A far off planet is estimated to be at a distance D from the earth. If its diametrically opposite extremes subtend an angle θ at an observatory situated on the earth, the approximate diameter of the planet is

Question

A far off planet is estimated to be at a distance D from the earth. If its diametrically opposite extremes subtend an angle θ at an observatory situated on the earth, the approximate diameter of the planet is (A) (θ/D) (B) (D/θ) (C) D θ (D) (1/D θ)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/4df1b03a45f1f8efd3ee87fce345318b-.png" /> θ=( text Arc length / text Radius ) θ=(d/D) ⇒ d=D θ

Q. A far off planet is estimated to be at a distance $D$ from the earth. If its diametrically opposite extremes subtend an angle $θ$ at an observatory situated on the earth, the approximate diameter of the planet is

$\frac{θ}{D}$

$\frac{D}{θ}$

$D θ$

$\frac{1}{D θ}$

$θ = \frac{Arc length}{Radius}$
$θ = \frac{d}{D}$
$\Rightarrow d = D θ$

Q. A far off planet is estimated to be at a distance D from the earth. If its diametrically opposite extremes subtend an angle θ at an observatory situated on the earth, the approximate diameter of the planet is

Dθ​

θD​

Dθ

Dθ1​