When the planet Jupiter is at a distance of 824.7 million km from the earth, its angular diameter is measured to be 35.72' ' of arc. The diameter of Jupiter can be calculated as
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a
1329×107 km
b
1.429×105 km
c
929×105 km
d
1829×105 km
answer is B.
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Detailed Solution
Distance of Jupiter from earth (d) = 8247 . million km=824.7×106 kmAngular diameter of Juptier (θ)=35.73"But 10=60"=(60×60)"1"=(160×60)0=160×60×π180rad=3.1460×60×180rad1"=4.85×10−6 rad∴ Angular diameter of Jupiter (θ)=(35.72×4.85×10−6)radIf D is the diameter of the Jupiter then, angular diameter(θ)=Dd=(35.72×4.85×10−6)×82.47×106=142873=1.429×105 km
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When the planet Jupiter is at a distance of 824.7 million km from the earth, its angular diameter is measured to be 35.72' ' of arc. The diameter of Jupiter can be calculated as