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Homework Help: Angular diameter

  1. Aug 18, 2008 #1
    1. The problem statement, all variables and given/known data
    This is the questions:

    1) The angular diameter of the sun measured from the earth is 0.52 degrees. Calculate:
    i) the angular diameter in radians
    ii) the sun's radius in meters
    iii) The surface area of the sun, assuming that it is a sphere

    2) Using L=aAT4 where L is the luminosity, a is the stefan-Boltzmann constant: 5.67X10^-8, A is the surface area, T is the temperature.

    Calculate the total power and the power per m^2 radiated by the earth at a temperature of 228K. You can assume that the earth is a sphere of radius 6400km.

    3. The attempt at a solution

    Question 1:
    Question i) is quite easy and found out that it is 0.00908
    Question ii) is the major problem. I tried to assume that it is a triangle and used the sine rule (since i know the distance of the sun to the earth is 149X10^11m while the other angles in the triangle should be (180-0.52)/2. However, this gave me an answer of 1.4X10^9. If i divide by 2 (to find the radius), i ger 7X10^8m.
    The answer at the back of the book is 1.4X10^9m. which is double my answer. I suspect that the book may be wrong but just wish to double check
    Question iii) if i knew the answer to question ii), i would be able to do this.

    Question 2: I thought that this question should be easy where i just put in the numbers into the equation... but i couldn't get the right answer...
    L=aAT^4
    L = (5.67X10^-8)*(4*pi*6400000^2)*(228^4)
    L = 7.89X10^16
    The book's answer is 201X10^15 W

    Thank you very much
     
    Last edited: Aug 18, 2008
  2. jcsd
  3. Aug 18, 2008 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi yiuscott! :smile:
    I think the book is wrong, and you are right … width = radius * radians. :smile:
    erm … 228K? … I don't think so! :rolleyes:

    Try 288K! :wink:
     
  4. Aug 18, 2008 #3
    Thanks for the reply.

    lol thanks. I can't imagine a textbook getting 2 questions wrong in a row. I should have spotted the problem with a 228K earth though... :rolleyes:
     
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