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Question
Find the minimum colatitude which can directly receive a signal from a geostationary satellite.
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Solution
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:
\[\cos \phi = \frac{6400}{42000}\]
\[ = \frac{16}{106} = \frac{8}{53}\]
\[i . e . , \phi = \cos^{- 1} \frac{8}{53}\]
\[ = \cos^{- 1} 0 . 15\]
\[\text { Now }, \theta = \frac{\pi}{2} - \phi\]
\[ \Rightarrow \theta = \frac{\pi}{2} - \cos^{- 1} 0 . 15\]
\[ \Rightarrow \theta = \sin^{- 1} 0 . 15\]
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