The moon is observed from 2 diametrically extremes A andB on earth. The angle of parallax is found to be 1°54'.if the diameter  of earth is about 1.276×10^7m estimate the distance  of the moon from the earth

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

 

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