 petametresImperial units>imperial  US units1.9174ul=mi}}Astronomical system of units>astronomical units2.06265ul=au}}   {{Valul=ly}}}}The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to {{convert|1|pc|ly|2|abbr=off|lk=out|disp=out}} or {{convert|1|pc|AU|0|abbr=off|lk=out|disp=out}} (AU), i.e. {{convert|30.9|e12km|e12mi|abbr=off|lk=on}}.{{efn|name=trillion|One trillion here is short scale, ie. 1012 (one million million, or billion in long scale).}} The parsec unit is obtained by the use of parallax and trigonometry, and is defined as the distance at which 1 AU subtends an angle of one arcsecondWEB, Cosmic Distance Scales – The Milky Way,heasarc.gsfc.nasa.gov/docs/cosmic/milkyway_info.html, 24 September 2014, ({{sfrac|3600}} of a degree). The nearest star, Proxima Centauri, is about {{convert|1.3|pc|ly|abbr=off}} from the Sun: from that distance, the gap between the Earth and the Sun spans slightly less than {{sfrac|3600}} of one degree of view.CONFERENCE, Benedict, G. F., etal, Astrometric Stability and Precision of Fine Guidance Sensor #3: The Parallax and Proper Motion of Proxima Centauri,clyde.as.utexas.edu/SpAstNEW/Papers_in_pdf/%7BBen93%7DEarlyProx.pdf, 380–384, 11 July 2007, Proceedings of the HST Calibration Workshop, Most stars visible to the naked eye are within a few hundred parsecs of the Sun, with the most distant at a few thousand parsecs, and the Andromeda Galaxy at over 700,000 parsecs.WEB, Farthest Stars,stardate.org/radio/program/2021-05-15, StarDate, University of Texas at Austin, 5 September 2021, 15 May 2021, The word parsec is a portmanteau of “parallax of one second” and was coined by the British astronomer Herbert Hall Turner in 1913JOURNAL, Dyson, F. W., Frank Watson Dyson, March 1913, The distribution in space of the stars in Carrington’s Circumpolar Catalogue, Monthly Notices of the Royal Astronomical Society, 73, 5, 342, 1913MNRAS..73..334D, 10.1093/mnras/73.5.334, free, [paragraph 14, page 342] Taking the unit of distance R* to be that corresponding to a parallax of 1″·0 [… Footnote:] * There is need for a name for this unit of distance. Mr. Carl Charlier, Charlier has suggested Sirius, Siriometer, but if the violence to the Greek language can be overlooked, the word Astron might be adopted. 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”., to simplify astronomers’ calculations of astronomical distances from only raw observational data. Partly for this reason, it is the unit preferred in astronomy and astrophysics, though the light-year remains prominent in popular science texts and common usage. Although parsecs are used for the shorter distances within the Milky Way, multiples of parsecs are required for the larger scales in the universe, including kiloparsecs (kpc) for the more distant objects within and around the Milky Way, megaparsecs (Mpc) for mid-distance galaxies, and gigaparsecs (Gpc) for many quasars and the most distant galaxies.In August 2015, the International Astronomical Union (IAU) passed Resolution B2 which, as part of the definition of a standardized absolute and apparent bolometric magnitude scale, mentioned an existing explicit definition of the parsec as exactly {{sfrac|{{Val|648000}}|{{pi}}}} au, or approximately {{Val|3.0856775814913673|e=16}} metres (based on the IAU 2012 definition of the astronomical unit). This corresponds to the small-angle definition of the parsec found in many astronomical references.BOOK, Allen’s Astrophysical Quantities, 2000, AIP Press / Springer, 978-0387987460, Cox, Arthur N., 4th, New York, 2000asqu.book.....C, BOOK, Binney, James, Galactic Dynamics, Tremaine, Scott, 2008, Princeton University Press, 978-0-691-13026-2, 2nd, Princeton, NJ, 2008gady.book.....B,

