The parsec (symbol: pc) is a unit of length used to measure large distances to astronomical objects outside the Solar System. A parsec is defined as the distance at which one astronomical unit subtends an angle of one arcsecond,^{[1]} which corresponds to 648000/π astronomical units. One parsec is equal to about 3.26 lightyears (30 trillion km or 19 trillion miles) in length. The nearest star, Proxima Centauri, is about 1.3 parsecs (4.2 lightyears) from the Sun.^{[2]} Most of the stars visible to the unaided eye in the night sky are within 500 parsecs of the Sun.
The parsec unit was probably first suggested in 1913 by the British astronomer Herbert Hall Turner.^{[3]} Named as a portmanteau of the parallax of one arcsecond, it was defined so as to make calculations of astronomical distances quick and easy for astronomers from only their raw observational data. Partly for this reason, it is the unit preferred in astronomy and astrophysics, though the lightyear 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 middistance galaxies, and gigaparsecs (Gpc) for many quasars and the most distant galaxies.
In August 2015, the 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 648000/π astronomical units, or approximately 3.08567758149137×10^{16} metres (based on the IAU 2012 exact SI definition of the astronomical unit). This corresponds to the smallangle definition of the parsec found in many contemporary astronomical references.^{[4]}^{[5]}
Parsec  

A parsec is the distance from the Sun to an astronomical object that has a parallax angle of one arcsecond (not to scale)


Unit information  
Unit system  astronomical units 
Unit of  length/distance 
Symbol  pc 
Unit conversions  
1 pc in ...  ... is equal to ... 
metric (SI) units  3.0857×10^{16} m ~31 petametres 
imperial & US units  1.9174×10^{13} mi 
astronomical units  2.06265×10^{5} au 3.26156 ly 
The parsec is defined as being equal to the length of the longer leg of an extremely elongated imaginary right triangle in space. The two dimensions on which this triangle is based are its shorter leg, of length one astronomical unit (the average EarthSun distance), and the subtended angle of the vertex opposite that leg, measuring one arc second. Applying the rules of trigonometry to these two values, the unit length of the other leg of the triangle (the parsec) can be derived.
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. 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.^{[6]} 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 3.5parsec distance of 61 Cygni.^{[7]}
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. 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 one astronomical unit (au), and the length of the 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 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.^{[3]} It was Turner's proposal that stuck.
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 (1/3600 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:
Because the astronomical unit is defined to be 149597870700 m,^{[8]} the following can be calculated:
Therefore, 1 parsec  ≈ 206264.806247096 astronomical units 
≈ 3.085677581×10^{16} metres  
≈ 19.173511577 trillion miles  
≈ 3.261563777 lightyears 
A corollary states that a parsec is also the distance from which a disc one astronomical unit in diameter must be viewed for it to have an angular diameter of one arcsecond (by placing the observer at D and a diameter of the disc on ES).
The length of the parsec used in IAU 2015 Resolution B2^{[9]} (exactly 648000/π astronomical units) corresponds exactly to that derived using the smallangle calculation. This differs from the classic inversetangent definition by about 200 km, i.e. only after the 11th significant figure. As the astronomical unit was defined by the IAU (2012) as an exact SI length in metres, so now the parsec corresponds to an exact SI length in metres. To the nearest meter, the smallangle parsec corresponds to 30,856,775,814,913,673 m.
The parallax method is the fundamental calibration step for distance determination in astrophysics; however, the accuracy of groundbased telescope measurements of parallax angle is limited to about 0.01 arcseconds, and thus to stars no more than 100 pc distant.^{[10]} This is because the Earth's atmosphere limits the sharpness of a star's image.^{[11]} Spacebased telescopes are not limited by this effect and can accurately measure distances to objects beyond the limit of groundbased observations. Between 1989 and 1993, the Hipparcos satellite, launched by the European Space Agency (ESA), measured parallaxes for about 100000 stars with an astrometric precision of about 0.97 milliarcseconds, and obtained accurate measurements for stellar distances of stars up to 1000 pc away.^{[12]}^{[13]}
ESA's Gaia satellite, which launched on 19 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 Centre, about 8000 pc away in the constellation of Sagittarius.^{[14]}
The parsec was apparently misused as a unit of time in Star Wars, when Han Solo describes the Millennium Falcon as "the ship that made the Kessel Run in less than twelve parsecs".
Distances expressed in fractions of a parsec usually involve objects within a single star system. So, for example:
Distances expressed in parsecs (pc) include distances between nearby stars, such as those in the same spiral arm or globular cluster. A distance of 1000 parsecs (3262 lightyears) is commonly 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:
A distance of one million parsecs is commonly denoted by the megaparsec (Mpc). Astronomers typically express the distances between neighbouring galaxies and galaxy clusters in megaparsecs.
Galactic distances are sometimes given in units of Mpc/h (as in "50/h Mpc", also written "50 Mpc h^{−1}"). h is a parameter in the range 0.5 < h < 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 ≈ c/H × z.^{[15]}
One gigaparsec (Gpc) is one billion parsecs — one of the largest units of length commonly used. One gigaparsec is about 3.26 billion lightyears, or roughly 1/14 of the distance to the horizon of the observable universe (dictated by the cosmic background radiation). Astronomers typically use gigaparsecs to express the sizes of largescale 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:
To determine the number of stars in the Milky Way, volumes in cubic kiloparsecs^{[a]} (kpc^{3}) 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^{[a]} (Mpc^{3}) 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.^{[18]}
In physical cosmology, volumes of cubic gigaparsecs^{[a]} (Gpc^{3}) are selected to determine the distribution of matter in the visible universe and to determine the number of galaxies and quasars. The Sun is the only star in its cubic parsec,^{[a]} (pc^{3}) but in globular clusters the stellar density could be from 100 to 1000 per cubic parsec.
1 pc^{3}  ≈ 2.938×10^{49} m^{3} 
1 kpc^{3}  ≈ 2.938×10^{58} m^{3} 
1 Mpc^{3}  ≈ 2.938×10^{67} m^{3} 
1 Gpc^{3}  ≈ 2.938×10^{76} m^{3} 
1 Tpc³  ≈ 2.938×10^{85} m^{3} 
There is a need for a name for this unit of distance. Mr. Charlier has suggested Siriometer ... Professor Turner suggests parsec, which may be taken as an abbreviated form of 'a distance corresponding to a parallax of one second'.
The XXVIII General Assembly of International Astronomical Union recommends [adopted] that the astronomical unit be redefined to be a conventional unit of length equal to exactly 149597870700 m, in agreement with the value adopted in IAU 2009 Resolution B2
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