The principle of 'parallax' in Art. 1(c ).4. is used in the determination of distacne of very distant stars. The baseline AB in the line joining the Earth's two locations six months apart in its orbit around the sun. That is, the baseline is about the diameter of the Earth 's orbit `~~3xx10^(11)m.` However, even the nearest stars are so distnat thet with such a long baseline, they show parallax only of the order of 1''(second) of arc or so . A parsec is a convenient unit of length on the astronomical scale. It is the distance of an objhect that will shown a parallax of 1'' (second) of arc fome oppsoite ends of a beasline equal to the distance from the Earth to the sun. How much is a parsec in terms of metres ?

Explanation

Here, length of baseline = distnace form earth to the sun `I = 1 A.U = 1.5xx10^(11)m`
Parallax angle, `theta = 1'' (1')/(60) = (1^@)/(60xx60) = (pi)/(180)xx(1)/(60xx60) radian`
r = 1 par sec =?
From ` I = r theta`
`r = (I)/(theta) = (1.5xx10^(11))/(pi//180xx60xx60)m = 3.1xx10^(16)m`
Hence, `1 parsec = 3.1xx10^(16)m`