FA-69368 / Orbital propagation / Member archive

True anomaly from eccentric anomaly: Cosine formula loses the descending half of the orbit · case 03

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

Member previewVariant 3 · 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 [-1.0, 0.4]	`[1.390842009, 0.783879078]`	`[4.892343298, 0.783879078]`	Failed

MEMBER ARCHIVE

The complete case is available to members.

This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

Member access is invitation-based. Sign in with your invited account to inspect the sources.