History and derivation

{{See also|Stellar parallax}}Imagining an elongated right triangle in space, where the shorter leg measures one au (astronomical unit, the average Earth–Sun distance) and the subtended angle of the vertex opposite that leg measures one arcsecond ({{frac|3600}} of a degree), the parsec is defined as the length of the adjacent leg. The value of a parsec can be derived through the rules of trigonometry. Simply put, the distance from Earth whereupon the radius of its solar orbit subtends one arcsecond.One of the oldest methods used by astronomers to calculate the distance to a star is to record the difference in angle between two measurements of the position of the star in the sky. The first measurement is taken from the Earth on one side of the Sun, and the second is taken approximately half a year later, when the Earth is on the opposite side of the Sun.{{efn|name=orbit|Terrestrial observations of a star’s position should be taken when the Earth is at the furthest points in its orbit from a line between the Sun and the star, in order to form a right angle at the Sun and a full au of separation as viewed from the star.}} The distance between the two positions of the Earth when the two measurements were taken is twice the distance between the Earth and the Sun. The difference in angle between the two measurements is twice the parallax angle, which is formed by lines from the Sun and Earth to the star at the distant vertex. Then the distance to the star could be calculated using trigonometry.WEB, Deriving the Parallax Formula,imagine.gsfc.nasa.gov/YBA/HTCas-size/parallax1-derive.html, High Energy Astrophysics Science Archive Research Center (HEASARC), NASA’s Imagine the Universe!, Astrophysics Science Division (ASD) at NASA’s Goddard Space Flight Center, 26 November 2011, The first successful published direct measurements of an object at interstellar distances were undertaken by German astronomer Friedrich Wilhelm Bessel in 1838, who used this approach to calculate the 3.5-parsec distance of 61 Cygni.JOURNAL, Bessel, F. W., Friedrich Wilhelm Bessel, 1838, Bestimmung der Entfernung des 61sten Sterns des Schwans, Determination of the distance of the 61st star of Cygnus,zenodo.org/record/1424605, Astronomische Nachrichten, 16, 5, 65–96, 1838AN.....16...65B, 10.1002/asna.18390160502, thumb|left|upright=1.36|Stellar parallax motion from annual parallax|alt=Diagrams illustrating the apparent change in position of a celestial object when viewed from different positions in Earth’s orbit.The parallax of a star is defined as 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 of the Earth’s orbit. Substituting the star’s parallax for the one arcsecond angle in the imaginary right triangle, the long leg of the triangle will measure the distance from the Sun to the star. A parsec can be defined as the length of the right triangle side adjacent to the vertex occupied by a star whose parallax angle is one arcsecond.The use of the parsec as a unit of distance follows naturally from Bessel’s method, because the distance in parsecs can be computed simply as the 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 arcseconds, the object is 2 pc away; etc.). No trigonometric functions 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. It was Turner’s proposal that stuck.

