When the observations are taken at an interval of 6 months, the angle of parallax for a star is 0.4''. Find the distance of star in par sec.

Answer

5.02 par sec

Explanation

Here, for observations at an interval of six
months, I = diameter of earth's orbit
`= 2xx1.5xx10^(11)m`
`=3xx10^(11)m`
`theta = 0.4'' = (0.4)/(60xx60)xx(pi)/(180)rad`
distance of star, r= ?
From `I = r theta`
`r = (I)/(theta) = (3xx10^(11)xx60xx60xx180)/(0.4xxpi)`
` = 1.547xx10^(17)m`
As 1 par `sec= 3.08xx10^(16)m`
`:. r = (1.547xx10^(17))/(3.08xx10^(16))` par sec = 5.02 par sec