Question

The Sun's angular diameter is measured to be $1920$. The distance D of the sun from the earth is $1.496\times {10}^{\prime \prime }$m. find the diameter of the sun?

Answer 1

Angular diameter of sun =
$\theta ={1920}^{\prime \prime }$
${1920}^{{}^{\prime \prime }}={\left(\frac{1920}{60}\right)}^1={32}^1$
=${\left(\frac{32}{60}\right)}^{{}^{\circ }}$
$1920={0.533}^{\circ }$
now, ${180}^{\circ }\equiv \pi$ rad
$\therefore {0.533}^{\circ }\equiv (?)$
$\therefore \theta =0.533\times \frac{\pi }{180}\approx 9.3\times {10}^{-3}$ rad
let diameter of sun be d given that $l=1.496\times {10}^{11}$m
Now , $\theta =\frac{arc}{radius}=\frac{d}{r}$
$\therefore d=\theta l$
$\therefore d=9.3\times {10}^{-3}\times 1.496\times {10}^{11}$
$\therefore d=13.91\times {10}^8$
$\therefore d=1.39\times {10}^{9}m$
diameter of sum is $1.39\times {10}^9$