on 17-Jun-2018 (Sun)

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 7005648000000000000♠ 648 000 / π astronomical units

One parsec is equal to about 3.26 light-years (30 trillion km or 19 trillion miles) in length.

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 ]}

Named as a portmanteau of the parallax of one arcsecond

it was defined so as to make calculations of astronomical distances quick and easy for astronomers from only their raw observational data.

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.

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.).

Calculating the value of a parsec [ edit ]

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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:

\({\displaystyle \mathrm {SD} ={\frac {\mathrm {ES} }{\tan 1''}}}\) \({\displaystyle \mathrm {SD} \approx {\frac {\mathrm {ES} }{1''}}={\frac {1\,{\mbox{au}}}{{\frac {1}{60\times 60}}\times {\frac {\pi }{180}}}}={\frac {648\,000}{\pi }}\,{\mbox{au}}\approx 206\,264.81{\mbox{ au}}.}\)

The astronomical unit is defined to be 149 597 870 700 m ,^[8]

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).