A source of radio waves is emitted from the center of our galaxy 1.8 x 104 light

Question

A source of radio waves is emitted from the center of our galaxy 1.8 x 104 light years away. 1.5 pW
(picowatts) of power from these waves blankets the entire surface of the Earth.
a) What is the intensity of the radio waves? (Take the diameter of the Earth to be 12.7 x 103 km.)
b) How much power do the radio waves carry?
c) How much power from these radio waves is received by the Arecibo radio antenna located in
Puerto Rico? (The Arecibo antenna is 300 m in diameter.) This is the minimum intensity wave
that can be detected by the Arecibo antenna!

Explanation / Answer

Area of earth exposed = *r*r = 1.266768 * 1014 m2

Intensity = Energy / Area [for distant earth area exposed is calculated above] = 1.185*10-26 W/m2

Energy radiated = Area (galaxy) * Intensity

= 4R2 * 1.5*10-12 / r2

= 3.33 MW [Megawatt]

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