Question

Chapter 33, Problem 016 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 4.0 x 101 m2. (a) What would be the total power that would be received by the antenna, assuming that its diameter is 400 m? (b) What would be the power of a source at 29000 ly distance from Earth that could provide such a signal? A light-year is the distance light travels in one year. (a) Number Units (b) Number Units

Answer 1

(a)The Intensity of the signal is, 1.4x 10-12 4.0x1017 = 3.5x10-30 W/m² The Power received by the antenna is, P = ITR = (3.5*10-30)( 7 (400)) =1.76x10-24 w (b)Surface Area at 29000ly A = 41R? = 47 ( 29000x3x10' x 365x 24x 3600) = 9.468x1041 m2 The Power of the source is, P. = 14 = (3.5x 10-50 (9.468x1042) = 3.31x1012 w