Question

Angular diameter of the Jupiter is $36"$. If the distance of the Jupiter form the Earth is $825$ million kilometer, find the diameter of Jupiter.

Answer 1

Let the diameter of jupiter be $dm$.

Distance of jupiter from the earth $\left(D\right)=825\times {10}^6\times {10}^{3}m=8.25\times {10}^{11}$

Angular diameter $\left(\theta \right)={36}^{\prime }=36\times 4.874\times {10}^{-6}rad=1.75\times {10}^{-4}$

As we know that,

$\theta =\frac{d}{D}$

$\Rightarrow d=\theta \times D$

$\Rightarrow d=1.75\times {10}^{-4}\times 8.25\times {10}^{11}=1.44\times {10}^{8}m=1.44\times {10}^{5}km$

Hence the diameter of the jupiter is $1.44\times {10}^{5}km$.