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Stellarparallax parsec1.svg
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 system astronomical units
Unit of length/distance
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 ). [lower-alpha 1] 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 ]

Unit of length Reference value of length

A unit of length refers to any discrete, pre-established length or distance having a constant magnitude which is used as a reference or convention to express linear dimension. The most common units in modern use are U.S. customary units in the United States and metric units elsewhere. British Imperial units are still used for some purposes in the United Kingdom and some other countries. The metric system is sub-divided into SI and non-SI units.

Astronomical object physical body of astronomically-significant size,mass,or role,naturally occurring in a universe;single,tightly bound contiguous entity (while an astronomical/celestial object is a complex,less cohesively bound structure,may consist of multiple bodies

An astronomical object or celestial object is a naturally occurring physical entity, association, or structures that exists in the observable universe. In astronomy, the terms object and body are often used interchangeably. However, an astronomical body or celestial body is a single, tightly bound, contiguous entity, while an astronomical or celestial object is a complex, less cohesively bound structure, which may consist of multiple bodies or even other objects with substructures.

Solar System planetary system of the Sun

The Solar System is the gravitationally bound planetary system of the Sun and the objects that orbit it, either directly or indirectly. Of the objects that orbit the Sun directly, the largest are the eight planets, with the remainder being smaller objects, such as the five dwarf planets and small Solar System bodies. Of the objects that orbit the Sun indirectly—the moons—two are larger than the smallest planet, Mercury.


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 kilo parsecs (kpc) for the more distant objects within and around the Milky Way, mega parsecs (Mpc) for mid-distance galaxies, and giga parsecs (Gpc) for many quasars and the most distant galaxies.

Astronomer scientist who studies celestial bodies

An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets, and galaxies – in either observational or theoretical astronomy. Examples of topics or fields astronomers study include planetary science, solar astronomy, the origin or evolution of stars, or the formation of galaxies. Related but distinct subjects like physical cosmology, which studies the Universe as a whole.

Herbert Hall Turner FRS was a British astronomer and seismologist.

A portmanteau or portmanteau word is a linguistic blend of words, in which parts of multiple words or their phones (sounds) are combined into a new word, as in smog, coined by blending smoke and fog, or motel, from motor and hotel. In linguistics, a portmanteau is defined as a single morph that represents two or more morphemes.

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.

Right triangle triangle in which one angle is a 90-degree angle

A right triangle or right-angled triangle is a triangle in which one angle is a right angle. The relation between the sides and angles of a right triangle is the basis for trigonometry.

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]

Star An astronomical object consisting of a luminous spheroid of plasma held together by its own gravity

A star is type of astronomical object consisting of a luminous spheroid of plasma held together by its own gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye from Earth during the night, appearing as a multitude of fixed luminous points in the sky due to their immense distance from Earth. Historically, the most prominent stars were grouped into constellations and asterisms, the brightest of which gained proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. However, most of the estimated 300 sextillion (3×1023) stars in the Universe are invisible to the naked eye from Earth, including all stars outside our galaxy, the Milky Way.

61 Cygni binary star in the Cygnus constellation

61 Cygni is a binary star system in the constellation Cygnus, consisting of a pair of K-type dwarf stars that orbit each other in a period of about 659 years. Of apparent magnitude 5.20 and 6.05, respectively, they can be seen with binoculars in city skies or with the naked eye in rural areas without photopollution.

Stellar parallax motion from annual parallax ParallaxV2.svg
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.

In mathematics and all natural sciences, the angular distance between two point objects, as viewed from a location different from either of these objects, is the angle of length between the two directions originating from the observer and pointing toward these two objects.

Celestial sphere imaginary sphere of arbitrarily large radius, concentric with the observer

In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, which may be centered on Earth or the observer. If centered on the observer, half of the sphere would resemble a hemispherical screen over the observing location.

