While working a problem in French's book today, I stumbled across a
simple result that I wasn't familiar with: The radius of curvature at
perihelion (or aphelion) is equal to the semi-latus rectum. (Recall
that the semi-latus rectum is the distance from a focus to the orbit
along a line parallel to the minor axis.)
It's pretty easy to verify this result and it might amuse you the
next time you're waiting in line.
If you're curious about the problem I was looking at (derive Kepler's
third law and the energy equation using algebra alone for an
elliptical orbit), see: