FA-69367 / Orbital propagation / Member archive

True anomaly from eccentric anomaly: Cosine formula loses the descending half of the orbit · case 02

After apoapsis the true anomaly folds back instead of continuing past pi.

Member previewVariant 2 · 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 [5.9, 0.7]	`[0.865156876, 0.350765098]`	`[5.418028431, 0.350765098]`	Failed

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