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Orbit equations

  1. Oct 30, 2006 #1
    So i solved the orbit equation:

    [tex]\frac{d^2}{d {\theta} ^2} \frac{1}{r} =0[/tex]

    the solution is:

    [tex]\frac{1}{r} = A \theta +B [/tex]

    I am supposed to concude that this particle will sprial towards the center but I dont see that through this equation. could someone explain this to me? thanks
  2. jcsd
  3. Oct 30, 2006 #2


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    Staff: Mentor

  4. Oct 30, 2006 #3
    the original equation is:

    [tex]\frac{d^2}{d {\theta} ^2} \frac{1}{r} + (1- \frac{ \mu k}{l^2}) \frac{1}{r} =0[/tex]

    describing the motion when the effective porential = 0, i get

    [tex]\frac{d^2}{d {\theta} ^2} \frac{1}{r} =0[/tex]

    so i was wondering how [tex]\frac{1}{r} = A \theta +B [/tex] tells me that I am sprial towards the center?
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