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Large radio telescopes, like the one in Arecibo, Puerto Rico, can detect extreme

ID: 1414109 • Letter: L

Question

Large radio telescopes, like the one in Arecibo, Puerto Rico, can detect extremely weak signals. Suppose one radio telescope is sensitive enough to detect a signal which lays down only 0.82 pW of power on an area of 4.1 × 1014 m2. (a) What would be the total power that would be received by the antenna, assuming that its diameter is 400 m? (b) What would be the power of a source at 21000 ly distance from Earth that could provide such a signal? A light-year is the distance light travels in one year.

Explanation / Answer

a)

intensity = P/A = 2 x 10^-27 W/m^2

power = Intensity x pi x 200^2

Power = 2.513 x 10^-22 W

b)

intensity should be same

P /A =  2 x 10^-27 W/m^2

P =