FA-69385 / Orbital propagation / Member archive

True anomaly from eccentric anomaly: True anomaly is left in (-pi, pi] · case 05

Descending-branch anomalies are reported as negative angles.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input [E, e] (radians, 0<=e<1, E any real). Return [nu, r/a] with nu = 2*atan2(sqrt(1+e) sin(E/2), sqrt(1-e) cos(E/2)) reduced to [0,2pi) and r/a = 1-e cos E, both rounded to 9 decimals.

Why this case matters

Orbit determination and mission planning chain many small conversions; one wrong branch or unit silently moves a spacecraft by kilometres.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
true anomaly from eccentric anomaly [7.0, 0.2]	`[-5.422936104, 0.849219549]`	`[0.860249203, 0.849219549]`	Failed

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