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Homework Help: Gravitation and Newton's Synthesis

  1. Dec 24, 2009 #1
    1. The problem statement, all variables and given/known data
    The asteroid Icarus, though only a few hundred meters across, orbits the Sun like the other planents. Its period is about 410 d. What is its mean distance from the Sun?

    2. Relevant equations

    Keplers Law
    T_1 ^2 / T_2 ^2 = S_1 ^3 / S_2 ^3

    3. The attempt at a solution

    I chose my second reference point to be the earth
    the distance from the earth to the sun is about 1.5 E 11 m
    the period of the Earht is one day or 8.64E4 s
    410 d is equal to 3.542E7 s

    from keplers law

    S_1 = CUBEROOT( (T_1^2 S_2^3)/T_2^2

    CUBEROOT( ((3.542 E 7 s)^2 (1.5 E 11 m)^3)/(8.64 E 4 s)^2
    I'm getting about 1.87 E 11 m
    the book says 1.62 E 11 m

    what am I doing wrong
  2. jcsd
  3. Dec 24, 2009 #2


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    Homework Helper

    What for the period of the earth is one day ???
  4. Dec 27, 2009 #3


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    Staff Emeritus
    Science Advisor
    Homework Helper

    Also, it is not necessary to convert the periods into seconds in this problem.
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