Q.The transmitting antenna of a TV tower has a height of 100 m, and the receiving antenna is also raised to a height of 25 m above the ground. Taking the radius of the Earth as $6.4\times10^{6}$ m, calculate the total maximum range of communication between the two antennas.

Using the line-of-sight antenna range formula $d=\sqrt{2Rh}$ and solving for h with d=64 km, R=6400 km gives h=0.32 km.

Working

The line-of-sight range of a transmitting antenna of height $h$, given the Earth's radius $R$, is

$d = \sqrt{2Rh} \ \Rightarrow\ h = \dfrac{d^2}{2R}$

Given $d=64$ km, $R=6400$ km: …

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Ground waves attenuate rapidly at high frequency, and sky waves fail above ~30 MHz because the ionosphere no longer reflects them (the waves penetrate it). UHF frequencies (300 MHz–3 GHz) therefore propagate as space waves — line …

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Working

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• Ground wave propagation: up to about 2 MHz (follows the earth's curvature).
• Sky wave propagation: about 2-30 MHz (reflected back by the ionosphere). …

GPS is a satellite navigation system giving a receiver's precise location and time anywhere on Earth.

The Global Positioning System (GPS) consists of a network (constellation) of navigation satellites orbiting the Earth, each continuously transmitting signals carrying its own precise position and the exact time.

A GPS receiver on the ground (or in a vehicle, ship, aircraft, or mobile phone) picks up signals from several of these satellites simultaneously. By measuring the time delay of the signals received from at least four satellites and using the technique of trilateration, the receiver calculates its own precise three-dimensional position (latitude, longitude, and …

Range d = √(2Rh) = √(2 × 6.4×10⁶ × 245) ≈ 5.6×10⁴ m = 56 km.

For a transmitting antenna of height h, the maximum line-of-sight coverage distance on the Earth (radius R = 6.4 × 10⁶ m) is

$d = \sqrt{2Rh}.$

Substituting h = 245 m:

…

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