Q: How does KSP calculate true anomaly?

[monstah]

True anomaly (ν) is the angle centered on primary (orbited body), from periapsis to position orbiting body (satellite). It is easily calculated from Eccentric anomaly (E), which in turn is calculated from Mean anomaly (M), which is linear on time.

The thing is, the equation that relates M and E (M = E - e*sin(E), where e is eccentricity) can't be solved for E. It is usually either approximated by a sine series or calculated by iteration, say, with Newton's method.

The sine series is pretty inaccurate when e is not "very small", and I'd say in KSP e is almost never "very small". Newton's method is safer, but I'm not sure calculating something by iteration, for every vessel/celestial body, for every frame, is the best way.

Does anyone know it KSP takes a third way out that I don't know of, or if it brute forces Newton?

[MrHappyFace]

As far as I know, they bypass the problem entirely by calculating the true anomaly from state vectors