Question

Example 1.1: What is the solid angle subtended
by the moon at any point of the Earth, given
the diameter of the moon is 3474 km and its
distance from the Earth 3.84x 10m
Solution: Solid angle subtended by the moon
at the Earth​

Answer 1

Answer:-

See below

Explanation:

Diameter of moon  = 3474 km.

Therefore, radius is 1737 km. The area will be,

A_m = \pi r^2 = (3.14)(1737)^2 = 9.473 \times 10^6 \ m^2Am=πr2=(3.14)(1737)2=9.473×106 m2

The distance from the Earth is given as,

= 3.84 \times 10^8 \ m=3.84×108 m

Squaring this value,

r^2 = (3.84 \times 10^8)^2 = 14.74 \times 10^{16} \ m^2r2=(3.84×108)2=14.74×1016 m2

Now the solid angle in steradians is,

\Omega = \frac{9.473 \times 10^6}{14.74 \times 10^{16}} = 0.642 \times 10^{-10}Ω=14.74×10169.473×106=0.642×10−10

And that should be the answer.