FAILURE MAP
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FA-69781 / Orbital propagation / Open access

Radial in-track cross-track projection: Cross-track axis is not normalized · case 01

Cross-track offsets are scaled by the angular momentum magnitude.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

C is the raw angular momentum vector.

THE FAILURE

C is the raw angular momentum vector.

Unsuccessful approach: Normalizing v x r flips the cross-track sign.

Case contract

Input [rc, vc, rd]: chief position and velocity and deputy position. R=rc/|rc|, C=(rc x vc)/|rc x vc|, I=C x R. Return the deputy offset rd-rc projected onto [R, I, C], rounded to 6.

Why this case matters

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

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    rc,vc,rd=x
    def dot(a,b): return sum(p*q for p,q in zip(a,b))
    def cross(a,b): return [a[1]*b[2]-a[2]*b[1],a[2]*b[0]-a[0]*b[2],a[0]*b[1]-a[1]*b[0]]
    def unit(a):
        m=math.sqrt(dot(a,a))
        return [q/m for q in a]
    R=unit(rc)
    C=cross(rc,vc)
    I=cross(C,R)
    d=[p-q for p,q in zip(rd,rc)]
    return [round(dot(d,R),6),round(dot(d,I),6),round(dot(d,C),6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]], [1.0, 2.0, 3.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]]', [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]], [0.0, 5.0, 0.0]), ('radial in-track cross-track projection [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]]', [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]], [10.0, -10.46518, -2.545584]), ('radial in-track cross-track projection [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]]', [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]], [0.980196, -3.240487, 2.353394]), ('radial in-track cross-track projection [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]]', [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]], [0.0, 1.414214, 0.0]), ('radial in-track cross-track projection [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]]', [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]], [0.1, 0.2, -0.3]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]], [0.0, 0.0, 0.0])], [('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]]', [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]], [0.0, 5.0, 0.0]), ('radial in-track cross-track projection [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]]', [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]], [0.980196, -3.240487, 2.353394]), ('radial in-track cross-track projection [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]]', [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]], [0.0, 1.414214, 0.0]), ('radial in-track cross-track projection [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]]', [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]], [0.1, 0.2, -0.3]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]], [0.0, 0.0, 0.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]], [1.0, 2.0, 3.0]), ('radial in-track cross-track projection [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]]', [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]], [10.0, -10.46518, -2.545584])], [('radial in-track cross-track projection [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]]', [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]], [10.0, -10.46518, -2.545584]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]], [0.0, 0.0, 0.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]], [1.0, 2.0, 3.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]]', [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]], [0.0, 5.0, 0.0]), ('radial in-track cross-track projection [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]]', [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]], [0.980196, -3.240487, 2.353394]), ('radial in-track cross-track projection [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]]', [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]], [0.0, 1.414214, 0.0]), ('radial in-track cross-track projection [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]]', [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]], [0.1, 0.2, -0.3])], [('radial in-track cross-track projection [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]]', [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]], [0.980196, -3.240487, 2.353394]), ('radial in-track cross-track projection [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]]', [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]], [10.0, -10.46518, -2.545584]), ('radial in-track cross-track projection [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]]', [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]], [0.0, 1.414214, 0.0]), ('radial in-track cross-track projection [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]]', [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]], [0.1, 0.2, -0.3]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]], [0.0, 0.0, 0.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]], [1.0, 2.0, 3.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]]', [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]], [0.0, 5.0, 0.0])], [('radial in-track cross-track projection [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]]', [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]], [0.0, 1.414214, 0.0]), ('radial in-track cross-track projection [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]]', [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]], [0.1, 0.2, -0.3]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]], [0.0, 0.0, 0.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]], [1.0, 2.0, 3.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]]', [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]], [0.0, 5.0, 0.0]), ('radial in-track cross-track projection [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]]', [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]], [10.0, -10.46518, -2.545584]), ('radial in-track cross-track projection [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]]', [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]], [0.980196, -3.240487, 2.353394])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]][1.0, 105000.0, 157500.0][1.0, 2.0, 3.0]Failed
radial in-track cross-track projection [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]][0.0, 262500.0, 0.0][0.0, 5.0, 0.0]Failed
radial in-track cross-track projection [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]][10.0, -518000.0, -126000.0][10.0, -10.46518, -2.545584]Failed
radial in-track cross-track projection [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]][0.980196, -165233.049915, 120000.0][0.980196, -3.240487, 2.353394]Failed
radial in-track cross-track projection [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]][0.0, 71846.8, 0.0][0.0, 1.414214, 0.0]Failed
radial in-track cross-track projection [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]][0.1, 0.2, -0.3][0.1, 0.2, -0.3]Passed
radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]][0.0, 0.0, 0.0][0.0, 0.0, 0.0]Passed

