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

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Question

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

Vedclass · Accepted Answer

$1.435 	imes 10^{5} \;km$

Vedclass · Answer

(A) Given: Distance $D = 824.7 	imes 10^{6} \;km = 8.247 	imes 10^{11} \;m$.Angular diameter $\alpha = 35.72''$.Convert angular diameter to radians: $1'' = 4.848 	imes 10^{-6} \;rad$.$\alpha = 35.72 	imes 4.848 	imes 10^{-6} \;rad \approx 1.7317 	imes 10^{-4} \;rad$.Using the formula for angular diameter: $d = \alpha 	imes D$.$d = (1.7317 	imes 10^{-4} \;rad) 	imes (8.247 	imes 10^{11} \;m) \approx 1.428 	imes 10^{8} \;m$.Converting to kilometers: $d \approx 1.428 	imes 10^{5} \;km$.Rounding to the nearest provided option,the diameter is $1.435 	imes 10^{5} \;km$.

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.

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