The

**parsec** is a

unitA unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...

of

lengthThe astronomical system of units, formally called the IAU System of Astronomical Constants, is a system of measurement developed for use in astronomy...

used in

astronomyAstronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

. It is about 3.26

light-yearA light-year, also light year or lightyear is a unit of length, equal to just under 10 trillion kilometres...

s, or just under 31 trillion (3.1)

kilometreThe kilometre is a unit of length in the metric system, equal to one thousand metres and is therefore exactly equal to the distance travelled by light in free space in of a second...

s (about 19 trillion

mileA mile is a unit of length, most commonly 5,280 feet . The mile of 5,280 feet is sometimes called the statute mile or land mile to distinguish it from the nautical mile...

s).

The name

*parsec* is "an abbreviated form of 'a distance corresponding to a

**par**allax of one

**sec**ond'." It was coined in 1913 at the suggestion of

BritishThe United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...

astronomerAn astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...

Herbert Hall TurnerHerbert Hall Turner was a British astronomer and seismologist.-Biography:Herbert Hall Turner was educated at Clifton College and Trinity College, Cambridge., In 1884 he accepted the post of Chief Assistant at Greenwich Observatory and stayed there for nine years...

. A parsec is the distance from the

SunThe Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

to an

astronomical objectAstronomical objects or celestial objects are naturally occurring physical entities, associations or structures that current science has demonstrated to exist in the observable universe. The term astronomical object is sometimes used interchangeably with astronomical body...

which has a

parallaxStellar parallax is the effect of parallax on distant stars in astronomy. It is parallax on an interstellar scale, and it can be used to determine the distance of Earth to another star directly with accurate astrometry...

angle of one arcsecond.

## History and derivation

The

**parsec** is equal to the length of the

adjacentAdjacent is an adjective meaning contiguous, adjoining or abuttingIn geometry, adjacent is when sides meet to make an angle.In graph theory adjacent nodes in a graph are linked by an edge....

side of an imaginary right triangle in space. The two dimensions on which this triangle is based are the

angleIn geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

(which is defined as 1 arcsecond), and the

oppositeOpposite may refer to:* Opposite , a word that means the opposite of a word* Botany: "Opposite" is a kind of arrangement of leaves* Additive inverse, in mathematics, taking the negative of a number...

side (which is defined as 1

Astronomical UnitAn astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

, which is the distance from the Earth to the sun). Using these two measurements, along with the rules of trigonometry, the length of the

adjacentAdjacent is an adjective meaning contiguous, adjoining or abuttingIn geometry, adjacent is when sides meet to make an angle.In graph theory adjacent nodes in a graph are linked by an edge....

side (the

**parsec**) can be found.

One of the oldest methods for astronomers to calculate the distance to a

starA star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

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 for the measurements 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. Then the distance to the star could be calculated using trigonometry. The first successful direct measurements of an object at interstellar distances were undertaken by

GermanGermany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...

astronomer Friedrich Wilhelm Bessel in 1838, who used this approach to calculate the distance of

61 Cygni61 Cygni,Not to be confused with 16 Cygni, a more distant system containing two G-type stars harboring the gas giant planet 16 Cygni Bb. sometimes called Bessel's Star or Piazzi's Flying Star, is a binary star system in the constellation Cygnus...

.

The

*parallax* of a star is taken to be half of the

angular distanceIn mathematics and all natural sciences , the angular distance between two point objects, as observed from a location different from either of these objects, is the size of the angle between the two directions originating from...

that a star appears to move relative to the

celestial sphereIn astronomy and navigation, the celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with the Earth and rotating upon the same axis. All objects in the sky can be thought of as projected upon the celestial sphere. Projected upward from Earth's equator and poles are the...

as Earth orbits the Sun. Equivalently, it is the subtended angle, from that star's perspective, of the semi-major axis of Earth's orbit. The star, the sun and the earth form the corners of an imaginary

right triangleA 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.-Terminology:The side opposite the right angle is called the hypotenuse...

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

EarthEarth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

to the

SunThe Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

(defined as 1

astronomical unitAn astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

(AU)), and the length of the

adjacentIn a right triangle, the cathetus , commonly known as a leg, is either of the sides that are adjacent to the right angle. It is occasionally called the periphrasis . The side opposite the right angle is the hypotenuse...

side gives the distance from the sun to the star. Therefore, given a measurement of the parallax angle, along with the rules of

trigonometryTrigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...

