When the planet Jupiter is at a distance of 8 | vedclass

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(A) Given: Distance $D = 824.7 	imes 10^{6} \; 	ext{km} = 8.247 	imes 10^{11} \; 	ext{m}$.Angular diameter $\alpha = 35.72''$.Convert angular diam

Vedclass · Accepted Answer

$1.428 	imes 10^{5} \; 	ext{km}$

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(A) Given: Distance $D = 824.7 	imes 10^{6} \; 	ext{km} = 8.247 	imes 10^{11} \; 	ext{m}$.Angular diameter $\alpha = 35.72''$.Convert angular diameter to radians: $1'' = 4.848 	imes 10^{-6} \; 	ext{rad}$.$\alpha = 35.72 	imes 4.848 	imes 10^{-6} \; 	ext{rad} \approx 1.7317 	imes 10^{-4} \; 	ext{rad}$.Using the formula for linear diameter $d = \alpha 	imes D$:$d = (1.7317 	imes 10^{-4} \; 	ext{rad}) 	imes (8.247 	imes 10^{11} \; 	ext{m}) \approx 1.428 	imes 10^{8} \; 	ext{m}$.Converting to kilometers: $d = 1.428 	imes 10^{5} \; 	ext{km}$.

When the planet Jupiter is at a distance of $824.7 \; \text{million km}$ from the Earth, its angular diameter is measured to be $35.72''$ of arc. Calculate the diameter of Jupiter.

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