Sadly, The Ancient Greek's response does not answer my question, which is about the fact that the satellite is movement is in all three (geometric) axes, not just "vertically".
I agree with the point that if vertical movement is defined as changes in altitude, then at apogee the change is zero along that axis. But this is manifestly untrue for the other two axes - at apogee they are unlikely to be zero - my question is, does the motion in those axes matter at all, and if so, does it affect the assumption in Robin Clark's analysis.