# Parsec

Parsec
A parsec is the distance from the Sun to an astronomical object that has a parallax angle of one arcsecond (not to scale)
General information
Unit systemastronomical units
Unit oflength/distance
Symbolpc
Conversions
1 pc in ...... is equal to ...
metric (SI) units   3.0857×1016 m
~31 petametres
imperial & US units   1.9174×1013 mi
astronomical units   2.06265×105 au
3.26156 ly

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 light-years or 31 trillion kilometres (31×1012 km) or 19 trillion miles (19×1012 mi).[a] The nearest star, Proxima Centauri, is about 1.3 parsecs (4.2 light-years) from the Sun.[2] Most of the stars visible to the unaided eye in the night sky are within 500 parsecs of the Sun.[citation needed]

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 to make calculations of astronomical distances from only their raw observational data quick and easy for astronomers. 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 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 3.08567758149137×1016 metres (based on the IAU 2012 exact SI definition of the astronomical unit). This corresponds to the small-angle definition of the parsec found in many contemporary astronomical references.[4]

## History and derivation

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 Earth-Sun 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.[5] 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.[6]

Stellar parallax motion from annual parallax

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.

### Calculating the value of a 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 (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:

${\displaystyle \mathrm {SD} ={\frac {\mathrm {ES} }{\tan 1''}}}$
${\displaystyle \mathrm {SD} \approx {\frac {\mathrm {ES} }{1''}}={\frac {1\,{\mbox{au}}}.}$

Because the astronomical unit is defined to be 149597870700 m,[7] the following can be calculated:

 Therefore, 1 parsec ≈ 206264.806247096 astronomical units ≈ 3.085677581×1016 metres ≈ 19.173511577 trillion miles ≈ 3.261563777 light-years

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).

Mathematically, to calculate distance, given obtained angular measurements from instruments in arcseconds, the formula would be:

${\displaystyle Distance_{star}={\frac {Distance_{earth-sun}}{\tan {\frac {\theta }{3600}}}}}$

where θ is the measured angle in arcseconds, Distanceearth-sun is a constant (1 AU or 1.5813×10−5 ly). The calculated stellar distance will be in the same measurement unit as used in Distanceearth-sun (e.g. if Distanceearth-sun = 1 AU, unit for Distancestar is in astronomical units; if Distanceearth-sun = 1.5813×10−5 ly, unit for Distancestar is in light years).

The length of the parsec used in IAU 2015 Resolution B2[8] (exactly 648000/π astronomical units) corresponds exactly to that derived using the small-angle calculation. This differs from the classic inverse-tangent 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 small-angle parsec corresponds to 30,856,775,814,913,673 m.

Other Languages
Afrikaans: Parsek
العربية: فرسخ فلكي
aragonés: Pársec
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беларуская: Парсек
беларуская (тарашкевіца)‎: Парсэк
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मराठी: पार्सेक
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اردو: پارسک
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