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Homework Help: Finding Dimensions for Period of a Planet

  1. Feb 3, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi! This is from Physics for Scientists and Engineers, Vol. 6 by Tipler and Mosca.

    44. Kepler's third law relates the period of a planet to its orbital radius r, the constant G in Newton's law of gravitation, and the mass of the Sun Ms . What combination of these factors gives the correct dimensions for the period of a planet?


    2. Relevant equations
    F = Gm1m2/r2
    G = [L3/MT2]
    T=C*ra*Mb*Gc
    3. The attempt at a solution

    I'm trying to solve for C in the final equation given.

    The big problem I'm having here comes after solving for the exponents in the third equation there...

    [T] = [L]a[M]b[[L3/MT2]c

    Next I distribute exponents and combine the like terms...

    [T] = La+3cMb-cT-2c

    Okay, now I solve for C using the T1 on the left side of the equation...

    -2c = 1
    c = -1/2

    Now I have C, the other variables come to me... eheAHEUAEU

    a+3(-1/2) = 0
    b-c = 0
    a = 3/2
    b = -1/2

    With the exponents solved for, I return to my original equation:

    T=C*ra*Mb*Gc

    Only now, I sub them in.

    T=C*r3/2*M-1/2*G-1/2

    THIS is where I have a problem! :( The answer given to this set was C = sqrt(GM)*r3/2.

    Can someone tell me what I'm doing wrong? I don't see how T gets removed or why the negative squareroots become positive while the 3/2 remains the same

    ANY HELP IS APPRECIATED !!! :( So stuck :(
     
    Last edited: Feb 3, 2010
  2. jcsd
  3. Feb 3, 2010 #2
    Made a mistake with T^(-2a).. it's actually T^(-2c)! Fixed that mistake. Sorry :X

    Still need help though... :(
     
    Last edited: Feb 3, 2010
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