, the distance from the sun to the star can be found. A parsec is defined as the length of the

adjacentIn a right triangle, the cathetus , commonly known as a leg, is either of the sides that are adjacent to the right angle. It is occasionally called the periphrasis . The side opposite the right angle is the hypotenuse...

side of this

right triangleA 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.-Terminology:The side opposite the right angle is called the hypotenuse...

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

reciprocalIn mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the...

of the parallax angle in arcseconds (

*i.e.* if the parallax angle is 1 arcsecond, the object is 1 pc distant from the sun; If the parallax angle is 0.5 arcsecond, the object is 2 pc distant;

*etc.*). No

trigonometric functionIn mathematics, the trigonometric functions are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle...

s are required in this relationship because the very small angles involved mean that the approximate solution of the

skinny triangleA 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...

can be applied.

Though it may have been used before, the term

*parsec* was first mentioned in an astronomical publication in 1913.

Astronomer RoyalAstronomer Royal is a senior post in the Royal Household of the Sovereign of the United Kingdom. There are two officers, the senior being the Astronomer Royal dating from 22 June 1675; the second is the Astronomer Royal for Scotland dating from 1834....

Frank Watson DysonSir Frank Watson Dyson, KBE, FRS was an English astronomer and Astronomer Royal who is remembered today largely for introducing time signals from Greenwich, England, and for the role he played in testing Einstein's theory of general relativity.- Biography :Dyson was born in Measham, near...

expressed his concern for the need of a name for that unit of distance. He proposed the name

*astron*, but mentioned that

Carl CharlierCarl Vilhelm Ludwig Charlier was a Swedish astronomer.He received his Ph.D. from Uppsala University in 1887, later worked there and at the Stockholm Observatory and was Professor of Astronomy and Director of the Observatory at Lund University from 1897.He made extensive statistical studies of the...

had suggested

*siriometer* and

Herbert Hall TurnerHerbert Hall Turner was a British astronomer and seismologist.-Biography:Herbert Hall Turner was educated at Clifton College and Trinity College, Cambridge., In 1884 he accepted the post of Chief Assistant at Greenwich Observatory and stayed there for nine years...

had proposed

*parsec*. It was Turner's proposal that stuck.

### Calculating the value of a parsec

In the diagram above

*(not to scale)*,

**S** represents the

SunThe Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

, and

**E** the

EarthEarth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

at one point in its orbit. Thus the distance

**ES** is one

astronomical unitAn astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

(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. By

trigonometryTrigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...

, the distance

**SD** is

Using small-angle approximation,

One AU ≈ metres, so 1 parsec ≈ ≈ .

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 diameterThe angular diameter or apparent size of an object as seen from a given position is the “visual diameter” of the object measured as an angle. In the vision sciences it is called the visual angle. The visual diameter is the diameter of the perspective projection of the object on a plane through its...

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

distance determination in astrophysicsThe 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...

; however, the accuracy of ground-based

telescopeA telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

measurements of parallax angle is limited to about 0.01 arcseconds, and thus to stars no more than 100 pc distant. This is because the Earth’s atmosphere limits the sharpness of a star's image. 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*Hipparcos was a scientific mission of the European Space Agency , launched in 1989 and operated between 1989 and 1993. It was the first space experiment devoted to precision astrometry, the accurate measurement of the positions of celestial objects on the sky...

satellite, launched by the

European Space AgencyThe European Space Agency , established in 1975, is an intergovernmental organisation dedicated to the exploration of space, currently with 18 member states...

(ESA), measured parallaxes for about 100,000 stars with an

astrometricAstrometry is the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. The information obtained by astrometric measurements provides information on the kinematics and physical origin of our Solar System and our Galaxy, the Milky...

precision of about 0.97

milliarcsecondA minute of arc, arcminute, or minute of angle , is a unit of angular measurement equal to one sixtieth of one degree. In turn, a second of arc or arcsecond is one sixtieth of one minute of arc....

s, and obtained accurate measurements for stellar distances of stars up to 1,000 pc away.

