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 number of antennas required? Calculate the tower height of these antennas in terms of earths radius?

Question

Philoid · Accepted Answer

Let us consider a 2-D earth first. We would need a minimum of 4 antennas.

Let the height of each antenna be h and the radius of earth be R.

From the diagram, on applying PGT we have

We also know that

where h_T and h_R are the height of the transmitting and receiving antenna respectively

Here, . Hence,

Substituting this in (1), we get

Hence, the height of the towers must be equal to the radius of the earth! We can extend this idea to 3-D with a minimum of 6 towers.