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,

\[\phi\] 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:

\[\cos \phi = \frac{6400}{42000}\]

\[ = \frac{16}{106} = \frac{8}{53}\]

\[i . e . , \phi = \cos^{- 1} \frac{8}{53}\]

\[ = \cos^{- 1} 0 . 15\]

\[\text { Now }, \theta = \frac{\pi}{2} - \phi\]

\[ \Rightarrow \theta = \frac{\pi}{2} - \cos^{- 1} 0 . 15\]

\[ \Rightarrow \theta = \sin^{- 1} 0 . 15\]