Question

The sun's angular diameter is measured to be ${1920}^{\prime \prime }$. The distance of the sun from the earth is $1.496\times {10}^{11}m$. What is the diameter of the sun?

• A. $1\times {10}^{9}m$
• B. $1.39\times {10}^{9}m$
• C. $13.9\times {10}^{9}m$
• D. $139\times {10}^{9}m$

Answer 1

The correct option is B $1.39\times {10}^{9}m$

Given, $\theta =1920"=\frac{1920}{3600}={0.53}^o=0.53\times \left(\pi /180\right)=0.0093$ radian

and $D=1.496\times {10}^{11}m$

Here, $\tan \theta =d/D$

As $\theta$ is very small so $\tan \theta \sim \theta$

So, diameter of the sun is $d=D\theta =1.496\times {10}^{11}\times 0.0093=1.39\times {10}^{9}m$