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Homework Help: Awkward integration

  1. Jul 1, 2010 #1
    Hi,
    I'm reading up on Kepler's problem at the moment, and there's a step in the book that I don't understand.

    Starting off with the equation of the path [tex]\phi=\int\frac{M dr/r^2}{\sqrt{2m[E-U(r)]-M^2/r^2}}+\mbox{constant}[/tex]

    The step involves subbing in [tex]U=-\alpha/r[/tex], 'and effecting elementary integration' to get
    [tex]\phi=\cos^{-1}\frac{(M/r)-(m\alpha/M)}{\sqrt{(2mE+\frac{m^2\alpha^2}{M^2}})}+\mbox{constant}[/tex]

    But it doesn't look very elementary to me:confused:

    Does anyone have any idea?

    Thanks.
     
  2. jcsd
  3. Jul 1, 2010 #2

    vela

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    Try the substitution w=1/r and then complete the square in the radical.
     
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