# What is the value of parallactic seconds (parsec) in S.I units?

$\begin{array}{1 1}(A)\;3.1 \times 10^{16}m \\(B)\;2.3 \times 10^{7}m \\(C)\;9 \times 10^{8}m \\(D)\;25 \times 10^{3}m \end{array}$

Parallactic-second is the distance at which are length of one astronomical unit subtends an angle of one second of arc.
Since $\theta= \large\frac{l}{r}$
Where l is the arc length at a distance r and $\theta$ is the angle subtended in radians, so
$r= \large\frac{l}{\theta}$
$l= I.A.U = 1.49 \times 10^{11} m$
$\theta= 1 sec= \large\frac{1}{60} \times \large\frac{1}{60}$ degree
$\qquad=\large\frac{1}{60} \times \frac{1}{60} \times \large\frac {\pi}{180}$
So, 1 parsec $=\large\frac{1A.U }{1\;sec}$
$\qquad= 3.1 \times 10^{16}\;m$
Hence A is the correct answer.
answered Jul 10, 2014 by
edited Jul 11, 2014