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Find force lawa from orbit equation

  1. Oct 13, 2009 #1
    1. The problem statement, all variables and given/known data
    The orbit of a particle moving on a central field is a circle passing through the origin, namely, [tex]r = r_0cos(\theta)[/tex]. Show that the force law is inverse fifth power.

    2. Relevant equations

    [tex]\frac{d^2u}{d\theta^2} + u = \frac{-mF(u^{-1})}{L^2u^2}[/tex]

    3. The attempt at a solution

    I keep getting that it is inverse third power....

    [tex]u = \frac{1}{r_0cos(\theta)}[/tex]
    [tex]\frac{d^2u}{d\theta^2} = u + \frac{tan^2(\theta)}{u}[/tex]


    [tex]F(u^{-1}) = \frac{-1}{m}\left(L^2u^2\left(u + \frac{tan^2(\theta)}{u}\right) + L^2u^2\right)[/tex]


    so [tex]f(r) = \frac{-2L^2}{m}\left(\frac{1}{r^3}+\frac{tan(\theta)}{r}\right)[/tex]

    Where am I going wrong?
    Last edited: Oct 13, 2009
  2. jcsd
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