What distance is one Parsec

(Diagram needed)

As the Earth orbits the sun, the apparent position of a (relatively) nearby star varies with relation to a background of much more distant stars. The parallax angle is the angle between observed positions at each 'end' of the orbit (as observed in July as opposed to January).

The distance from the Sun (not the Earth although with vast distances this difference is fairly trivial) to the star being observed can be calculared by trigonometry, given that the distance from the Earth to the Sun is defined as 1 AU (Astronomical Unit) : d = 1/ tan(p) but the angle p is so small that the small angle approximation tan(p) = p gives

d = 1/p

The angle in question is incredibly small so one degree is subdivided into 60 arcminutes, each of which is divided into 60 arcseconds (so 1 arcsec = 1/3600 ths of a degree). A parsec is the distance of a star from the sun if the observed angle of parallax was 1 arcsec. This allows distance (in parsecs) to be given as 1/p (in arcseconds)