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Problem involving Newton's Law of Gravitation

  1. Dec 27, 2007 #1
    1. A planet has a mass 1/2 that of Earth and a radius 2 times that of Earth. What is the acceleration due to gravity on the surface of the planet in terms of g?



    2.
    a)F=G*m1*m2/r[tex]^{2}[/tex]
    b)F=mg



    3. I figured that I would let the two equations equal to each other so...

    G*m1*m2/r[tex]^{2}[/tex]=mg
    It simplifies to be g=G*m/r[tex]^{2}[/tex]
    However, I don't know where to go from there to get the acceleration in terms of g.

    Any suggestions would be greatly appreciated. Thanks
     
  2. jcsd
  3. Dec 27, 2007 #2

    Doc Al

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    Staff: Mentor

    You're on the right track. Maybe rewriting it this way will give you a hint:
    [tex]g_{earth} = G M_{earth}/R_{earth}^2[/tex]

    (Express M and R for the planet in terms of M and R for the earth.)
     
  4. Dec 27, 2007 #3
    So then you would get this correct:

    [tex]g_{earth} = G (1/2)M_{earth}/(2*R_{earth})^2[/tex]

    Which you can then simplify to be:

    [tex]g_{earth} = G M_{earth}/8R_{earth}[/tex]

    However, I don't know where to go from there to find the acceleration:confused:
     
  5. Dec 27, 2007 #4

    Doc Al

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    Staff: Mentor

    Almost. You'd get:

    [tex]g_{planet} = G M_{planet}/R_{planet}^2[/tex]

    [tex]g_{planet} = G (1/2)M_{earth}/(2*R_{earth})^2[/tex]

    Which simplifies to:

    [tex]g_{planet} = (1/8) G M_{earth}/R_{earth}^2[/tex]

    I'll leave it to you to interpret the right hand side in terms of g for earth.
     
  6. Dec 27, 2007 #5
    Should I plug in the values for M_earth, R_earth, and G to find out what g_planet equals?

    And then I do g_planet=(g/x) to solve for x to find out in terms of what value for g is right? Doing this method... I get accelerated is g/8. However, is the proper way to solve this problem or am I doing more work than required?
     
  7. Dec 27, 2007 #6

    Doc Al

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    Staff: Mentor

    That's definitely the hard way. We already determined that the acceleration due to gravity on the planet equals:

    [tex]g_{planet} = (1/8) G M_{earth}/R_{earth}^2[/tex]

    But you should recognize the equation we stated with:

    [tex]g_{earth} = G M_{earth}/R_{earth}^2[/tex]

    Substituting this last equation into the first gives:

    [tex]g_{planet} = (1/8) g_{earth} = g/8[/tex]

    That's all you need to do--no calculations needed.
     
  8. Dec 27, 2007 #7
    Thanks for the help, Doc Al!
     
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