Q 2.24: When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be 35.72" of arc. Calculate the diameter of Jupiter.

S safeer

Given,

The distance of Jupiter, D = $\dpi{100} 824.7 \times10^6\ km$

Angular diameter, $\dpi{100} \Theta = 35.72''$$\dpi{100} = 35.72 \times 4.848 \times 10^{-6} rad$         ($\dpi{100} \because 1'' = 4.848 \times 10^{-6} rad$)

Let diameter of Jupiter = d km

$\dpi{100} \\ \therefore d = \theta \times D = 824.7 \times 10^6 \times 35.72 \times 4.848 \times 10^{-6} \\ = 1.428 \times 10^{5}\ km$    $\dpi{100} (\because \theta = \frac{d}{D})$

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