The minimum number of geostationary satellites required to televise a programme all over the earth is:

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answer is D.

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Detailed Solution

Concept: Geostationary satellites have the same angular velocity as earth. Therefore, using the method, we can determine the number of satellites that will be required if one of the satellites covers a solid angle of 120 degrees on the centre of the planet.
Geostationary refers to the fact that a satellite seems to be stationary to a ground observer when they see it in the sky. The earth is orbited by geostationary satellites, which rotate from west to east in the same direction as the earth. They are 42,400 kilometres from the earth's core and 36,000 kilometres above the equator. Their angular velocity is the same as that of the earth, therefore their orbit takes 24 hours, or the same amount of time as it takes for the earth to circle once on its axis.
Now, a geostationary satellite forms a solid angle in the middle of the earth when it is around 42,400 kilometres from the planet's core. This solid angle can be calculated using the formula,

Ω = 2 π (1 - cosθ)

This solid angle, for a geostationary satellite, is known to be about 120 degrees.
Therefore, the solid angle must be 360 degrees in order to cover the entire earth's surface.