Trigonometry In geometry, study of the relationship between angles and lengths

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. In particular, 3rd-century astronomers first noted that the ratio of the lengths of two sides of a right-angled triangle depends only of one acute angles of the triangle. These dependencies are now called trigonometric functions.

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

Parsec (1).svg

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 , [7] the following can be calculated:

Therefore, 1 parsec206264.806247096 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:

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.

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 0.01 arcseconds, and thus to stars no more than 100 pc distant. [9] This is because the Earth's atmosphere limits the sharpness of a star's image. [10] 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 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. [11]

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. [12]

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:

The jet erupting from the active galactic nucleus of M87 is thought to be 70001500000000000001.5 kiloparsecs (70194626297201092014890 ly) long. (image from Hubble Space Telescope) M87 jet.jpg
The jet erupting from the active galactic nucleus of M87 is thought to be 1.5 kiloparsecs (4890  ly ) long. (image from Hubble Space Telescope)

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 1000 parsecs (3262 light-years) 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:

Megaparsecs and gigaparsecs

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. [13]

One gigaparsec (Gpc) is one billion parsecs — one of the largest units of length commonly used. One gigaparsec is about 3.26 billion light-years, 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 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:

Volume units

To determine the number of stars in the Milky Way, volumes in cubic kiloparsecs [lower-alpha 2] (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 [lower-alpha 2] (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. [16]

In physical cosmology, volumes of cubic gigaparsecs [lower-alpha 2] (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 the only star in its cubic parsec, [lower-alpha 2] (pc3) but in globular clusters the stellar density could be from 100 to 1000 per cubic parsec.

The parsec is apparently used incorrectly as a measurement of time not distance in Han Solo's claim in A New Hope, the first Star Wars film, that he "made the Kessel Run in less than 12 parsecs". This was retconned in Solo: A Star Wars Story . [17]

See also


  1. One trillion here is taken to be 1012 (one million million, or billion in long scale).
  2. 1 2 3 4
    1 pc3 2.938×1049 m3
    1 kpc32.938×1058 m3
    1 Mpc32.938×1067 m3
    1 Gpc32.938×1076 m3
    1 Tpc³2.938×1085 m3

Related Research Articles

Astronomical unit mean distance between Earth and the Sun, common length reference in astronomy

The astronomical unit is a unit of length, roughly the distance from Earth to the Sun. However, that distance varies as Earth orbits the Sun, from a maximum (aphelion) to a minimum (perihelion) and back again once a year. Originally conceived as the average of Earth's aphelion and perihelion, since 2012 it has been defined as exactly 149597870700 metres or about 150 million kilometres. The astronomical unit is used primarily for measuring distances within the Solar System or around other stars. It is also a fundamental component in the definition of another unit of astronomical length, the parsec.

Absolute magnitude is a measure of the luminosity of a celestial object, on a logarithmic astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent magnitude that the object would have if it were viewed from a distance of exactly 10 parsecs, with no extinction of its light due to absorption by interstellar dust particles. By hypothetically placing all objects at a standard reference distance from the observer, their luminosities can be directly compared on a magnitude scale. As with all astronomical magnitudes, the absolute magnitude can be specified for different wavelength ranges corresponding to specified filter bands or passbands; for stars a commonly quoted absolute magnitude is the absolute visual magnitude, which uses the visual (V) band of the spectrum. Absolute magnitudes are denoted by a capital M, with a subscript representing the filter band used for measurement, such as MV for absolute magnitude in the V band.

Parallax difference in the apparent position of an object viewed along two different lines of sight

Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. Due to foreshortening, nearby objects show a larger parallax than farther objects when observed from different positions, so parallax can be used to determine distances.

Andromeda Galaxy spiral galaxy within the Local Group

The Andromeda Galaxy, also known as Messier 31, M31, or NGC 224, is a spiral galaxy approximately 780 kiloparsecs from Earth, and the nearest major galaxy to the Milky Way. Its name stems from the area of the Earth's sky in which it appears, the constellation of Andromeda.

