A satellite in stationary orbit above a point on the equator is intended to send energy to ground stations by a coherent microwave beam of wavelength one meter from a one-km mirror.
Text Solution
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Sol. The revolving angular velocity ω of the synchronous satellite is equal to the spin angular velocity of the earth and is given by
m (R + h) ω 2 = 
.
Hence the height of the stationary orbit is
h = 
– R = 3.59 × 10 4 km,
using G = 6.67 × 10 –11 Nm 2 kg –2 , M = 5.98 × 10 24 kg, R = 6.37 × 10 4 km.
Due to diffraction, the linear size of the required receptor is about
= 1 × 
= 3.59 × 10 4 m.
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