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:
$$\begin{gathered} \cos \mathrm{\varphi }=\frac{6400}{42000} \\ =\frac{16}{106}=\frac{8}{53} \\ \mathrm{i}.\mathrm{e}.,\mathrm{\varphi }={\cos }^{-1}\frac{8}{53} \\ ={\cos }^{-1}0.15 \\ \mathrm{Now},\theta =\frac{\pi }{2}-\varphi \\ \Rightarrow \theta =\frac{\pi }{2}-{\cos }^{-1}0.15 \\ \Rightarrow \theta ={\sin }^{-1}0.15 \end{gathered}$$