Solar mass standard unit of mass in astronomy

The solar mass (M) is a standard unit of mass in astronomy, equal to approximately 2×1030 kg. It is used to indicate the masses of other stars, as well as clusters, nebulae, and galaxies. It is equal to the mass of the Sun (denoted by the solar symbol ⊙︎). This equates to about two nonillion (two quintillion in the long scale) kilograms:

Stellar parallax apparent shift of position of a nearby star against the background of distant objects during Earths orbital period

Stellar parallax is the apparent shift of position of any nearby star against the background of distant objects. Created by the different orbital positions of Earth, the extremely small observed shift is largest at time intervals of about six months, when Earth arrives at exactly opposite sides of the Sun in its orbit, giving a baseline distance of about two astronomical units between observations. The parallax itself is considered to be half of this maximum, about equivalent to the observational shift that would occur due to the different positions of Earth and the Sun, a baseline of one astronomical unit (AU).

Microquasar subclass of X-ray binaries

A microquasar, the smaller version of a quasar, is a compact region surrounding a black hole with a mass several times that of our sun, and its companion star. The matter being pulled from the companion star forms an accretion disk around the black hole. This accretion disk may become so hot, due to friction, that it begins to emit X-rays. The disk also projects narrow streams or "jets" of subatomic particles at near-light speed, generating a strong radio wave emission.

Messier 87 Galaxy in the Virgo Galactic Cluster

Messier 87 is a supergiant elliptical galaxy in the constellation Virgo. One of the most massive galaxies in the local Universe, it has a large population of globular clusters—about 12,000 compared with the 150–200 orbiting the Milky Way—and a jet of energetic plasma that originates at the core and extends at least 1,500 parsecs, traveling at relativistic speed. It is one of the brightest radio sources in the sky and a popular target for both amateur and professional astronomers.

Cosmic distance ladder succession of methods by which astronomers determine the distances to celestial objects

The cosmic distance ladder is the succession of methods by which astronomers determine the distances to celestial objects. A real direct distance measurement of an astronomical object is possible only for those objects that are "close enough" to Earth. The techniques for determining distances to more distant objects are all based on various measured correlations between methods that work at close distances and methods that work at larger distances. Several methods rely on a standard candle, which is an astronomical object that has a known luminosity.

Space Interferometry Mission

The Space Interferometry Mission, or SIM, also known as SIM Lite, was a planned space telescope proposed by the U.S. National Aeronautics and Space Administration (NASA), in conjunction with contractor Northrop Grumman. One of the main goals of the mission was the hunt for Earth-sized planets orbiting in the habitable zones of nearby stars other than the Sun. SIM was postponed several times and finally cancelled in 2010. In addition to detecting extrasolar planets, SIM would have helped astronomers construct a map of the Milky Way galaxy. Other important tasks would have included collecting data to help pinpoint stellar masses for specific types of stars, assisting in the determination of the spatial distribution of dark matter in the Milky Way and in the local group of galaxies and using the gravitational microlensing effect to measure the mass of stars. The spacecraft would have used optical interferometry to accomplish these and other scientific goals.

The angular diameter, angular size, apparent diameter, or apparent size is an angular measurement describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is the angular aperture. The angular diameter can alternatively be thought of as the angle through which an eye or camera must rotate to look from one side of an apparent circle to the opposite side. Angular radius equals half the angular diameter.

Eta Sagittarii Star

Eta Sagittarii is a binary star system in the southern zodiac constellation of Sagittarius. Based upon parallax measurements, it is located at a distance of 146 light-years from Earth. It was formerly known as Beta Telescopii (β Tel). In India, where part of the constellation of Sagittarius represents an Elephant, this star forms the creature's tail.

