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MTW Gravitation: Exersise 25.16 Periastron Shift

  1. Apr 22, 2012 #1
    Hello, I am trying to work out this exercise for my personal research connected with my bachelor thesis. The task is to compare equations (25.42) and (25.47) and express $u_0$ in terms of \tilde{L}. I have so far put the two equations together getting


    After this I tried putting some terms together but I think I am missing another equation since there are in fact two unknowns: $u_0$ and $\tilde{E}_0$ or is there some trick I am missing?

    For those without access to MTW, here are the equations: \\


    and (25.47)


    Thank you.
  2. jcsd
  3. Apr 22, 2012 #2


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    Each equation expresses (du/dφ)2 in terms of a cubic in u. Expand out the cubics and equate the coefficients of each power of u.
  4. Apr 22, 2012 #3
    Thank you for the advice. I ended up with:



    The second one is a quadratic equation, so I can write the solution

    {u_0}_{1,2}=\frac{1\pm\sqrt{1-\frac{12}{\tilde{L}^2}}}{6} .

    But this would give a condition for \tilde{L}, which I find suspicious. Also which of the two roots is correct? It stays possitive in both cases and I can't come with any other clue to help me choose. Any additional hints, please?
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