Q. 36

A satellite is to be placed in equatorial geostationary orbit around earth for communication.(a) Calculate height of such a satellite.(b) Find out the minimum number of satellites that are needed to cover entire earth so that at least one satellites is visible from any point on the equator.[M = 6 × 1024 kg, R = 6400 km, T = 24h, G = 6.67 × 10 - 11 SI units]

(a) For a geostationary satellite, the centripetal force must equal the gravitational force. Let the mass of earth be M and the satellite be m, then

Where r is the radius of the orbit of the satellite and ω is its angular velocity

where T is the time period of revolution, then

Now the height h of the satellite from the surface of the earth,

where R is the radius of earth.

For a geostationary satellite, the time period is 24 hours or 86400 seconds,

(b) A geostationary satellite is visible form the equator in the region shown in the figure having an angle 2θ,

Now from the figure we have

Now 2θ = 162.58, therefore to cover the earth with such satellites so that from any point on the equator a satellite can be seen,

Therefore, we need a minimum of 3 satellites.

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