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Polar Equation using sketch

  1. Feb 21, 2004 #1
    A particle moves on a circular orbit in a central force field. The origin of the force lies on the circle.

    Find the polar equation of the orbit.


    I am confused as to how to set up this question.
     

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  3. Feb 21, 2004 #2

    Dr Transport

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    Start with the equation for the invers radius of the orbit with respect to angle

    [tex] {d^2u}\over {d/ \theta^2} + u = [/tex]
     
  4. Feb 21, 2004 #3

    Dr Transport

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    Can't work it right now, back later....... anyway it is r^-5.
     
  5. Feb 22, 2004 #4
    I need a few more steps to be explained. I am sure that if you could please explain them to me that I will get it.
     
  6. Feb 22, 2004 #5
    Also, I ahve never sen that queation before. IS it derived somewhere on the net?

    Are you saying that the polar equation is r^(-5)? I need some help here desparately.
     
    Last edited: Feb 22, 2004
  7. Feb 22, 2004 #6

    Dr Transport

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    My typing is bad, and it was late.

    Start with Goldstein 3-34a,

    [tex] \frac{d^2 u}{d\theta^2} + u = -\frac{m}{l^2u^2}f(1/u) [/tex]
     
  8. Feb 22, 2004 #7

    Dr Transport

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    My typing is bad, and it was late.

    Start with Goldstein 3-34a,

    [tex] \frac{d^2 u}{d\theta^2} + u = -\frac{m}{l^2u^2}f(1/u) [/tex]

    set [tex] 1/u = 2acos\theta [/tex] and crank away. The answer should pop out when you eliminate the [tex] \theta [/tex].

    For some reason, the \frac is not working........
     
  9. Feb 22, 2004 #8

    Dr Transport

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    I guess it did work in the final compile......
     
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