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  4. 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

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

Physical World, Units and Measurements

Solution:

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