If the whole earth is to be connected by LOS communication using space waves ( no restriction of antenna size or tower height), what is the minimum no of antennaas required ? Calculate the tower height of these antennas in terms of earth's radius?

Explanation

Let `h_t` be the height of transmitting antenna or receiving antenna in
order to cover the entire surface of earth through communication, figure.
`d_(m)^(2) = (R + h_t)^2 + (R + h_(t))^2 = 2 (R + h_(t))^2`
Now `d_(m) = sqrt(2h_tR) + sqrt(2h_tR) = 2sqrt(2h_tR) :. 8h_tR = 2(R + h_t)^2 or 4h_tR = R^2 + 2Rh_t + h_(t)^(2)`
or ` R^2 - 2h_t R + h_(t)^(2) = 0 or (R - h_(t))^2 = 0 or R = h_t`
Since space wave frequency is used so `lambda lt lt h_t`, hence only tower height is to be taken into consideration. In
three dimensions of earth, 6 antenna towers each of height `h_t = R` would be used to cover the entire surface
of earth with communication programme.