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
$D=b/\theta =\frac{1.276\times 10^7}{3.33\times 10^{-2}}$
$=3.83\times 10^{8}m$