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Mechanics - Orbits under Central Force

  1. Dec 29, 2008 #1
    1. The problem statement, all variables and given/known data
    A particle moving in a plane is attracted towards a point (fixed) by a force zr^-5. The particle is projected from an apse at distance a with speed SQRT(z/(2a^4)).

    Show that the orbit is r=acos(theta)

    Using the Orbit Eq: d^2 u/dC^2 + u = za^-5/(hu)^2

    h = angular momentum, or r(speed) in this case, u = 1/r



    I get down to (du/dC)^2 + u^2 = -4/[(a^3)u] + A

    where C = theta, A = integration constant.

    Am I correct so far?
     
  2. jcsd
  3. Jan 2, 2009 #2

    Dick

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    za^-5/(hu)^2 should be zu^5/(hu)^2 shouldn't it? Rather than solving the equation, why don't you just substitute u=1/(a*cos(theta)) and see if the solution works?
     
  4. Jan 4, 2009 #3
    Why is that?
     
  5. Jan 4, 2009 #4

    Dick

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    Because if the radial force per unit mass is z/r^5 and r=1/u that turns into zu^5.
     
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