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The Arecibo radio telescope in Puerto Rico can detect a wavewith an intensity as

ID: 1680531 • Letter: T

Question

The Arecibo radio telescope in Puerto Rico can detect a wavewith an intensity as low as 1 x 10-23 W/m2.As a “best-case” scenario for communication withextraterrestrials, consider the following: suppose an advancedcivilization located at point A, a distance x away from Earth, issomehow able to harness the entire power output of a Sun-like star,converting that power completely into a radio-wave signal which istransmitted uniformly in all directions from A.

a) in order for Arecibo to detect this radio signal, what is themaximum value for x in light-years?

b) How does this maximum value compare with the 100,000-ly sizeof our Milky Way galazy?

The intensity of sunlight at Earth’s orbital distance fromthe Sun in 1350 W/m2.

Explanation / Answer

Given that Distance of the sun from earth d = 1 A.U = [1 / 63241] ly =1.581 x 10-5 ly Ip = 1 x 10-23 W/m2 Is = 1350 W/m2 We know that        I = P / A          = P /4r2 From the above relation we have        I 1 / r2 So that we can write      Ip / Is = (x /d)2 ==> x = d * [Ip/Is]            = 1.581 x 10-5 ly * [1 x 10-23 / 1350]            = 1.360 x 10-10 ly (b) when compare with the 100,000-ly size of our Milky Way galazyis                 = 0.7352 x 1016 ly