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 direction of observation is $1^{\circ }{54}^{\prime }$. Given the diameter of earth to be about $1.276\times {10}^7$ m, compute the distance of the moon from the Earth.

• A. $4.34\times {10}^8$ m
• B. $3.84\times {10}^8$ m
• C. $4.84\times {10}^9$ m
• D. $1.26\times {10}^8$ m

Answer 1

Answer: (B)

$3.84\times {10}^8$ m

The parallax angle in radians is: $\theta =(1+\frac{54}{60})\times \frac{\pi }{180}$$=0.03316rad$

Hence, the distance between moon and earth:

$=\frac{DiameterofEarth}{\theta }$
$=\frac{1.276\times {10}^{7}m}{0.03316}$
$=3.84\times {10}^{8}m$