= Solution
For an attractive <inverse-square force>, write $V(r)=-\kappa/r$ with $\kappa>0$, and take nonzero conserved <angular momentum> $J$. The <conic section> orbit has
$$
r=\frac{J^2/(m\kappa)}{1+e\cos\psi},\qquad
e^2=1+\frac{2EJ^2}{m\kappa^2}.
$$
The physically allowed cases are \b[<ellipse> for $-m\kappa^2/(2J^2)\leq E<0$, <parabola> for $E=0$, and <hyperbola> for $E>0$]. The minimum allowed <energy> gives the circular special case $e=0$. Here $E$ is measured relative to infinity. Zero <angular momentum> instead gives radial collision or escape trajectories, interpreted as degenerate limits rather than regular closed <ellipses>.
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