Question

# 1 parsec = _________ metres.

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Solution

## Step 1 :GivenParsec 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. $Anglesubtended\left(\theta \right)=\frac{Radiusofearth\text{'}sorbit}{Dis\mathrm{tan}ce}\phantom{\rule{0ex}{0ex}}Dis\mathrm{tan}ce=\frac{Radiusofearth\text{'}sorbit}{Anglesubtended}\phantom{\rule{0ex}{0ex}}1Parsec=\frac{1AU}{1arcsecond}\phantom{\rule{0ex}{0ex}}1AU=1.5×{10}^{11}m\phantom{\rule{0ex}{0ex}}1arcsecond=\frac{1}{3600}×\frac{\mathrm{\pi }}{180}\phantom{\rule{0ex}{0ex}}So,1Parsec=\frac{1.5×{10}^{11}m}{\frac{1}{3600}×\frac{\mathrm{\pi }}{180}}\phantom{\rule{0ex}{0ex}}=3.1×{10}^{6}m$ Hence, 1 parsec = 3×1016meters.

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