NASAThe National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...

's

*FAME* satelliteFull-sky Astrometric Mapping Explorer was a proposed astrometric satellite designed to determine with unprecedented accuracy the positions, distances, and motions of 40 million stars within our galactic neighborhood...

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. ESA's

*Gaia* satellite, due to be launched in late 2012, is intended to measure one billion stellar distances to within 20 microarcseconds, producing errors of 10% in measurements as far as the

Galactic CenterThe Galactic Center is the rotational center of the Milky Way galaxy. It is located at a distance of 8.33±0.35 kpc from the Earth in the direction of the constellations Sagittarius, Ophiuchus, and Scorpius where the Milky Way appears brightest...

, about 8,000 pc away in the

constellationIn modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....

of

SagittariusSagittarius is a constellation of the zodiac, the one containing the galactic center. Its name is Latin for the archer, and its symbol is , a stylized arrow. Sagittarius is commonly represented as a centaur drawing a bow...

.

### Distances less than a parsec

Distances measured in fractions of a parsec usually involve objects within a single star system. So, for example:

- One astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

(AU), the distance from the Sun to the Earth, is .
- The most distant space probe
A robotic spacecraft is a spacecraft with no humans on board, that is usually under telerobotic control. A robotic spacecraft designed to make scientific research measurements is often called a space probe. Many space missions are more suited to telerobotic rather than crewed operation, due to...

, *Voyager 1*The Voyager 1 spacecraft is a 722-kilogram space probe launched by NASA in 1977, to study the outer Solar System and eventually interstellar space. Operating for as of today , the spacecraft receives routine commands and transmits data back to the Deep Space Network. At a distance of as of...

, was away from Earth . It took *Voyager* 30 years to cover that distance.
- The Oort cloud
The Oort cloud , or the Öpik–Oort cloud , is a hypothesized spherical cloud of comets which may lie roughly 50,000 AU, or nearly a light-year, from the Sun. This places the cloud at nearly a quarter of the distance to Proxima Centauri, the nearest star to the Sun...

is estimated to be approximately 0.6 pc in diameterIn geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle...

.

### Parsecs and kiloparsecs

Distances measured in

*parsecs* include distances between nearby

starA star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s, such as those in the same spiral arm or

globular clusterA globular cluster is a spherical collection of stars that orbits a galactic core as a satellite. Globular clusters are very tightly bound by gravity, which gives them their spherical shapes and relatively high stellar densities toward their centers. The name of this category of star cluster is...

. A distance of one thousand parsecs (approximately 3,262 ly) is commonly denoted by the

*kiloparsec* (kpc). Astronomers typically use kiloparsecs to measure distances between parts of a

galaxyA galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...

, or within groups of galaxies. So, for example:

- One parsec is approximately 3.262 light-years.
- The nearest known star to the Earth, other than the Sun, Proxima Centauri
Proxima Centauri is a red dwarf star about 4.2 light-years distant in the constellation of Centaurus. It was discovered in 1915 by Robert Innes, the Director of the Union Observatory in South Africa, and is the nearest known star to the Sun, although it is too faint to be seen with the naked eye...

, is 1.29 parsecs away.
- The center
The Galactic Center is the rotational center of the Milky Way galaxy. It is located at a distance of 8.33±0.35 kpc from the Earth in the direction of the constellations Sagittarius, Ophiuchus, and Scorpius where the Milky Way appears brightest...

of the Milky WayThe Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...

is about 8 kpc from the Earth, and the Milky Way is about 30 kpc across.
- The Andromeda Galaxy
The Andromeda Galaxy is a spiral galaxy approximately 2.5 million light-years from Earth in the constellation Andromeda. It is also known as Messier 31, M31, or NGC 224, and is often referred to as the Great Andromeda Nebula in older texts. Andromeda is the nearest spiral galaxy to the...

(M31The Messier objects are a set of astronomical objects first listed by French astronomer Charles Messier in 1771. The original motivation of the catalogue was that Messier was a comet hunter, and was frustrated by objects which resembled but were not comets...

) is slightly less than 800 kpc away from the Earth.

