Question

A far off planet is estimated to be at a distan
D from the earth. If its diametrically opposite
extremes subtend an angle o at an observaton
situated on the earth, the approximate diameter of
the planet is
(1) theta/D
(2) D/ theta
(3) Dtheta
(4) 1/ theta
​

Answer 1

Answer:

D theta

D theta THETA=ARC/RADIUS

D theta THETA=ARC/RADIUSARC=THETA×RADIUS

D theta THETA=ARC/RADIUSARC=THETA×RADIUSHERE RADIUS IS "D"

D theta THETA=ARC/RADIUSARC=THETA×RADIUSHERE RADIUS IS "D"THEREFORE ANSWER IS D THETA

Answer 2

Answer:

Approximate diameter of the planet is $d = D \theta$.

Explanation:

Given the distance of far off planet from the earth is D.

The angle between the diametrically opposite extremes from an observation situated on the earth θ.

• Let the separation between the extremes be $d$.
• Measurement of large distances usually done by the parallax method.
• As the planet is very far away, D is very large and θ is very small and  hence $\dfrac{d}{D} < < 1$ .
• Then, the length d can be assumed as an arc of length d of a circle from a center point C as shown in the figure and the distance D as the radius.
• Both sides the radius are same, i.e., CA=CB
• Thus, $AB = d = D \theta$, where θ is measured in radians.

Therefore, approximate diameter of the planet is $d = D \theta$.

So, the correct answer is option 3.