Large radio telescopes, like the one in Arecibo, Puerto Rico, can detect extreme

Question

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 0.81 pW of power on an area of 7.0 x 10^16 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 21000 ly distance from Earth that could provide such a signal? A light-year is the distance light travels in one year.

Explanation / Answer

Data: Power, P = 0.81 x 10^-12 W Area, A = 7 x 10^16 m^2 Diameter, D = 330 m Radius, R = 165 m Diameter, D = 330 m Radius, R = 165 m Solution: (a) Iintensity of the signal, I = P/A                                           = 0.81 x10^-12 / 7 x10^16                                           = 1.16 x10^-29 W/m^2

Power received by the antenna: P' = I * R^2     = 1.16 x10^-29 * *(165)^2     = 9.9 x10^-25 W Ans: Power received by the antenna, P' = 9.9 x 10^-25 W


(b) Surface Area at 21000ly: A' = *(21000 ly * 3.0x10^8m/s * 365*24*3600 s)^2        = 1.24 x10^41m^2

Power of the source, Ps = I *A'     = 1.16 x 10^-29 * 1.24 x10^41     = 1.44 x10^12 W Ans: Power of the source, Ps = 1.44 x 10^12 W

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