Question

The moon is observed from two diametrically opposite points A and B on the Earth . The angle Ф subtended at the moon by the two directions of observation is 1.267ₓ10⁷ m, compute the distance of the moon from the Earth.

Answer 1

Given:

The moon is observed from two diametrically opposite points A and B on the Earth . The angle Ф subtended at the moon by the two directions of observation is 1.267×10⁷ m,

To find:

Distance between moon and earth.

Calculation:

Let distance between moon and Earth be D ;

The angular diameter of Earth from moon is $\phi$

The distance between the 2 observatories on earth be d = 1.267 × 10^7 m.

We know that for high values of D , the general relationship is :

$\therefore \: \phi = \dfrac{d}{D}$

$= > \: \phi = \dfrac{1.267 \times {10}^{7} }{D}$

$= > \: D= \dfrac{1.267 \times {10}^{7} }{ \phi}$

So, final answer is:

$\boxed{ \bold{\: D= \dfrac{1.267 \times {10}^{7} }{ \phi} }}$

Answer 2

Answer:

refer the attachment

hope it helps