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Modified Newtonian Dynamics

  1. Nov 5, 2007 #1
    1. The problem statement, all variables and given/known data

    For very low rates of acceleration, Newton's 2nd law has to be modified where F<vector>=m*f(a/a0)*a<vector>. For "small" values of a<vector>, f(a/a0) = a/a0.
    Determine the component equations of motion for the case of f(a/a0) = a/a0 in polar coordinates (don't try to solve the radial equation!). Show that the angular momentum is conserved.

    2. Relevant equations

    F<vector> = m*f(a/a0)*r<double dot>

    3. The attempt at a solution

    Since we are dealing with orbits, I am assuming the the two forces are the gravitational and centripetal forces (or are they the same thing). I also can determine r<double dot> in polar coordinates.
    Last edited: Nov 5, 2007
  2. jcsd
  3. Nov 5, 2007 #2


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    Angular momentum is m*r(t)xv(t). (x is cross product). What's the derivative of angular momentum? What properties of the force and the cross product can help you prove this derivative is zero?
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