Question

1 parsec = _________ metres.

Answer 1

Step 1 :Given

1. Parsec is the distance at which the mean radius of the earth's orbit subtends an angle of one arc second.

Step 2 : Calculation of 1 parsec

1. The radius of the earth's orbital is 1 astronomical unit (AU) = 1.5×10¹¹m

2. 1 arc second = $\frac{1}{3600}$th of a degree.

3. $$\begin{gathered} Anglesubtended\left(\theta \right)=\frac{Radiusofearth\text{'}sorbit}{Dis\tan ce} \\ Dis\tan ce=\frac{Radiusofearth\text{'}sorbit}{Anglesubtended} \\ 1Parsec=\frac{1AU}{1arcsecond} \\ 1AU=1.5\times {10}^{11}m \\ 1arcsecond=\frac{1}{3600}\times \frac{\mathrm{\pi }}{180} \\ So,1Parsec=\frac{1.5\times {10}^{11}m}{\frac{1}{3600}\times \frac{\mathrm{\pi }}{180}} \\ =3.1\times {10}^{6}m \end{gathered}$$

Hence, 1 parsec = 3×10¹⁶meters.