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Gravitational Force Problem - Help

  1. Apr 16, 2015 #1
    1. The problem statement, all variables and given/known data
    As a moon follows it's orbit around a planet, the maximum gravitational force exerted on the moon by the planet exceeds the minimum gravitational force by 11%. Find the ratio rmax / rmin, where rmax is the moon's maximum distance from the center of the planet and rmin is the minimum distance.


    2. Relevant equations
    Newton's law of Gravitation F = G m1m2 / r2

    3. The attempt at a solution
    I found the ratio to be, rmax / rmin = 0.949 to 3 significant digits.
    My text book says the ratio is 1.05. I think the text if wrong. Can someone try this problem and let me know what you get.
    Thanks,
    R.
     
  2. jcsd
  3. Apr 16, 2015 #2

    SammyS

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    If rmax / rmin < 1, then rmax < rmin .

    Does that make any sense?

    Where is the gravitational force greater, at rmin or at rmax?
     
  4. Apr 16, 2015 #3

    berkeman

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    Staff: Mentor

    At first I thought you were right, but there is an ambiguity in the notation. Is rmax the radius where the force is max, or is it the maximum radius? You get the two different answers depending on how you define the subscripts of the radius variable...
     
  5. Apr 16, 2015 #4

    kreil

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    Hint

    [tex]F_{max} = \frac{Gm_1m_2}{r_{min}^2}[/tex]
     
  6. Apr 17, 2015 #5
    The gravitational force is greatest at rmin.
    The confusion was over whether rmin meant the point where the moon is closest to the planet, or if it meant the variable r of the Gravitational formula for Fmin. From the responses I got, I was not the only one confused by the wording of the problem.
     
  7. Apr 17, 2015 #6
    I'm glad I was not the only one confused by the wording of the problem. The hint given by kreil clarified it, and the problem works out fine then. Thanks for your input.
     
  8. Apr 17, 2015 #7
    That makes it perfectly clear what I was missing when reading the problem. Now the problem works as expected.

    Thanks for opening my eyes..

    Regards,
    Rich
     
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