Question

The moon is observed from
two diametrically opposite points A and B
on Earth. The angle θ subtended at the
moon by the two directions of observation
is 1o 54′ . Given the diameter of the Earth to
be about 1.276 × 107 m, compute the
distance of the moon from the Earth.

Answer 1

Answer:

Given that the parallax angle, θ = 1° 54' = 114'

114' = 114× 60'' = 6840''

We know that 1'' = 4.85 × 10-6 rad

Therefore 1° 54' = 6840'' × (4.85 × 10-6 ) rad

θ = 3.32×10-2 rad

Given the diameter of earth, b = 1.276 × 107 m

begin math size 12px style We space know space that space straight D space equals space straight b over straight theta straight D space equals space fraction numerator 1.276 cross times 10 to the power of 7 over denominator 3.32 space cross times 10 to the power of negative 2 end exponent end fraction equals 3.843 cross times 10 to the power of 8 space straight m end style

 

Hence the distance of the moon from the earth = 3.843 × 108 m