Question

Express parsec in terms of metres.

• A. $3.1\times {10}^{16}m$
• B. $3\times {10}^{8}m$
• C. $3.1\times {10}^{18}m$
• D. $3.1\times {10}^{32}m$

Answer 1

The correct option is A $3.1\times {10}^{16}m$

Parsec or parallactic second refers to the distance at which an arc of length equal to one astronomical unit subtends an angle of one second at a point.
$\theta =\frac{l}{r}$
or, $r=\frac{1}{\theta }$
$\therefore 1parsec=\frac{1AU}{1\prime \prime }$
I AU is the average distance between the earth and the sun and is equal to $1.5\times {10}^{11}m$
$1parsec=\frac{1.5\times {10}^{11}}{\left(\frac{3}{3600}\right)\times \left(\frac{\pi }{180}\right)}$
$\simeq 3.1\times {10}^{16}m$
We can also prove that
$1parsec=3.26ly$