Parsec

For other uses, see Parsec (disambiguation).

See 1 E+16 m for comparable lengths, and scientific notation for an explanation of the notation used in this article.

Template:Unit of length

A parsec is the distance from the Earth to an astronomical object which has a parallax angle of one arcsecond.

The parsec (symbol pc) is a unit of length used in astronomy. The length of the parsec is based on the method of trigonometric parallax, one of the oldest methods for measuring the distances to stars.

The name parsec stands for "parallax of one second of arc", and one parsec is defined to be the distance from the Earth to a star that has a parallax of 1 arcsecond. The actual length of a parsec is approximately 3.086×10¹⁶ m, 3.262 light-years or 19,176,075,967,324.937 miles.

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 angle subtended, from that star's perspective, by the semi-major axis of the Earth's orbit. The use of the parsec as a unit of distance follows naturally from this 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. (See diagram above.)

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 (par-allax sec-ond).

Usage and Measurement

The parallax method is the fundamental calibration step for distance determination in astrophysics, and the natural 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 (ly).

Other than the Sun, which has a parallax of 90 degrees, there is no known star whose parallax is more than 1 arcsecond (that is, there is no know star whose distance from Earth is less than 1 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 billion 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 4.85×10⁻⁶ pc.
• the most distant space probe, Voyager 1, was 4.6×10⁻⁴ pc away from Earth in September 2004. It took Voyager 27 years to cover that distance.
• the Oort cloud is postulated to be approximately 0.6 pc 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), the most distant object visible to the naked eye, is a little under 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 = 100h km/s/Mpc). The Hubble constant becomes relevant when converting an observed redshift z into a distance using the formula d ≈ c / Hz (where c is the velocity of light).

One gigaparsec (Gpc) is one billion 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 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 billion light-years). See observable universe.

Volume units

In order to determine the number of stars in the Milky Way Galaxy volumes in kpc³ (1 cubic kiloparsec ≈ 2.938 × 10⁵⁸ m³) 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 Mpc³ (1 cubic megaparsec ≈ 2.938 × 10⁶⁷ m³) 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 Mpc³.

In Cosmology volumes of Gpc³ (1 cubic gigaparsec ≈ 2.938 × 10⁷⁶ m³) 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 (1 pc³ ≈ 2.938 × 10⁴⁹ m³) but in globular clusters the stellar density per pc³ could be from 100 to 1,000.

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. D is a point in space at a distance of one parsec from the Sun. By definition, the angle D is one arcsecond, and the distance ES is one astronomical unit (AU). By trigonometry, the distance SD is

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

One AU = 149,597,870,700 m, so 1 parsec ≈ 3.085 678×10¹⁶ meters ≈ 3.261 564 light-years.

References

• Dr. Michael Guidry. "Astronomical Distance Scales". Astronomy 162. {{cite web}}: Unknown parameter |accessmonthday= ignored (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help)

See also

• Conversion of units
• Small-angle approximation
• Attoparsec: a unit humorously used by some hackers. It is approximately 3.1 centimetres — just a little over an inch.
• Light-year
• Cosmic Distance Ladder