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Substended angle, rotational kinematics

  1. Aug 28, 2011 #1
    The moon has a diameter of 3.48 x 10^6 m and is a distance of 3.85 x 10^8m from the earth. The sun has a diameter of 1.39 x 10^9 m and is 1.50 x 10^11 m from the earth.

    (a.) What are the angles (in radians) subtended by the moon and the sun, as measured by a person standing on the earth.

    Because the large planetary masses are so very far away, we can assume that s = diameter

    Θ = s/r

    For the moon:
    S = 3.48E6 m
    r = 3.85E8 m
    Θ = s/r = 3.48E6/3.85E8
    Θ = 0.009038961 radians


    For the sun:
    S = 1.39E9 m
    r = 1.50E11 m
    Θ = s/r = 1.39E9/1.50E11
    Θ = 0.0092666667 radians

    (b.) Based on the answers to part (a.), is a total eclipse of the sun really "total"?

    No, because the angles are not perfectly equal.

    (c.) What is the ratio (as a percentage) of the apparent circular area of the moon to the apparent circular area of the sun?


    For part C, do I just use Pi(radius)2 and compare the two areas? I just don't understand stand what they mean by "apparent" circular area. Is this problem just to emphasize how much larger the sun is than the moon?
     
    Last edited: Aug 28, 2011
  2. jcsd
  3. Aug 28, 2011 #2

    kuruman

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    By "apparent" circular area they mean the circular area as it appears to you. Imagine that the moon and the sun as you see them in the sky are two circles on a table in front of you. What will you say the ratio of the areas is?
     
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