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Central force motion and particles

  1. Oct 5, 2011 #1
    1. The problem statement, all variables and given/known data

    The problem involves two particles of masses m and M; initially, m is at [tex]r=∞[/tex] and has a velocity [tex]v=v_o[/tex]. The path of m is deflected, ie pulled towards M due to its gravitational pull.

    Question: Find the mass M (in terms of the quantities given) at a distance d where the particles are now acting on each other.

    2. Relevant equations

    Initial energy of m


    E_i = \frac{1}{2}mv_o^2

    [tex]E_f = \frac{1}{2}μv_o^2 + U(r) = \frac{1}{2}μv_o^2 + (\frac{-GMm}{d})

    [tex]\frac{1}{2}μv_o^2 = \frac{l^2}{2μd^2}


    3. The attempt at a solution

    I've tried using combinations of the above, but in the end, I am not confident that I am correct in my assumptions of E_f, otherwise this would be an easy algebraic game. I also considered that E_f should include the effective potential, but at distance d, the two particles haven't yet crossed, though they are at a distance such that the vector between them is orthogonal to the path of m at that point. Any guidance is appreciated!
  2. jcsd
  3. Oct 6, 2011 #2
    Am I missing something obvious?
  4. Oct 6, 2011 #3


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    Staff: Mentor

    Is this a question that you made up?

    What is mu? What is l (lower-case L)?
  5. Oct 6, 2011 #4
    No, it's on an assignment... mu=Mm/(M+m) and l is the magnitude of the angular momentum. I can use l since the direction of L is constant as it's only in one plane - yes?
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