Question

Jupiter's angular diameter measures 35.72 ". If Earth's distance from Jupiter is 824.10 ^ 6 km, find the diameter of Jupiter.​

Answer 1

Answer :-

Diameter of Jupiter is 1.43 × 10⁵ km.

Explanation :-

• Angular diameter of Jupiter , θ = 35.72"  (35.72 arc second )
• distance of earth from Jupiter , D = 824 × 10⁶ km

( Given value of angular diameter is the angle in arc second unit )

Formula used :

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so,

Let, diameter of Jupiter = d

Converting Angular diameter given in arc second into radian

Since , 1 arc second = 1 / 60 arc minute

and , 1 arc minute = 1/ 60 degrees

therefore,

➟ θ = 35.72" = 1/60 × 1/60 × 35.72  degrees

➟ θ = 35.72" = (9.9 × 10⁻³) °

Now, since 1° = π / 180 Radian

therefore ,

➟ θ = (9.9 × 10⁻³) ° = (9.9 × 10⁻³) × π / 180 Rad

➟ θ = (9.9 × 10⁻³) ° = 5.5 π × 10⁻⁵ Rad

Calculating Diameter of Jupiter

➟ θ = d / D

➟ 5.5 π × 10⁻⁵ = d / ( 824 × 10⁶ )

➟ d = 5.5 π × 10⁻⁵ × 824 × 10⁶

➟ d = 14243.428 × 10

➟ d = 142434.28 km

➟ d = 1.43 × 10⁵ km

Therefore,

Diameter of Jupiter is 1.43 × 10⁵ km.

Answer 2

Diameter of Jupiter is 1.43 × 10⁵ km.

Hope you understand :)