cardamom
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Homework Statement
The problem involves two particles of masses m and M; initially, m is at r=∞ and has a velocity v=v_o. 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.
Homework Equations
Initial energy of m
<br /> <br /> E_i = \frac{1}{2}mv_o^2<br />
E_f = \frac{1}{2}μv_o^2 + U(r) = \frac{1}{2}μv_o^2 + (\frac{-GMm}{d})<br />
\frac{1}{2}μv_o^2 = \frac{l^2}{2μd^2}<br /> <br /> <br />
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!