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Taylor series expansion for gravitational force

  1. Feb 7, 2012 #1
    1. The problem statement, all variables and given/known data
    The magnitude of the gravitational force exerted by the Earth on an object of mass m at the Earth's surface is
    Fg = G*M*m/ R^2
    where M and R are the mass and radius of the Earth.
    Let's say the object is instead a height y << R above the surface of the Earth. Using a Taylor series or binomial expansion, find a polynomial expression in y for the force of gravity acting on this object, correct to first order (i.e., in this case, the lowest "non-trivial" order of the Taylor series).


    2. Relevant equations
    taylor series equation


    3. The attempt at a solution
    I set up the equation as Fg=G*M*m/(R+y)^2 centered around y=0

    I'm just lost on how to set this up, what is the right equation and point to center around?
     
  2. jcsd
  3. Feb 7, 2012 #2
    (R+y)^-2 = R^-2(1 + y/R)^-2 Expand this about y = 0

    Using as input "R^-2(1 + y/R)^-2"

    In the following link, you may need a free plugin,

    http://www.wolframalpha.com/input/?i=R^-2%281+%2B+y%2FR%29^-2&cdf=1

    See series expansion in the above link.
     
  4. Feb 7, 2012 #3
    Thanks for the help
     
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