As you may know, as eccentricity gets smaller, the location of apoapsis/periapsis becomes less well-defined. Rather equivalently, I've noticed that if eccentricity is < 4e-7 when converting from Keplerian elements to Cartesian and back again, significant errors start to creep in.
I'd like to know how small of an eccentricity my code should realistically be expected to handle. I know these issues are handled well by equinoctial elements, but would rather avoid that complication if possible.
Wikipedia says, "Neptune's largest moon Triton has an eccentricity of 1.6 × 10−5, the smallest eccentricity of any known body in the Solar System."
That's very fine and interesting, but what about artificial satellites? What is the smallest eccentricity achieved by one of those?