Your answer is partially correct. Try again. Large radio telescopes, like the on

Question

Your answer is partially correct. Try again. Large radio telescopes, like the one in Arecibo, Puerto Rico, can detect extremely weak signals. Suppose one radio telescope is sensitive enough to detect a signal which lays down only 1.4 pW of power on an area of 3.8 times 10^13 m2. What would be the total power that would be received by the antenna, assuming that its diameter is 290 m? What would be the power of a source at 17000 ly distance from Earth that could provide such a signal? A light-year is the distance light travels in one year.

Explanation / Answer

We know that
power = Intensity*area
Intensity = Power/area = 1.4*10-12 /3.8*1013 = 3.68*10-26 W/m2
(1) When diameter = 290 m
therefore area = 4Pi*r2 where r isthe radius
Area = 4*Pi*(290/2)2 = 264207.94 m2
Power = Intensity *Area = 3.68*10-26  * 264207.94 = 9.7339*10-21 W
(b) 1 light year = 9.41*1015 m
So distance will work as radius therefore
area = 4Pi*r2 = 4*Pi*(17000*9.41*1015)2 = 3.2158*1041 m2
Power = intensity*area = 3.68*10-26 * 3.2158*1041 = 11.834*1015 W

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