Question

The moon is observed from two diametrically opposite points $A$ and $B$ on earth. The angle $\theta$ subtended at the moon by the two directions of observation is $1^{\circ} 54^{\prime}$; given that the diameter of the earth to be about $1.276 \times 10^{7} m$. Compute the distance of the moon from the earth.

• A. $4.5 \times 10^{9} m$
• B. $3.83 \times 10^{8} m$
• C. $2.5 \times 10^{4} m$
• D. $4 \times 10^{7} m$

Answer 1

Answer: (B)

We have, $\theta=1^{\circ} 54^{\prime}=(60+54)^{\prime}=114^{\prime}=(114 \times 60)^{\prime}$
Since, $1^{\prime \prime} =4.85 \times 10^{-6} rad $
$=(114 \times 60)^{\prime \prime} \times\left(4.85 \times 10^{-6}\right) rad$
$=3.33 \times 10^{-2} rad$
Also, diameter of earth, $b=1.276 \times 10^{7} m$
Hence, the earth-moon distance is given as
$D=b / \theta=\frac{1.276 \times 10^{7}}{3.33 \times 10^{-2}}$
$=3.83 \times 10^{8} m$