Physics

# 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.

##### SOLUTION
Let the diameter of jupiter be $d \; m$.
Distance of jupiter from the earth $\left( D \right) = 825 \times {10}^{6} \times {10}^{3} m = 8.25 \times {10}^{11}$
Angular diameter $\left( \theta \right) = 36' = 36 \times 4.874 \times {10}^{-6} rad = 1.75 \times {10}^{-4}$
As we know that,
$\theta = \cfrac{d}{D}$
$\Rightarrow d = \theta \times D$
$\Rightarrow d = 1.75 \times {10}^{-4} \times 8.25 \times {10}^{11} = 1.44 \times {10}^{8} m = 1.44 \times {10}^{5} km$
Hence the diameter of the jupiter is $1.44 \times {10}^{5} km$.

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Subjective Medium Published on 18th 08, 2020
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