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What is the mass of saturn?

  1. Feb 18, 2012 #1
    titan, a moon of saturn, has a 16 day orbital period and an orbital radius of 1,222,000 km. what is the mass of saturn?

    my attempt:

    t = 2*pi*r^(3/2)/sqrt(g*m)
    t = 16 days = 1,382,400 s
    r = 1,222,000/2 km = 611,000,000 m

    1,382,400 = 2*pi*611,000,000^(3/2)/sqrt(6.67e-11*m) => m = 7.065e25 kg

    the answer should be 5.6e26 kg, what am i doing wrong?
     
  2. jcsd
  3. Feb 18, 2012 #2

    SammyS

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    Hello Fysicsx. Welcome to PF !

    Where does the following equation come from?

    t = 2*pi*r(3/2)/√(g*m)

    What is g in this equation?
     
  4. Feb 18, 2012 #3
    hi sammys,

    thanks for the warm welcome

    f_g = g*m_1*m_2/r^2 (law of gravitation)
    v = sqrt(g*m/r) (circular orbit)

    v = 2*pi*r/t
    t = 2*pi*r/v = 2*pi*r*sqrt(r/(g*m)) = 2*pi*r^(3/2)/sqrt(g*m) (circular orbit)

    g is the gravitational constant 6.67e-11 m^3*kg^-1*s^-2
     
  5. Feb 18, 2012 #4

    SammyS

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    You divided r by 2.

    Solve this for r, not v : v = sqrt(g*m/r)
     
  6. Feb 18, 2012 #5
    oops that was careless lol. thanks for your help, sammys.
     
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