Question

1 parsec is approximately equal to ( when AU is an astronomical unit) 2* 105 AU 2* 106AU 2* 108 AU 2* 1010 AU

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Solution

One parsec is the distance at which one AU subtends an angle of one arc second. It is equal to 3.26 light years $\mathrm{One}\mathrm{parsec}=3.26\mathrm{light}\mathrm{years}\phantom{\rule{0ex}{0ex}}=3.26\mathrm{light}\mathrm{years}×\frac{63239.7\mathrm{AU}}{1\mathrm{light}\mathrm{year}}\phantom{\rule{0ex}{0ex}}=206161.4\mathrm{AU}\phantom{\rule{0ex}{0ex}}\mathbf{=}\mathbf{2}\mathbf{×}{\mathbf{10}}^{\mathbf{5}}\mathbf{}\mathbf{AU}\mathbf{}\mathbf{\left(}\mathbf{approx}\mathbf{\right)}$

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