> I got off the rails a bit staring at the diagram. A circle is of course a very specific case of an ellipse — seems off-topic to even include that specificity

> I got off the rails a bit staring at the diagram. A circle is of course a very specific case of an ellipse — seems off-topic to even include that specificity except for the fact that everyone does include it in a conic section diagram. Circles are mathematically special and horrible and can cause real singularities in the mathematics. Normally you measure Keplerian elements relative to the Periapsis which is the closest approach of the orbit. A perfectly circular orbit has no closest approach, it is all closest. Circular, equatorial, polar and parabolic orbits often need to be treated specially. For any algorithm those are often corner cases, they definitely need testing. I've found division by zero errors in a professionally written implementation of Shepperd's method of orbit propagation in a circular retrograde orbit. That same method of orbit propagation has fairly horrible problems with near-parabolic orbits, intrinsically.