Question

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

Answer 1

$\varphi =1°{54}^{\prime }={114}^{\prime }=(114\times 60)"=114\times 60\times 4.85\times {10}^{-6}rad=3.32\times {10}^{-2}rad$

Basis,$b=AB=1.276\times {10}^{7}m$

So,the distance of the moon from the earth,

$S=\frac{B}{\varphi }=\frac{1.276\times {10}^7}{3.32\times {10}^{-2}}=3.84\times {10}^8$