Calculating the value of a parsec

By the 2015 definition, {{Val|1|u=au}} of arc length subtends an angle of {{Val|1|u=arcsecond}} at the center of the circle of radius {{Val|1|u=pc}}. That is, 1 pc = 1 au/tan({{Val|1|u=arcsecond}}) ≈ 206,264.8 au by definition.JOURNAL, B. Luque, F. J. Ballesteros, Title: To the Sun and beyond, 2019, 10.1038/s41567-019-0685-3, Nature Physics, 15, 12, 1302, 2019NatPh..15.1302L, free, Converting from degree/minute/second units to radians, Therefore,pi ~ mathrm{pc} = 180 times 60 times 60 ~ mathrm{au} = 180 times 60 times 60 times 149,597,870,700 ~ mathrm{m} = 96,939,420,213,600,000 ~ mathrm{m} (exact by the 2015 definition)Therefore,1 ~ mathrm{pc} = frac{96,939,420,213,600,000}{pi} ~ mathrm{m} = 30,856,775,814,913,673 ~ mathrm{m} (to the nearest metre).Approximately, In the diagram above (not to scale), S represents the Sun, and E the Earth at one point in its orbit (such as to form a right angle at S{{efn|name=orbit}}). Thus the distance ES is one astronomical unit (au). The angle SDE is one arcsecond ({{sfrac|3600}} of a degree) so by definition D is a point in space at a distance of one parsec from the Sun. Through trigonometry, the distance SD is calculated as follows:begin{align}mathrm{SD} &= frac{mathrm{ES} }{tan 1’’} &= frac{mathrm{ES}}{tan left (frac{1}{60 times 60} times frac{pi}{180} right )} & approx frac{1 , mathrm{au} }{frac{1}{60 times 60} times frac{pi}{180}} = frac{648,000}{pi} , mathrm{au} approx 206,264.81 ~ mathrm{au}.end{align}Because the astronomical unit is defined to be {{Val|149597870700|ul=m}},{{Citation |title=RESOLUTION B2 |date=31 August 2012 |editor-last=International Astronomical Union |contribution=RESOLUTION B2 on the re-definition of the astronomical unit of length |contribution-url=http://www.iau.org/static/resolutions/IAU2012_English.pdf |place=Beijing |publisher=International Astronomical Union |quote=The XXVIII General Assembly of the International Astronomical Union recommends [adopted] that the astronomical unit be redefined to be a conventional unit of length equal to exactly {{Val|149597870700|u=m}}, in agreement with the value adopted in IAU 2009 Resolution B2}} the following can be calculated:{| style="margin-left:1em”Therefore, 1 parsec206264.806247096}} astronomical units3.085677581|e=16}} metres30.856775815}} trillion kilometres19.173511577}} trillion milesTherefore, if {{Val|1|ul=ly}} ≈ {{Convert|1|ly|m|disp=out|sigfig=3}}, A corollary states that a parsec is also the distance from which a disc that is one au in diameter must be viewed for it to have an angular diameter of one arcsecond (by placing the observer at D and a disc spanning ES).Mathematically, to calculate distance, given obtained angular measurements from instruments in arcseconds, the formula would be:text{Distance}_text{star} = frac {text{Distance}_text{earth-sun}}{tan{frac{theta}{3600}}}where θ is the measured angle in arcseconds, Distanceearth-sun is a constant ({{Val|1|u=au}} or {{Convert|1|au|ly|disp=out|sigfig=5}}). The calculated stellar distance will be in the same measurement unit as used in Distanceearth-sun (e.g. if Distanceearth-sun = {{Val|1|u=au}}, unit for Distancestar is in astronomical units; if Distanceearth-sun = {{Convert|1|au|ly|disp=out|sigfig=5}}, unit for Distancestar is in light-years).The length of the parsec used in IAU 2015 Resolution B2{{Citation |title=RESOLUTION B2 |date=13 August 2015 |editor-last=International Astronomical Union |contribution=RESOLUTION B2 on recommended zero points for the absolute and apparent bolometric magnitude scales |contribution-url=http://www.iau.org/static/resolutions/IAU2015_English.pdf |place=Honolulu |publisher=International Astronomical Union |quote=The XXIX General Assembly of the International Astronomical Union notes [4] that the parsec is defined as exactly (648 000/pi) au per the AU definition in IAU 2012 Resolution B2}} (exactly {{sfrac|{{Val|648000}}|{{pi}}}} astronomical units) corresponds exactly to that derived using the small-angle calculation. This differs from the classic inverse-tangent definition by about {{Val|200|u=km}}, i.e.: only after the 11th significant figure. As the astronomical unit was defined by the IAU (2012) as an exact length in metres, so now the parsec corresponds to an exact length in metres. To the nearest meter, the small-angle parsec corresponds to {{Val|30856775814913673|u=m}}.

Usage and measurement

The parallax method is the fundamental calibration step for distance determination in astrophysics; however, the accuracy of ground-based telescope measurements of parallax angle is limited to about {{Val|0.01|u=arcsecond}}, and thus to stars no more than {{Val|100|u=pc}} distant.WEB, Astronomy 162,www.astronomy.ohio-state.edu/~pogge/Ast162/Unit1/distances.html, Pogge, Richard, Ohio State University, This is because the Earth’s atmosphere limits the sharpness of a star’s image.{{cn|date=August 2022}} 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 astrometric precision of about {{Val|0.97|ul=mas}}, and obtained accurate measurements for stellar distances of stars up to {{Val|1000|u=pc}} away.WEB, The Hipparcos Space Astrometry Mission,www.rssd.esa.int/index.php?project=HIPPARCOS, 28 August 2007, WEB, From Hipparchus to Hipparcos,wwwhip.obspm.fr/hipparcos/SandT/hip-SandT.html, Turon, Catherine, ESA’s Gaia satellite, which launched on 19 December 2013, is intended to measure one billion stellar distances to within {{Val|20|u=microarcsecond}}s, producing errors of 10% in measurements as far as the Galactic Centre, about {{Val|8000|u=pc}} away in the constellation of Sagittarius.WEB, GAIA,sci.esa.int/science-e/www/area/index.cfm?fareaid=26, European Space Agency,

