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Question
Solve the numerical example.
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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Solution
Given: Angular diameter (α) = 35.72''
= 35.72'' × 4.847 × 10-6 rad
≈ 1.73 × 10-4 rad
Distance from Earth (D) = 824.7 million km
= 824.7 × 106 km
= 824.7 × 109 m.
To find: Diameter of Jupiter (d)
Formula: d = α D
Calculation: From the formula,
d = 1.73 × 10-4 × 824.7 × 109
= 1.428 × 108 m
= 1.428 × 105 km
The diameter of Jupiter is 1.428 × 105 km.
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