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Planetary motion and a space station

  1. Jul 5, 2017 #1
    1. The problem statement, all variables and given/known data
    A space station is in orbit between the Earth and the moon. The force due to gravity on the space station from the moon is the same as the force due to gravity from the Earth. (FGmoon = FGearth). How far away from the Earth is the space station? How far from the moon is the space station?

    2. Relevant equations + attempt at a solution

    a8kkYXK.png

    I keep getting 0.213 for r(earth) and I have no idea how to solve for the variable, can someone please help me?
     
  2. jcsd
  3. Jul 6, 2017 #2

    haruspex

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    It (nearly) all made sense until the final step. You had 3.844.108m-rmoon=9.02 rmoon. How did you proceed from there?

    The other small mistake is that in your "given" you defined rmoon and rearth as the radii of those two bodies, but thereafter used them as the respective distances from their centres to the space station.
     
  4. Jul 6, 2017 #3
    I figured it out now I think since like you said, it didn't make sense when I tried to use them as their distance, so what I ended up doing was this:

    VOFJuHd.png
    sorry for the crappy formatting but does this seem to be correct?
     
  5. Jul 6, 2017 #4

    haruspex

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    Yes.
     
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