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Determine the mass of Jupiter using data about a moon

  1. Mar 25, 2015 #1
    1. The problem statement, all variables and given/known data
    Determine the mass of Jupiter using the data for the moon Io.
    Mass of Io: ##8.9*10^{22}##
    Period: ##1.77## Earth days
    Mean distance from Jupiter in km: ##422*10^3##

    2. Relevant equations
    Centripetal acceleration ##a = \frac{v^2}{R} ##
    Universal law: ##\frac{GMm}{R^2} ##

    3. The attempt at a solution
    ##\frac{m_Iv^2}{R} = \frac{m_IM_JG}{R^2} ##
    ## v^2 = \frac{M_JG}{R} ##
    ##M_J = \frac{v^2R}{G} ##
    ##\frac{(2\pi R)^2R}{G} = 1.419*10^{37} ## kg. My answer = wrong
    Just like in the post about binary star systems, I see no error in my calculations, yet I am ten magnitudes too great...
    Correct answer is ##1.9*10^{27}##
     
    Last edited: Mar 25, 2015
  2. jcsd
  3. Mar 25, 2015 #2

    gneill

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    Staff: Mentor

    ##2 \pi R## is not a velocity.
     
  4. Mar 25, 2015 #3
    Thanks Gniell. Once again I forgot to divide ## 2\pi R ## by T. I solved the problem again, corrected my mistake, and got the right answer.
     
  5. Mar 25, 2015 #4

    tms

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    Just a little ##\LaTeX## note: you can say ##8.9 \times 10^{22}## (8.9 \times 10^{22}) instead of using an asterisk.
     
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