### Megaparsecs and gigaparsecs

A distance of one million parsecs (approximately 3,262,000 light-years) is commonly denoted by the

*megaparsec* (Mpc). Astronomers typically measure the distances between neighbouring

galaxiesA galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...

and

galaxy clusterA galaxy cluster is a compact cluster of galaxies. Basic difference between a galaxy group and a galaxy cluster is that there are many more galaxies in a cluster than in a group. Also, galaxies in a cluster are more compact and have higher velocity dispersion. One of the key features of cluster is...

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

redshiftIn physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...

*z* into a distance

*d* using the formula

*d* ≈ (

*c*The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

/

*H*) ×

*z*.

One

*gigaparsec* (Gpc) is one

billion1,000,000,000 is the natural number following 999,999,999 and preceding 1,000,000,001.In scientific notation, it is written as 109....

parsecs—one of the largest distance measures commonly used. One gigaparsec is about 3.262 billion light-years, or roughly one fourteenth of the distance to the

horizonThe horizon is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not. At many locations, the true horizon is obscured by trees, buildings, mountains, etc., and the resulting...

of the

observable universeIn Big Bang cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light from those objects has had time to reach us since the beginning of the cosmological expansion...

(dictated by the cosmic background radiation). Astronomers typically use gigaparsecs to measure large-scale structures such as the size of, and distance to, the CfA2 Great Wall; the distances between galaxy clusters; and the distance to

quasarA quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...

s.

For example:

- The Andromeda Galaxy
The Andromeda Galaxy is a spiral galaxy approximately 2.5 million light-years from Earth in the constellation Andromeda. It is also known as Messier 31, M31, or NGC 224, and is often referred to as the Great Andromeda Nebula in older texts. Andromeda is the nearest spiral galaxy to the...

is 0.77 Mpc away from the Earth.
- The nearest large galaxy cluster
A galaxy cluster is a compact cluster of galaxies. Basic difference between a galaxy group and a galaxy cluster is that there are many more galaxies in a cluster than in a group. Also, galaxies in a cluster are more compact and have higher velocity dispersion. One of the key features of cluster is...

, the Virgo ClusterThe Virgo Cluster is a cluster of galaxies whose center is 53.8 ± 0.3 Mly away in the constellation Virgo. Comprising approximately 1300 member galaxies, the cluster forms the heart of the larger Local Supercluster, of which the Local Group is an outlying member...

, is about 16.5 Mpc away from the Earth.
- The galaxy RXJ1242-11, observed to have a supermassive black hole
A supermassive black hole is the largest type of black hole in a galaxy, in the order of hundreds of thousands to billions of solar masses. Most, and possibly all galaxies, including the Milky Way, are believed to contain supermassive black holes at their centers.Supermassive black holes have...

core similar to the Milky WayThe Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...

's, is about 200 Mpc away from the Earth.
- The particle horizon (the boundary of the observable universe
In Big Bang cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light from those objects has had time to reach us since the beginning of the cosmological expansion...

) has a radius of about 14 Gpc (46.5 billion light-years).

## Volume units

To determine the number of stars in the Milky Way Galaxy, volumes in cubic kiloparsecs (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

superclusterSuperclusters are large groups of smaller galaxy groups and clusters and are among the largest known structures of the cosmos. They are so large that they are not gravitationally bound and, consequently, partake in the Hubble expansion.-Existence:...

s, volumes in cubic megaparsecs (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

voidThe Boötes void or the Great Void is a huge and approximately spherically shaped region of space, containing very few galaxies. It is located in the vicinity of the constellation Boötes, hence its name...

in Bootes is measured in cubic megaparsecs. In

cosmologyCosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...

, volumes of cubic gigaparsecs (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 alone in its cubic parsec, (pc

^{3}) but in globular clusters the stellar density per cubic parsec could be from 100 to 1,000.

## See also

- Conversion of units
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.- Process :...

- Cosmic distance ladder
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...

- Light-year
A light-year, also light year or lightyear is a unit of length, equal to just under 10 trillion kilometres...

- Small-angle approximation
- Spectroscopic parallax
Spectroscopic parallax is an astronomical method for measuring the distances to stars. Despite its name, it does not rely on the apparent change in the position of the star . This technique can be applied to any main sequence star for which a spectrum can be recorded...