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

Question

Find the minimum colatitude which can directly receive a signal from a geostationary satellite. (Let $R$ be the radius of the earth and $r$ be the radius of the geostationary orbit)

Professor PC Thomas Classes · Answer

The signal from the satellite is tangent to the earth. The angle $	heta$ between the equator and the tangent point satisfies $\cos	heta = \frac{R}{r}$. Colatitude is measured from the pole, so it equals $90^\circ - 	heta$. Thus, $\sin(colatitude) = \cos	heta = \frac{R}{r}$, making colatitude $= \sin^{-1}(\frac{R}{r})$.