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Can someone verify my answer?

  1. Sep 6, 2015 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations
    fg=Gm1m2/r^2

    3. The attempt at a solution

    Let FgE be the force of gravity of Earth, and FgM be force of gravity of the moon.

    We need a net gravitational force of 0 N. So:

    FgE-FgM=0
    FgE=FgM

    Can someone attempt to solve this and see if the answer matches the book answer which is 3.8 x 10^7.

    I have tried this with many different methods, and the closest I got was 4.2 x 10^7. So if someone gets the same answer as me or the book, can you please reply.
     

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  3. Sep 6, 2015 #2

    ehild

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    Show your work in detail, please. And what is 4.2 x 10^7???? mass? distance? force? In what unit?
     
  4. Sep 6, 2015 #3
    Distance/radius so its in m, and I got the answer eventually having to use the quadratic formula.
     
  5. Sep 6, 2015 #4
    What I did was:

    Let mE be mass of Earth
    Let mM be mass of the moon
    Let mR be mass of the rocket

    GmEmR/r^2=GmMmR/(3.8x10^8-r)^2

    (3.8x10^8-r)^2(GmEmR)=r^2(GmMmR)

    G and MR cancel

    (3.8x10^8-r)^2(mE)=r^2(mM)

    (5.926x10^24)r^2-4.56x10^34r+8.664x10^41=0

    I then used the quadratic formula to solve for r, getting 342017105.1 m. This is the radius from the Earth to the rocket to distance from the moon to the rocket would be:
    3.8x10^8m-342017105.1 m=3.8x10^7m.

    HOWEVER, i am wondering is there an easier approach to solving this?
     
  6. Sep 6, 2015 #5

    ehild

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    You can write the equation in the form
    (3.8x10^8-r)^2=r^2(mM/mE).
    Take the square root of both sides, you get a first order equation.
     
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