FA-69615 / Orbital propagation / Member archive

Hyperbolic Kepler solver: Asymptote angle uses +1/e · case 05

The reported departure asymptote lies on the wrong side of the latus rectum.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input [M, e] with e>1 (else None). Solve e sinh H - H = M by Newton from H=asinh(M/e) (60 iterations max, stop when step<1e-13). Return [H, nu, nu_inf] rounded to 9 with nu=2 atan(sqrt((e+1)/(e-1)) tanh(H/2)) and asymptote nu_inf=acos(-1/e).

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
hyperbolic kepler solver [0.0, 3.0]	`[0.0, 0.0, 1.230959417]`	`[0.0, 0.0, 1.910633236]`	Failed

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