The angular diameter of a planet measured from earth is 90". If the diameter of the planet is π × 106 m , then its distance from the earth is

Question

The angular diameter of a planet measured from earth is 90". If the diameter of the planet is π × 106 m , then its distance from the earth is (A) 3.6× 109 m (B) 7.2× 109 m (C) 3.6× 106 m (D) 7.2× 106 m

Tardigrade Admin · Accepted Answer

Given θ=9011=90 × (π/180 × 60 × 60)=(π/7200) D=π × 106 m d=(D/θ)=(π × 106 × 7200/π) =7.2 × 109 M

Q. The angular diameter of a planet measured from earth is $90"$ . If the diameter of the planet is $π \times 1 0^{6} m$ , then its distance from the earth is

$3.6 \times 1 0^{9} m$

$7.2 \times 1 0^{9} m$

$3.6 \times 1 0^{6} m$

$7.2 \times 1 0^{6} m$

$1.8 \times 1 0^{8} m$

Given $θ = 9 0^{11} = 90 \times \frac{π}{180 \times 60 \times 60} = \frac{π}{7200}$
$D = π \times 1 0^{6} m d = \frac{D}{θ} = \frac{π \times 1 0 ^{6} \times 7200}{π}$
$= 7.2 \times 1 0^{9} M$

Q. The angular diameter of a planet measured from earth is 90". If the diameter of the planet is π×106m , then its distance from the earth is

3.6×109m

7.2×109m

3.6×106m

7.2×106m

1.8×108m

Given θ=9011=90×180×60×60π​=7200π​ D=π×106md=θD​=ππ×106×7200​ =7.2×109M