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# Parsec

The parsec (abbreviated pc) is a unit of length used in astronomy. It stands for "parallax of one arc second". It is based on the method of trigonometric parallax, the most ancient and standard method of determining stellar distances. The angle subtended at a star by the mean radius of the Earth's orbit, around the Sun, is called the parallax. The parsec is the reciprocal of a parallax of 1 arcsecond. The parsec is the distance at which two objects, separated by 1 AU, appear to be separated by an angle of 1 arcsecond. It is therefore 360×60×60/2π AU = ~2.06264806255 AU = ~3.085 677 580 666 31 × 1016m, = 3.26 light years. (see diagram below)

For historical reasons, astronomers usually express distances to astronomical objects in units of parsecs, instead of light years. The first direct measurements of an object at interstellar distances (of the star 61 Cygni, by Friedrich Wilhelm Bessel in 1838) were done using trigonometry using the width of the Earth's orbit as a baseline. The parsec follows naturally from this method.

There is no star whose parallax is 1 arcsec. The greater the parallax of the star the closer it is to the Earth, and the smaller its distance in parsecs. Therefore the closest star to the Earth will have the largest measured parallax. This belongs to the star Proxima Centauri, with a parallax of 0.762 arcsecs, and lying approximately 4.28 light years, or 1.3 parsecs, away from us.

The measurement of distances of celestial bodies from the Earth in parsecs is a key aspect of astrometry, the science of making positional measurements of celestial bodies.

Because of the extremely small scale of parallactic shifts, ground-based parallax methods provide reliable measurements of stellar distances of no more than 325 light years, or about 100 parsecs, corresponding to parallaxes of no less than 1/100 of 1 arcsecond, or 10 mas (1 mas or milliarcsecond = 1/1000 arcsecond).

Between 1989 and 1993 the Hipparcos satellite, launched by the European Space Agency (ESA) in 1989, measured parallaxes for about 100,000 stars, with a precision of about 0.97 mas, and obtained accurate measurements for stellar distances of around 1000 pc.

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 2000 pc. However, the mission's funding was withdrawn by NASA in January 2002.

The ESA's GAIA satellite, due to be launched in mid-2012, will be of sufficiently high astrometric precision to measure stellar distances to within 10% accuracy as far as the galactic centre about 8 kpc away in the Sagittarius constellation.

Distances in Parsecs One kiloparsec, abbreviated kpc, is one thousand parsecs. One megaparsec, abbreviated Mpc, is one million parsecs.



How to calculate the value of a parsec

In the diagram above, S represents the Sun, and E the Earth at one point in its orbit. D is an object 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. By trigonometry, the distance SD is

$SD = {{ES} \over {\tan 1}} \approx 206 265 AU$

One astronomical unit is equal to approximately 1.49568×108 km, so

$1pc \approx 206 265 \times 1.49568 \times 10^{11} m \approx 3.08506 \times 10^{16} m$

See also: conversion of units.

In computer science, Parsec is an XML syntax analyzer, like Lark

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