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Homework Help: Motion in a Central Gravitational Force

  1. Feb 26, 2017 #1
    1. The problem statement, all variables and given/known data
    Discuss the motion of a particle in a central inverse-square-law force field for a superimposed force whose magnitude is inversely proportional to the cube of the distance from the particle to the force center, that is:
    F(r) = -k/r2 - λ/r3 and k,λ>0​
    Show that the motion is described by a precessing ellipse.

    2. Relevant equations
    The one given in the question

    3. The attempt at a solution
    I honestly don't know where to begin, we derived an equation in class that we could find the force law if a particular known orbit r=r(θ), and I was thinking of using it:
    (d2/dθ2)(1/r) + (1/r) = -μr2F(r)/l2
    but I don't know what to do with the left hand side, but again it's just a guess as to what to start with.
    Sorry for not using the math commands, they didn't want to work for some reason.
  2. jcsd
  3. Feb 26, 2017 #2

    Simon Bridge

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    Science Advisor
    Homework Helper

    You need to solve the differential equation.

    For equations, you can type out LaTeX markup directly.

    You may want to back up a bit and make sure you understand the motivation for deriving the equation you used in the first place... see if the same approach still applies here.
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