The Arecibo radio telescope in Puerto Rico can detect a radio wave with an intensity as low as 1 × 10−23 W/m2. As a “best-case” scenario for communication with extraterrestrials. consider the following: suppose an advanced civilization located at point A. a distance x away from Earth, is somehow able to harness the entire power output of a Sun-like star, converting that power completely into a radio-wave signal which is transmitted uniformly in all directions from A. (a) In order for Arecibo to detect this radio signal, what is the maximum value for x in light-years (1 ly ≈ 1016 m)? (b) How does this maximum value compare with the 100,000-ly size of our Milky Way galaxy? The intensity of sunlight at Earth’s orbital distance from the Sun is 1350 W/m2.
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