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|u=parsec}}.
• The most distant space probe, Voyager 1, was {{Val|0.0007897|u=parsec}} from Earth {{As of|2024|February|lc=on}}. Voyager 1 took {{Val|46|u=years}} to cover that distance.
• The Oort cloud is estimated to be approximately {{Val|0.6|u=parsec}} in diameter

subtends

Parsecs and kiloparsecs

Distances expressed in parsecs (pc) include distances between nearby stars, such as those in the same spiral arm or globular cluster. A distance of {{Convert|1000|pc|ly|sigfig=4}} is denoted by the kiloparsec (kpc). Astronomers typically use kiloparsecs to express distances between parts of a galaxy or within groups of galaxies. So, for example :

• Proxima Centauri, the nearest known star to earth other than the sun, is about {{Convert|1.3|pc|ly|sigfig=3}} away by direct parallax measurement.
• The distance to the open cluster Pleiades is {{Val|130|10|u=pc}} ({{Val|420|30|u=ly}}) from us per Hipparcos parallax measurement.
• The centre of the Milky Way is more than {{Convert|8|kpc|ly}} from the Earth and the Milky Way is roughly {{Convert|34|kpc|ly}} across.
• ESO 383-76, one of the largest known galaxies, has a diameter of {{Convert|540.9|kpc|e6ly|1|abbr=unit}}.
• The Andromeda Galaxy (M31) is about {{Convert|780|kpc|e6ly|abbr=unit}} away from the Earth.

Megaparsecs and gigaparsecs

Astronomers typically express the distances between neighbouring galaxies and galaxy clusters in megaparsecs (Mpc). A megaparsec is one million parsecs, or about 3,260,000 light years.WEB,astronomy.com/magazine/ask-astro/2020/02/why-is-a-parsec-326-light-years, Why is a parsec 3.26 light-years?, Astronomy.com, 1 February 2020, 20 July 2021, Sometimes, galactic distances are given in units of Mpc/h (as in “50/h Mpc”, also written “{{nowrap|50 Mpc h−1}}“). h is a constant (the “dimensionless Hubble constant“) in the range {{nowrap|0.5 < h < 0.75}} reflecting the uncertainty in the value of the Hubble constant H for the rate of expansion of the universe: {{nowrap|1=h = {{sfrac|H|100 (km/s)/Mpc}}}}. The Hubble constant becomes relevant when converting an observed redshift z into a distance d using the formula {{nowrap|d ≈ {{sfrac|c|H}} × z}}.WEB, Galaxy structures: the large scale structure of the nearby universe,pil.phys.uniroma1.it/twiki/bin/view/Pil/GalaxyStructures, dead,pil.phys.uniroma1.it/twiki/bin/view/Pil/GalaxyStructures," title="web.archive.org/web/20070305202144pil.phys.uniroma1.it/twiki/bin/view/Pil/GalaxyStructures,">web.archive.org/web/20070305202144pil.phys.uniroma1.it/twiki/bin/view/Pil/GalaxyStructures, 5 March 2007, 22 May 2007, One gigaparsec (Gpc) is one billion parsecs — one of the largest units of length commonly used. One gigaparsec is about {{Convert|1|Gpc|e9ly|sigfig=3|abbr=unit|disp=out}}, or roughly {{sfrac|14}} of the distance to the horizon of the observable universe (dictated by the cosmic microwave background radiation). Astronomers typically use gigaparsecs to express the sizes of large-scale structures such as the size of, and distance to, the CfA2 Great Wall; the distances between galaxy clusters; and the distance to quasars.For example:

• The Andromeda Galaxy is about {{Convert|0.78|Mpc|e6ly|abbr=unit}} from the Earth.
• The nearest large galaxy cluster, the Virgo Cluster, is about {{Convert|16.5|Mpc|e6ly|abbr=unit}} from the Earth.JOURNAL, Mei, S., Blakeslee, J. P., Côté, P., etal, 2007, The ACS Virgo Cluster Survey. XIII. SBF Distance Catalog and the Three-dimensional Structure of the Virgo Cluster, The Astrophysical Journal, 655, 1, 144–162, astro-ph/0702510, 2007ApJ...655..144M, 10.1086/509598, 16483538,
• The galaxy RXJ1242-11, observed to have a supermassive black hole core similar to the Milky Way’s, is about {{Convert|200|Mpc|e6ly|abbr=unit}} from the Earth.
• The galaxy filament Hercules–Corona Borealis Great Wall, currently the largest known structure in the universe, is about {{Convert|3|Gpc|e9ly|abbr=unit}} across.
• The particle horizon (the boundary of the observable universe) has a radius of about {{Convert|14|Gpc|e9ly|abbr=unit}}.JOURNAL, Lineweaver, Charles H., Davis, Tamara M., 1 March 2005, Misconceptions about the Big Bang,www.scientificamerican.com/article.cfm?id=misconceptions-about-the-2005-03&page=5, dead, Scientific American, 292, 3, 36–45, 2005SciAm.292c..36L, 10.1038/scientificamerican0305-36,www.scientificamerican.com/article.cfm?id=misconceptions-about-the-2005-03&page=5," title="web.archive.org/web/20110810231727www.scientificamerican.com/article.cfm?id=misconceptions-about-the-2005-03&page=5,">web.archive.org/web/20110810231727www.scientificamerican.com/article.cfm?id=misconceptions-about-the-2005-03&page=5, 10 August 2011, 4 February 2016,

