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Kepler's 2nd law and potential energy relation

  1. Nov 23, 2007 #1
    1. The problem statement, all variables and given/known data

    A particle moves under the influence of a central potential V(r). Show that Kepler's second law, that the radius vector from the force centre to the particle sweeps out area at a constant rate, is true whatever the form of V, as long as it is central. Derive the law in the form
    .
    dA/dT = 0.5 r^2 (theta)

    Where (r,theta) are polar coordinates in the orbital plane with origin at the force centre. There is meant to be a dot above theta!!
    2. Relevant equations



    3. The attempt at a solution

    All i have at the moment (after trawling the net, and searching in books) is a statement and a derivation for the above equation given. But i don't know how to link it to the potential energy.

    I get the equation given as equal to L/2m and the fact that it is a constant. The statement i have is:

    It is true no matter what the forms of the force and potential energy functions are because it is entirely a result of the conservation of angular momentum.

    Any thoughts on how to include the potential energy in a more quantitative way??
     
    Last edited: Nov 23, 2007
  2. jcsd
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