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 0.93 pW of power on an area of 3.9 x 10¹¹ m². (a) What would be the total power that would be received by the antenna, assuming that its diameter is 380 m? (b) What would be the power of a source at 28000 ly distance from Earth that could provide such a signal? A light-year is the distance light travels in one year.

Answer 1

a)

Here ,

Total power = Intensity * are

Total Power = 0.93*pi*(380/2)^2/(3.9*10^11)

Total Power = 2.704 *10^-7 pW

the total Power received is 2.704 *10^-19 J

B)

Distance = 28000 ly

d = (28000*365*24*3600*3*10^8)

d = 2.649*10^20 m

therefore ,

Total Power = I*4*pi*d^2

Total Power = 0.93*10^-12 * 4*3.141*(2.649*10^20)^2/3.9*10^11

Total power = 2.1024 *10^18 W

the power of a source at 28000 ly distance from Earth that could provide such a signal is 2.1024 *10^18 W