Numerical

**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 × 10^{6} km

= 824.7 × 10^{9} m.

**To find:** Diameter of Jupiter (d)

**Formula:** d = α D

**Calculation:** From the formula,

d = 1.73 × 10^{-4} × 824.7 × 10^{9 }

= 1.428 × 10^{8} m

= 1.428 × 10^{5} km

The diameter of Jupiter is 1.428 × 10^{5} km.

Concept: Measurement of Length

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