A source of radio waves is emitted from the center point of our galaxy 1.9 x 104

Question

A source of radio waves is emitted from the center point of our galaxy 1.9 x 104 light years away. Nine
picowatts of power from these waves blanket the surface of the Earth facing the center point.
a) What is the intensity of the radio waves? (Take the diameter of the Earth to be 1.27 x 104 km.)
b) How much power do the radio waves carry?
c) How much power from these radio waves is received by the Greenbank radio telescope (GBT)
assuming the radio dish is pointed towards the center of the galaxy? The GBT dish is 100 m in
diameter. (This is approximately the minimum intensity wave that can be detected by the GBT!)

Explanation / Answer

a)

A = Re^2 = 3.1416 * 1.27e7*1.27e7/4 = 1.26677e14 m2

I = P/A = 9e-12/1.26677e14 = 7.10468e-26 7.10e-26 W/m2

b)

P = I A = I 4 R^2

P = 7.10468e-26 * 4 * 3.1416* (1.9e4*9.461e15*1.9e4*9.461e15)

P = 2.8849e16 2.88e16 W

c)

P = I A = I R^2

P = 7.10468e-26 * 3.1416 * 100*100/4 = 5.58e-22 W

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