Question

Example 2.3 The moon is observed from
two diametrically opposite points A and B
on Earth. The angle o subtended at the
moon by the two directions of observation
is 1° 54'. Given the diameter of the Earth to
be about 1.276 x 107 m, compute the
distance of the moon from the Earth.
​

Answer 1

$\huge{\mathfrak{\underline{\red{Answer!}}}}$

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:

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