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SOLUTIONS TO EXERCISE 11

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energy: TOC for Knowledge Concepts, Exercises, and Solutions


(a) The collecting area of the radio telescope is 

  A = pi*r^2 = 3.14 * (35 m /2)^2 = 962 sq. meter. 

So the luminosity on this telescope is the flux from Voyager 2 to 
Earth, times the collecting area of the dish:

  L = F * A = 1.59 * 10^(-24) W/m^2 * 962 m^2 = 1.53 * 10^(-21) Watts.

The amount of energy received in one hour (remember that a watt equals
a joule per second) is thus

  E = L * t = 1.53 * 10^(-21) W * 3600 sec = 5.51 * 10^(-18) joule.

(b) Since flux is L/(4*pi*r^2), we can figure out the distance you
would need to be away from the light bulb by using the flux on Earth
from Voyager 2 and the luminosity of the light bulb.

   1.59 * 10^(-24) W/m^2 = 1.3 W / (4 * pi * r^2) ; thus,

   r^2 = 1.3 W / (1.59 * 10^(-24) W/m^2 * 4 * 3.14) 

    r  = sqrt(6.51 * 10^22 m^2) = 2.55 * 10^11 m = 2.55 * 10^8 km.

This is equivalent to (2.55 * 10^8)/1.61 = 158 million miles, 
slightly longer than the distance between Earth and the Sun.

(c) How much luminosity from the light bulb arrives in your eye at that 
distance?  A good estimate of the size of your pupil might be about half a
centimeter (5 mm) in diameter at maximum dilation.  In that case,

  L = F * A = 1.59 * 10^(-24) W/m^2 * 3.14 * (0.0025 m)^2 

    = 3.12 * 10^(-29) Watts.  

That's less than one visible light photon per century!