A telescope observes two points on a distant planet. The linear separation between the points is π × 10^6 m , and they subtend an angle of 6' (minutes of arc) at the telescope. The distance to the planet from the

Question

Quantrex Academy · Accepted Answer

Correct answer: B. 1.8 × 10^9 m

The plane angle subtended by an arc of length

s

at a distance

D

is given by

\theta = \dfrac{s}{D}

, provided

\theta

is measured in radians.

Given:

s = \pi \times 10^6 \text{ m}

\theta = 6'

First, convert the angle into radians:

6' = \left(\dfrac{6}{60}\right)^\circ = 0.1^\circ

0.1^\circ = 0.1 \times \dfrac{\pi}{180} \text{ rad} = \dfrac{\pi}{1800} \text{ rad}

Now, calculate the distance

D

:

D = \dfrac{s}{\theta} = \dfrac{\pi \times 10^6}{\dfrac{\pi}{1800}}

D = 1800 \times 10^6 \text{ m} = 1.8 \times 10^9 \text{ m}

Answer:

1.8 \times 10^9 \text{ m}

A telescope observes two points on a distant planet. The linear...

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