Consider a civilization broadcasting a signal with a power of 1.9×104 watts. The

Question

Consider a civilization broadcasting a signal with a power of 1.9×104 watts. The Arecibo radio telescope, which is about 300 meters in diameter, could detect this signal if it is coming from as far away as 138 light-years. Suppose instead that the signal is being broadcast from the other side of the Milky Way Galaxy, about 70000 light-years away.

Q)How large a radio telescope would we need to detect this signal? (Hint: Use the inverse square law for light.)

Need Diameter in Meters THANKS!!
Have already tried 156,716.42 m diameter, so that is incorrect.

Explanation / Answer

I have an answer that is different in the third significant digit. Let A be area of antenna, R be distance, D be diameter of antenna, I intensity of signal. I get:

Anew/Aold = Iold/Inew

Anew = Aold(Iold/Inew).      Now Iold/Inew is (Rnew/Rold)2 = (70000/138)2

Since A = (D/2)2 = (/4)D2, we have

(/4)Dnew2 = (/4)Dold2(70000/138)2

Dnew = (Dold2(70000/138)2)1/2 = Dold(70000/138) = 152174 m

which is a little different from the other answer.

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