Question

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

• A. $1.39\times {10}^{9}m$.
• B. $1.39\times {10}^{10}m$.
• C. $1.39\times {10}^{11}m$.
• D. $1.39\times {10}^{12}m$.

Answer 1

Answer: (A)

$1.39\times {10}^{9}m$.

Here,
Distance of the sun from the earth, d = $1.494\times {10}^{11}m$

Sun's angular diameter, $\alpha =1920$"

$1"=4.85\times {10}^{-6}rad$

$\alpha =1920\times 4.85\times {10}^{-6}$ rad = $9.31\times {10}^{-3}$ rad

Sun's diameter,$D=\alpha d$

$D=(9.31\times {10}^{-3})(1.496\times {10}^{11})m$

$=1.39\times {10}^{9}m$