The principle of 'parallax' in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth's two locations six months apart in its orbit around the Sun. That is, the baselinne is about the diameter of the Earth's orbit `3 times 10^(11)` m. However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1'' (second) of arc or so. A parsec is a convvenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of 1'' (second) of arc from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of metres ?

Explanation

Here, length of baseline
`" "` = distance from each to the sun
`" "=1 A.U =1.5 times 10^(11) m`
Parallax angle, `theta=1..`
`=(1.)/60=1^(@)/(60 times 60)=pi/180 times 1/(60 times 60)"radian"`
r = 1 par sec = ?, From `l=rtheta rArr r=l/theta`
`=(1.5 times 10..)/(pi//180 times 60 times 60)m=3.1 times 10^(16)m`
Hence 1 parsec `=3.1 times 10^(16)m`