Question

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?

• A. 2
• B. 3
• C. 4
• D. 6

Answer 1

Answer: (D)

6

Answer 2

: Let $h_{T}$be the height of transmitting antenna or receiving antenna in order to cover the entire 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 $d_{m} = \sqrt{2h_{T}R} + \sqrt{2h_{T}R} = 2\sqrt{2h_{T}R}$

$\therefore 8h_{T}R = 2(R + h_{T})^{2}$

$or4h_{T}R = R^{2} + 2h_{T}R + h_{T}^{2}$

Or $R^{2} - 2h_{T}R + h_{T}^{2}$

Or $(R - h_{T})^{2} = 0orR = h_{T}$

Since space wave frequency is used so $\lambda < < h_{T}$hence only tower height is to be taken into consideration. In three dimensions of earth, 6 antenna towers each height $h_{T} = R$would be used to cover the entire surface of earth with communication porgramme