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Homework Help: Angular Resolution Question

  1. Apr 17, 2010 #1
    1. The problem statement, all variables and given/known data
    A radio telescope observes two stars orbiting each other, using radio waves of wavelength 20.0 cm. The stars are 10^7m away from the Earth. The telescope, which has a diameter of 20.0km, can just resolve the two stars. What is the distance between the two stars?

    2. Relevant equations

    theta(min) = 1.22* wavelength/Diameter of circular aperture

    3. The attempt at a solution

    I got 1.22(0.2)/20000 = theta (min). Then I changed it into degrees because I'm more comfortable using them. I got 0.000699 degrees. Then I divided that by half to get the angle to one of the stars. Using the small angle approximation I got 0.000699*10^17m = 3.49x10^13. Then I doubled it to get the distance between the stars 6.99x10^13m. The answer is apparently 1.22x10^12m. Help plz :)
  2. jcsd
  3. Apr 18, 2010 #2


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    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi danmend ! Welcome to PF! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    6.99x1013 divided by 1.22x1012 = 57.29 = 180/π …

    now do you see why it's so much easier to use radians? :smile:
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