The Arecibo radio telescope, shown below, in Puerto Rico, is sensitive enough to
ID: 2304513 • Letter: T
Question
The Arecibo radio telescope, shown below, in Puerto Rico, is sensitive enough to detect a signal of intensity 2x10 4. 27 2 W/m. The antenna dish diameter is 305m. a) What is the total power received by the antenna for such a signal? b) What would be the power output of a source at the center of our galaxy 4 that could provide such a signal? The galactic center is 2.3x10 light- years away. Take the source as radiating uniformly in all directions. (Our own Prof Ingrid Stairs did pulsar observations at Arecibo before the hurricane)Explanation / Answer
a) Here signal intensity is the power transferred per unit area. Therefore
Total Power = Signal Intensity *Area = 2*10-27 W/m2 * pi*(305/2)2 = 1.46 *10-22 W
b) 1 light year is 9.461*1015 m. For a signal to have intensity SI at a distance r the Power output is
Power Output = SI *4*pi*r2
Power Output = 2*10-27 *4*pi*(2.3*104 *9.461*1015)2 =1.19*1015 W
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