Past exam of the physics 1 paper of the University of Oxford / 2017 resit / 2 / b / Solution

A radial outward kick has no angular impulse about the centre. ThereforeThe 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.