Question

The moon is observed from two diametrically opposite points A and B on earth .The angle subtended at the moon by the two directions of observation is 1° 54'.Given the diameter of the earth to be about 1.276×10to the power 7m, compute the distance of the moon from the earth

Answer 1

Answer:

We have theta = 1°54´ = 114´

$= (114×60)´´ × (4.85×{10}^{ - 6} )rad$

$= 3.32 \times {10}^{ - 2} rad$

Since $1´´ = 4.85× {10}^{ - 6} rad.$

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

Hence, We have the earth-moon distance,

D = b/ theta

$= \frac{1.276 \times {10}^{7} }{3.32 \times {10}^{ - 2} }$

$= 3.84 \times {10}^{8} m$

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