Question

The Sun's angular diameter is measured to be 1920". The distance D of the sun from the earth is 1.496 $\times {10}^{11}$ m. So find the diameter of the Sun.

Answer 1

We know that $1^{\prime \prime }=\left(\frac{1}{3600}\right)\times \frac{\pi }{180}rad$

Angular diameter $\theta ={1920}^{\prime \prime }=1920\times \frac{\pi }{3600\times 180}rad=0.0093rad$

Diameter $d=\theta r=0.0093\times 1.496\times {10}^{11}m=1.39\times {10}^{9}m$