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Approximate value of g

  1. May 30, 2007 #1
    1. The problem statement, all variables and given/known data
    [​IMG]
    2. Relevant equations
    So I know that there's an inverse relationship between the value of g and r; the farther I get away from earth, the weaker the gravitational force -> weaker acceleration....

    BUT I'm not sure how the (1-x)^-2 thing is related, need help with that. Also, how do I set up for Newton's universal law of gravitation?


    3. The attempt at a solution
    Uh... In process. :eek:)

    Thanks in advance!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 31, 2007 #2

    andrevdh

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    Homework Helper

    From Newton's universal gravitational law we have:

    [tex]W = mg = GMm\ \frac{1}{r^2}[/tex]

    following

    [tex]g = GM\ \frac{1}{r^2}[/tex]

    now use the hint ...
     
  4. Jun 7, 2007 #3
    I still don't really understand... :grumpy:
     
  5. Jun 7, 2007 #4
    in newtons equation, put distance=(re+delta r)

    then write it as d= re(1+ (delta r/re))

    d has a power of -2

    and at 100 km. "delta r/re" is between -1 and 1 since the radius of the earth is greater than 100 km

    does this help or do you need more?
     
  6. Jun 7, 2007 #5
    I think I almost have it. The only thing that I'm still wondering is about the relation part, what does the minus sign mean?
     
  7. Jun 7, 2007 #6
    because you are given an equation that is stating the change in g (delta g), that minus indicates a decrease.
    think about what happens to g as the distance from the center of the earth increases by considering newton's equation
     
  8. Jun 8, 2007 #7

    andrevdh

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    Homework Helper

    the minus sign means that for a positive [tex]\Delta r[/tex] (going further up) the change in the gravitational acceleration decreases (is negative). So that the new gravitational acceleration is given by

    [tex]g_{new} = g_{old} + \Delta g[/tex]
     
  9. Jun 13, 2007 #8
    Ok, sorry to bring this up again.

    Talking to some of my classmates, some of them think that this is supposed to be a proof using Taylor series stuff, and that at the end that's where the -2 comes from. Any thoughts on that?
     
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