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555.


Problem 41.24 (RHK)


Frank D. Drake, an active investigator in SETI (Search for Extra-Terrestrial Intelligence) programme, has said that the large radio telescope in Arecibo, Puerto Rico, “can detect a signal which lays down on the entire surface of the Earth a power of only one picowatt”. We have to find (a) the power actually received by the Arecibo antenna for such a signal. The antenna diameter is 305 m. (b) We have to find the power output of a source at the centre of our galaxy that could provide such a signal. The galactic centre is away. We can take the source as radiating uniformly in all directions.


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(a)

Radius of the Earth, .

The surface of the Earth,

The intensity of the weakest signal that can be detected by the Arecibo radio telescope will therefore be

Diameter of the Arecibo antenna .

Therefore, the power received by the Arecibo radio telescope for the weakest signal will be

(b)

Distance of the galactic centre is

where we have used that

Therefore, the power of the source emitting the signal from the centre of our galaxy will be