The parsec ("parallax of one arcsecond", symbol pc) is a unit of length, equal to just under 31 million million kilometres (about 19 million million miles), or about 3.26 light-years. The parsec measurement unit is used in astronomy and is defined as the length of the adjacent side of an imaginary right triangle in space. The two dimensions that form this triangle are the parallax angle (defined as 1 arcsecond) and the opposite side (which is defined as 1 astronomical unit (AU), the distance from the Earth to the Sun). Given these two measurements, along with the rules of trigonometry, the length of the adjacent side (the parsec) can be found.

One of the oldest methods for astronomers to calculate the distance to a particular star 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. Thus, the distance between the two measurements was known to be twice the distance between the Earth and the Sun. The distance to the star could be found using calculations of trigonometric parallax. Since it is based on an angle and the distance between the Earth and the Sun, it is fundamentally derived from the degree and the AU. The length of a parsec is about 30.857 petametres, 3.26156 light-years or . The first documented use of the term parsec was in 1913, and attributed to Herbert Hall Turner.

History

The first direct measurements of an object at interstellar distances were undertaken by German astronomer Friedrich Wilhelm Bessel in 1838, who used the width of the Earth's orbit as a baseline to calculate the distance of 61 Cygni using parallax and trigonometry. The parallax of a star is half of the angular distance a star appears to move relative to the celestial sphere as Earth orbits around the Sun; or, reciprocally, it is the subtended angle, from that star's perspective, of the semi-major axis of Earth's orbit.

The use of the parsec as a unit of distance follows naturally from Bessel's method, since distance (in parsecs) is simply the reciprocal of the parallax angle (in arcseconds). That is, it is the distance at which the semi-major axis of the Earth's orbit would subtend an angle of one second of arc.

Though it had probably been used before, the term parsec was first mentioned in an astronomical publication in 1913, when Astronomer Royal Frank Watson Dyson expressed his concern for the need of a name for that unit of distance: he proposes the name astron, but mentions that Carl Charlier had suggested siriometer, and Herbert Hall Turner had suggested parsec (parallax second).

Usage and measurement

The parallax method is the fundamental calibration step for distance determination in astrophysics, and the obvious unit for such measurements, the parsec, has become the most commonly used unit of distance in scholarly astronomical publications. Articles aimed at a wider audience, such as in newspapers and popular science magazines, often use a more intuitive unit, the light-year. Other than the Sun, which has a parallax of 90 degrees, there is no known star whose parallax is more than one arcsecond (that is, there is no known star whose distance from Earth is less than one parsec). The next closest star is Proxima Centauri with a parallax of 0.77233 arcseconds; it is thus 1.295 pc (4.225 ly) away from the Earth.
Refraction caused by the atmosphere, also known as astronomical seeing, limits ground-based telescopes to parallax angle measurement accuracies of less than approximately 0.01 arcsec, so reliable measurements, those with errors of 10% or less, can only be achieved at stellar distances of no more than about 100 pc, or 326 ly. 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 100,000 stars with an astrometric precision of about 0.97 milliarcseconds, and obtained accurate measurements for stellar distances of stars up to 1,000 pc away. NASA's FAME satellite was due to be 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 December 2011, is intended to measure one thousand million stellar distances to within 20 microarcseconds, producing errors of 10% in measurements as far as the Galactic Center, about 8,000 pc away in the constellation of Sagittarius.

Distances in parsecs

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 (AU) — the distance from the Sun to the Earth — is .

• The most distant space probe, Voyager 1, was away from Earth . It took Voyager 30 years to cover that distance.

• The Oort cloud is postulated to be approximately in diameter.

Parsecs and kiloparsecs

Distances measured in parsecs include distances between nearby stars, such as those in the same spiral arm or globular cluster. 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 galaxy, 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, is Proxima Centauri, 1.29 parsecs away.

• The center of the Milky Way is about 8 kpc from the Earth, and the Milky Way is about 30 kpc across.

• The Andromeda Galaxy (M31) is slightly less than 800 kpc away from the Earth.

Megaparsecs and gigaparsecs

A distance of one million parsecs (approximately 3,262,000 ly or 2×10¹⁹ miles) is commonly denoted by the megaparsec (Mpc). Astronomers typically measure the distances between neighboring galaxies and galaxy clusters 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 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 using the formula d ≈ (c / H) × z (where c is the speed of light).

One gigaparsec (Gpc) is one thousand million parsecs — one of the largest distance measures commonly used. One gigaparsec is about 3.262 thousand million light-years, or roughly one fourteenth of the distance to the horizon of the observable universe (dictated by the cosmic background radiation). Astronomers typically use gigaparsecs to measure large-scale structures such as the size of, and distance to, the Great Wall; the distances between clusters of galaxies; and the distance to quasars.

For example:

• The Andromeda Galaxy is 0.77 Mpc away from the Earth.

• The nearest large galaxy cluster, the Virgo Cluster, is about 18 Mpc away from the Earth.

• The galaxy RXJ1242-11, observed to have a supermassive black hole core similar to the Milky Way's, is about 200 Mpc away from the Earth.

• The particle horizon (the observable part of the universe) has a radius of about 14 Gpc (46.5 thousand million light-years). (See observable universe.)

Volume units

In order to determine the number of stars in the Milky Way Galaxy volumes in cubic kiloparsecs (kpc³) are selected in various directions. All the stars in these volumes are counted and the total number of stars is statistically determined. The number of globular clusters, dust clouds and interstellar gas is determined in a similar fashion. In order to determine the number of galaxies in superclusters, volumes in cubic megaparsecs (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 void in Bootes is measured in cubic megaparsecs. In cosmology, volumes of cubic gigaparsecs (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 alone in its cubic parsec, (pc³) but in globular clusters the stellar density per cubic parsec could be from 100 to 1,000.

Calculating the value of a parsec

Diagram of 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. By trigonometry, the distance SD is

$SD\; =\; \backslash frac\{\backslash mathrm\{ES\}\}\{\backslash tan\; 1^\{\backslash prime\backslash prime\}\}\; \backslash approx\; \backslash frac\{\backslash mathrm\{ES\}\}\{1^\{\backslash prime\backslash prime\}\}\; =\; \backslash frac\{360\; \backslash times\; 60\; \backslash times\; 60\}\{2\; \backslash pi\}\; \backslash ,\; \backslash mbox\{AU\}\; \backslash approx\; 206,264.8\; \backslash mbox\{\; AU\}.$

One AU = 149,597,870,691 m, so 1 parsec ≈ 3.085 678×10¹⁶ metres ≈ 3.261 564 light-years.

See also

• Attoparsec

• Conversion of units

• Cosmic Distance Ladder

• Light-year

• Small-angle approximation