Volume units

To determine the number of stars in the Milky Way, volumes in cubic kiloparsecs{{efn|name=vol|{{aligned table1Approximation {{Val>2.938u=m3}}1≈ {{Vale=58|u=m3}}1≈ {{Vale=67|u=m3}}1≈ {{Vale=76|u=m3}}1≈ {{Vale=85|u=m3}}}}}} (kpc3) 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 superclusters, volumes in cubic megaparsecs{{efn|name=vol}} (Mpc3) are selected. All the galaxies in these volumes are classified and tallied. The total number of galaxies can then be determined statistically. The huge Boötes void is measured in cubic megaparsecs.JOURNAL, Kirshner, R. P., Oemler, A. Jr., Schechter, P. L., Shectman, S. A., 1981, A million cubic megaparsec void in Bootes, The Astrophysical Journal, 248, L57, 1981ApJ...248L..57K, 10.1086/183623, 0004-637X, In physical cosmology, volumes of cubic gigaparsecs{{efn|name=vol}} (Gpc3) are selected to determine the distribution of matter in the visible universe and to determine the number of galaxies and quasars. The Sun is currently the only star in its cubic parsec,{{efn|name=vol}} (pc3) but in globular clusters the stellar density could be from {{Val|100|-|1000|u=pc−3}}.The observational volume of gravitational wave interferometers (e.g., LIGO, Virgo) is stated in terms of cubic megaparsecs{{efn|name=vol}} (Mpc3) and is essentially the value of the effective distance cubed.

In popular culture

The parsec was seemingly used incorrectly as a measurement of time by Han Solo in the first Star Wars film, when he claimed his ship, the Millennium Falcon “made the Kessel Run in less than 12 parsecs”. The claim was repeated in (Star Wars: The Force Awakens|The Force Awakens), but this was changed in (Solo: A Star Wars Story), by stating the Millennium Falcon traveled a shorter distance (as opposed to a quicker time) due to a more dangerous route through the Kessel Run, enabled by its speed and maneuverability.WEB, 30 May 2018, ‘Solo’ Corrected One of the Most Infamous ‘Star Wars’ Plot Holes,www.esquire.com/entertainment/movies/a20967903/solo-star-wars-kessel-distance-plot-hole/, Esquire, It is also used ambiguously as a spatial unit in The Mandalorian as opposed to a unit of distance.WEB, Choi, Charlse, 5 November 2019, ‘Star Wars’ Gets the Parsec Wrong Again in ‘The Mandalorian’,www.space.com/star-wars-the-mandalorian-parsec.html, 6 May 2020, space.com, In the book A Wrinkle in Time, “Megaparsec” is Mr. Murry’s nickname for his daughter Meg.WEB, In “A Wrinkle in Time,” what is Mr. Murry’s nickname for Meg?,www.enotes.com/homework-help/wrinkle-time-what-mr-murrays-nickname-for-meg-39431b, 6 May 2020,

See also

• Attoparsec
• Distance measure

Notes

{{notes}}

References

{{reflist}}

External links

• WEB, Astronomical Distance Scales,csep10.phys.utk.edu/guidry/violence/distances.html, Guidry, Michael, Astronomy 162: Stars, Galaxies, and Cosmology, University of Tennessee, Knoxville, dead,csep10.phys.utk.edu/guidry/violence/distances.html," title="archive.today/20121212134512csep10.phys.utk.edu/guidry/violence/distances.html,">archive.today/20121212134512csep10.phys.utk.edu/guidry/violence/distances.html, 12 December 2012, 26 March 2010,
• WEB, pc Parsec,www.sixtysymbols.com/videos/parsec.htm, Merrifield, Michael, Sixty Symbols, Brady Haran for the University of Nottingham,

{{Units of length used in Astronomy}}