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

The inward radial kick also leaves angular momentum unchanged and increases orbital energy by $m{\delta }^2/2$. Its eccentricity and semi-major axis equal those in case $b$, but the orientation of its eccentricity vector is reflected about the initial radius. The satellite initially moves inward on its ellipse, toward pericentre. Neither radial kick decreases the orbital energy.