If the whole earth is to be connected by line of sight communication using space waves (no restriction of antenna size or tower height). What is the minimum number of antennas required?

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)`