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?

Options

A. 2
B. 3
C. 4
D. 6

Answer

D

Explanation

Let `h_(t)` be the height of transmitting antenna or receiving antenna in order to cover the ent ire surface of earth through communication as shown in figure.

`d_(m)^(2)=(R+h_(T))^(2)+(R+h_(T))^(2)=2(R+h_(T))^(2)`
As `d_(m)=sqrt(2h_(T)R)+sqrt(2h_(T)R)=2sqrt(2h_(T)R)`
`therefore 8h_(T)R=2(R+h_(T))^(2)`
or `4h_(T)=R^(2)+2Rh_(T)+h_(T)^(3)`
or `R^(2)-2h_(T)R+h_(T)^(2)`
or `R^(2)-2h_(T)R+h_(T)^(3)`
or `(R-h_(T))^(3)=0` or `R=h_(T)`