Virgo Stellar Stream galaxy

The Virgo Stellar Stream, also known as Virgo Overdensity, is the proposed name for a stellar stream in the constellation of Virgo which was discovered in 2005. The stream is thought to be the remains of a dwarf spheroidal galaxy that is in the process of merging with the Milky Way. It is the largest galaxy visible from the Earth, in terms of the area of the night sky covered.

In astrometry, the moving-cluster method and the closely related convergent point method are means, primarily of historical interest, for determining the distance to star clusters. They were used on several nearby clusters in the first half of the 1900s to determine distance. The moving-cluster method is now largely superseded by other, usually more accurate distance measures.

Dark Energy Survey

The Dark Energy Survey (DES) is a visible and near-infrared survey that aims to probe the dynamics of the expansion of the Universe and the growth of large-scale structure. The collaboration is composed of research institutions and universities from the United States, Brazil, the United Kingdom, Germany, Spain, and Switzerland.

Knowledge of the location of Earth has been shaped by 400 years of telescopic observations, and has expanded radically in the last century. Initially, Earth was believed to be the center of the Universe, which consisted only of those planets visible with the naked eye and an outlying sphere of fixed stars. After the acceptance of the heliocentric model in the 17th century, observations by William Herschel and others showed that the Sun lay within a vast, disc-shaped galaxy of stars. By the 20th century, observations of spiral nebulae revealed that our galaxy was one of billions in an expanding universe, grouped into clusters and superclusters. By the end of the 20th century, the overall structure of the visible universe was becoming clearer, with superclusters forming into a vast web of filaments and voids. Superclusters, filaments and voids are the largest coherent structures in the Universe that we can observe. At still larger scales the Universe becomes homogeneous meaning that all its parts have on average the same density, composition and structure.

Light-year unit of length that light travels within one Earthyear; equal to just under 10 trillion kilometres (or about 6 trillion miles)

The light-year is a unit of length used to express astronomical distances and measures about 9.46 trillion kilometres (9.46 x 1012 km) or 5.88 trillion miles (5.88 x 1012 mi). As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in vacuum in one Julian year (365.25 days). Because it includes the word "year", the term light-year is sometimes misinterpreted as a unit of time.

A skinny triangle in trigonometry is a triangle whose height is much greater than its base. The solution of such triangles can be greatly simplified by using the approximation that the sine of a small angle is equal to the angle in radians. The solution is particularly simple for skinny triangles that are also isosceles or right triangles: in these cases the need for trigonometric functions or tables can be entirely dispensed with.

Bedin I Dwarf spheroidal galaxy located in the constellation Pavo

Bedin I is a dwarf spheroidal galaxy located in the constellation Pavo. It is situated behind the globular cluster NGC 6752, though is around 28.38 million light-years from Earth. Bedin I is one of the oldest galaxies known, having formed around 10–13 billion years ago, and is one of the most isolated dwarf galaxies known, situated around 2.12 million light-years away from NGC 6744, its nearest neighbor with which it may be physically associated. As such, it has been deemed by astronomers as a "fossil" from the early universe. It was accidentally discovered by Italian astronomer Luigi Bedin, whose team was studying white dwarfs in NGC 6752 using the Hubble Space Telescope in September 2018; the discovery was announced in a paper published in January 2019.

Donatiello I Dwarf spheroidal galaxy located in the constellation Andromeda

Donatiello I, also known as Mirach's Goblin, is a dwarf spheroidal galaxy located in the constellation Andromeda, located between 8.1 and 11.4 million light-years from Earth. It is a possible satellite galaxy of the dwarf lenticular galaxy NGC 404, "Mirach's Ghost", which is located 60 arcminutes away. It is otherwise one of the most isolated dwarf spheroidal galaxies known, being physically located around 211,000 light-years away from NGC 404. The galaxy is named after its discoverer, amateur astrophotographer Giuseppe Donatiello, who sighted the galaxy in a 2016 review of his archival long exposures from 2010 and 2013. Follow-up observations with the Roque de los Muchachos Observatory led to a scientific paper on its discovery being published in December 2018.


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