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When the planet Jupiter is at a distance of 824.7 million kilometres from the Earth, its angular diameter is measured to be 35.72″ of arc. Calculate the diameter of Jupiter
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Solution 1
Distance of Jupiter from the Earth, D = 824.7 × 10^{6} km = 824.7 × 10^{9} m
Angular diameter = 35.75" = 35.72 x 4.874 x 10^{-6} rad
Diameter of Jupiter = d
Using the relation,
`theta = d/D`
`d = thetaD = 824.7 xx 10^9 xx 35.72 xx 4.872 xx 20^(-6)`
=143520.76 x 10^{3} = 1.435 x 10^{5} km
Solution 2
Given angular diameter θ = 35.72= 35.72 x 4.85 x 10^{-6} rad
= 173.242 x 10^{-6} = 1.73 x 10^{-4} rad
Diameter of Jupiter D = θ x d = 1.73 x 10^{-4} x 824.7 x 10^{9} m
=1426.731 x 10^{3} = 1.43 x 10^{8} m
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