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Homework Help: Time to go around the Moon

  1. Feb 28, 2010 #1
    1. The problem statement, all variables and given/known data

    During an Apollo lunar landing mission, the command module continued to orbit the Moon at an altitude of about 100km. How long did it take to go around the Moon once?

    Rm= 1.74x10^6 m
    Mm= 7.35x10^22 kg
    G= 6.67x10^-11
    r= Rm + 100,000 m

    2. Relevant equations

    v= sqrt(Gm/r)

    V=2pi*r/t

    3. The attempt at a solution

    after using the first equation, i got v= 1,679 m/s

    i plugged this into the second equation to solve for T, and got
    T= 2.9x10^9 s

    This seems way too high to be the answer...
     
  2. jcsd
  3. Feb 28, 2010 #2
    It would appear you forgot to consider "r= Rm + 100,000 m"
     
  4. Feb 28, 2010 #3
    You're right I didn't, but this time got 1.89x10^10.

    Here is my work:
    v=sqrt(6.67x10^-11)(7.35x10^22)/[(1.74x10^6)+100,000]
    v= sqrt(2.66x10^6)
    v= 1,631 m/s

    1,631= 2(3.14)(1.74x10^6 + 100,000)/T
    1631= 1.16x10^7/T

    T=1.89x10^10 s
     
  5. Feb 28, 2010 #4
    Continuing your work:

    [tex]1631 = \frac{1.16 \times 10^7}{T}[/tex]

    [tex]T = \frac{1.16 \times 10^7}{1631} \neq 1.89 \times 10^{10} s[/tex]

    You have a simple arithmetic error in there somewhere.
     
  6. Feb 28, 2010 #5
    Okay I believe I figured it out, and got 7,112 s instead, which seems much more reasonable. Thank you!
     
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