= Solution
For a repulsive <inverse-square force>, $V(r)=+\kappa/r$. The <effective potential> is positive and decreases from infinity to zero, so a trajectory reaching a finite <radius> has $E>0$. For nonzero <angular momentum>, it is the accessible branch of a \b[<hyperbola>], with $e^2=1+2EJ^2/(m\kappa^2)>1$. There are no bound <ellipses> or finite-distance zero-energy <parabolas>. At zero <angular momentum>, the motion is straight inward followed by straight outward after reflection at a radial turning point.
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