Chapter 33, Problem 016 Your answer is partially correct. Try again. Large radio

Question

Chapter 33, Problem 016 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 1.5 pW of power on an area of 3.8 x 1014 m2. (a) What would be the total power that would be received by the antenna, assuming that its diameter is 330 m? (b) What would be the power of a source at 19000 ly distance from Earth that could provide such a signal? A light-year is the distance light travels in one year (a) Numbef T 3.38e-22 Units [ w (b) Number 1.8e15 Units I w

Explanation / Answer

A) Here the intensity that should be received by the Arecibo antenna should be equal to intensity of that signal on earth.

Then intensity received, Ir = Pr/a

Pr = power received

a =area of cross section of antenna = ?D2/4

D = 330 m

Then a =?(330m)2/4

Power on the earth Pearth = 1.5*10-12W

Area on the earth A= 3.8 x 1014 m2

Then Ir=Ie

       Pr/a = Pearth/A

    Power received by antenna Pr = (1.5*10-12W /3.8x1014 m2)*?(330m)2/4

                                                   = 3.376*10-22 W

B) r = distance of the source to the antenna = 1.9*104ly*9.46 *1015m/ly

Powerof the source is Ps = 4?r2Ie

                                      = 4?*( 1.9*104ly*9.46 *1015m/ly)2*(1.5*10-12W /3.8 x1014 m2)

                                        = 1.60*1015 W

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