Question

Find the minimum colatitude which can directly receive a signal from a geostationary satellite.

Answer 1

Consider that B is the position of the geostationary satellite.

In the given figure,

$$\varphi$$ is the latitude and θ is the colatitude of a place which can directly receive a signal from a geostationary satellite.

In triangle OAB, we have:

$$\cos \varphi =\frac{6400}{42000}$$

$$=\frac{16}{106}=\frac{8}{53}$$

$$i.e.,\varphi ={\cos }^{-1}\frac{8}{53}$$

$$={\cos }^{-1}0.15$$

$$\text{ Now },\theta =\frac{\pi }{2}-\varphi$$

$$\Rightarrow \theta =\frac{\pi }{2}-{\cos }^{-1}0.15$$

$$\Rightarrow \theta ={\sin }^{-1}0.15$$