= Solution
A radial outward kick has no <angular impulse> about the centre. Therefore
$$
\boxed{\Delta L=0,\qquad \Delta E=\frac12m\delta^2>0.}
$$
The initial position is on the outward-moving portion of a bound <elliptic Kepler orbit>, between <pericentre> and <apocentre>, rather than at either turning point. The <eccentricity> is $e=\delta/v_c$ and the <semilatus rectum> remains $r_0$. The <orbital energy> change is second order: it vanishes to first order in the impulse but is positive for any nonzero kick.
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