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Universal Gravitation Question!

  1. Jul 13, 2010 #1
    1. The problem statement, all variables and given/known data
    At a certain point between Earth and the Moon, the net gravitational force exerted on an object by the Earth and the Moon is ZERO. The mass of the Moon is 1.2% the Mass of the Earth. The centre to centre distance between the Moon and the Earth is 3.84*10^5 km.

    i) WHERE IS THIS POINT LOCATED?
    ii) What is the meaning of the quadratic root whose value exceeds the Earth-Moon distance?

    2. Relevant equations
    Fg=Gm1m2/R^2

    3. The attempt at a solution
    Fnet=0
    Fnet=Fmoon-Fearth
    Fmoon=Fearth
    Rmoon=x
    Rearth=3.84*10^8m-x
    Mmoon=1.2
    Mearth=100

    Uh....what's next? And am I right so far?
     
  2. jcsd
  3. Jul 13, 2010 #2

    Doc Al

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    Staff: Mentor

    So far, so good. Now use the Gravity equation to get expressions for Fmoon and Fearth. Hint: Let the mass of the object be 'm'.
     
  4. Jul 13, 2010 #3
    Do I need to put a value in for 'm' or can I just get rid of it since its on both sides of the equation.
     
  5. Jul 13, 2010 #4

    Doc Al

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    What do you think? :wink:
     
  6. Jul 13, 2010 #5
    100/(3.84*10^8m-x)^2 = 1.2/x^2

    Is that right? Do I isolate for x?
     
  7. Jul 13, 2010 #6

    Doc Al

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    Looks good to me. You'll have to solve for x. Rearrange terms to put the quadratic into standard form.
     
  8. Jul 13, 2010 #7
    I'm not getting the right answer which is supposed to be 3.5*10^5m from Earth's centre. I will try again.
     
  9. Jul 13, 2010 #8

    Doc Al

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    Realize that you've defined your variable X to be the distance from the Moon's center. Once you have X, you can then figure out the distance from the Earth's center.
     
  10. Jul 28, 2010 #9
    Ok thanks, I think the textbook answer was just wrong. :)
     
  11. Jul 28, 2010 #10

    Doc Al

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    I suspect that the book's answer was in km, not m.
     
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