Question

The moon is observed from two diametrically opposite point's A and B on earth. The angle theta subtended at moon by two directions of observation is 1°.54' . Given the diameter of the earth to be about 1.276× 10⁷ m .compute the distance of the moon From earth.​

Answer 1

Answer:

The diametrically opposite points on the earth are A and B.

The angle theta subtended by the moon = 1°54'.

The diameter of earth = 1.276 × 10⁷ m.

We need to find the distance of the moon from Earth.

Let us find the angle subtended theta by the moon in seconds.

∅ = 1°54' = 60'+54' = 114' = 6840"

Now, let us concert it in radians :

1" = 4.85 × 10^{-6} rad

So, 6840" = 4.85 × 10^{-6} × 6840

⇒ 33174 × 10^{-6}

⇒ 3.32 × 10^{-2} rad

Now, We know : d = Arc/∅

⇒ d = 1.276 × 10⁷ m/3.32 × 10^{-2} rad

⇒ d = 0.3843 × 10^{7-(-2)}

⇒ d = 0.3843 × 10⁹

⇒ d = 3.84 × 10⁸

Hence, the Distance of moon from the earth is 3.84 × 10⁸ m.