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Central force problem

  1. Apr 30, 2007 #1
    1. The problem statement, all variables and given/known data

    A particle moves in a circular orbit under the action of a force
    f(r)=-(k/r^2).If k is suddenly reduced to half its value, what would be the nature of the orbit?

    2. Relevant equations

    e=sqrt[1+(2*L^2*E)/(mk^2)]

    3. The attempt at a solution

    My attempt:
    Clearly,the particle moves under attractive central force.Now,for the circular orbit,eccentricity e=0 and as the motion is bound,the energy is negative.
    If k is reduced to k/2, eccentricity changes to
    e=1+(8*L^2*E)/(mk^2)=6*L^2*E/(mk^2)

    Since e becomes negative as E is negative,no motion is possible.

    Am I correct?
     
  2. jcsd
  3. Apr 30, 2007 #2

    berkeman

    User Avatar

    Staff: Mentor

    I didn't check your math, but your solution for e being negative sounds reasonable. But that doesn't mean "no motion is possible". It means that something happens to the formerly circular motion of the particle. Think about it in a real-life physical sense. The particle is moving around in a circle, the central force is suddenly cut in half, describe how the particle moves next....
     
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