SHA-256 / baab0f5fbcfe22d02fb7d55d39b5abcdeadbe821ad652722b1f025f6e108e066

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    rc,vc,rd=x
    def dot(a,b): return sum(p*q for p,q in zip(a,b))
    def cross(a,b): return [a[1]*b[2]-a[2]*b[1],a[2]*b[0]-a[0]*b[2],a[0]*b[1]-a[1]*b[0]]
    def unit(a):
        m=math.sqrt(dot(a,a))
        return [q/m for q in a]
    R=unit(rc)
    C=unit(cross(vc,rc))
    I=cross(C,R)
    d=[p-q for p,q in zip(rd,rc)]
    return [round(dot(d,R),6),round(dot(d,I),6),round(dot(d,C),6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]], [1.0, 2.0, 3.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]]', [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]], [0.0, 5.0, 0.0]), ('radial in-track cross-track projection [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]]', [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]], [10.0, -10.46518, -2.545584]), ('radial in-track cross-track projection [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]]', [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]], [0.980196, -3.240487, 2.353394]), ('radial in-track cross-track projection [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]]', [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]], [0.0, 1.414214, 0.0]), ('radial in-track cross-track projection [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]]', [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]], [0.1, 0.2, -0.3]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]], [0.0, 0.0, 0.0])], [('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]]', [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]], [0.0, 5.0, 0.0]), ('radial in-track cross-track projection [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]]', [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]], [0.980196, -3.240487, 2.353394]), ('radial in-track cross-track projection [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]]', [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]], [0.0, 1.414214, 0.0]), ('radial in-track cross-track projection [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]]', [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]], [0.1, 0.2, -0.3]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]], [0.0, 0.0, 0.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]], [1.0, 2.0, 3.0]), ('radial in-track cross-track projection [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]]', [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]], [10.0, -10.46518, -2.545584])], [('radial in-track cross-track projection [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]]', [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]], [10.0, -10.46518, -2.545584]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]], [0.0, 0.0, 0.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]], [1.0, 2.0, 3.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]]', [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]], [0.0, 5.0, 0.0]), ('radial in-track cross-track projection [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]]', [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]], [0.980196, -3.240487, 2.353394]), ('radial in-track cross-track projection [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]]', [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]], [0.0, 1.414214, 0.0]), ('radial in-track cross-track projection [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]]', [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]], [0.1, 0.2, -0.3])], [('radial in-track cross-track projection [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]]', [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]], [0.980196, -3.240487, 2.353394]), ('radial in-track cross-track projection [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]]', [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]], [10.0, -10.46518, -2.545584]), ('radial in-track cross-track projection [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]]', [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]], [0.0, 1.414214, 0.0]), ('radial in-track cross-track projection [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]]', [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]], [0.1, 0.2, -0.3]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]], [0.0, 0.0, 0.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]], [1.0, 2.0, 3.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]]', [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]], [0.0, 5.0, 0.0])], [('radial in-track cross-track projection [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]]', [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]], [0.0, 1.414214, 0.0]), ('radial in-track cross-track projection [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]]', [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]], [0.1, 0.2, -0.3]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]], [0.0, 0.0, 0.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]]', [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]], [1.0, 2.0, 3.0]), ('radial in-track cross-track projection [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]]', [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]], [0.0, 5.0, 0.0]), ('radial in-track cross-track projection [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]]', [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]], [10.0, -10.46518, -2.545584]), ('radial in-track cross-track projection [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]]', [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]], [0.980196, -3.240487, 2.353394])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7001.0, 2.0, 3.0]][1.0, -2.0, -3.0][1.0, 2.0, 3.0]Failed
radial in-track cross-track projection [[7000.0, 0.0, 0.0], [1.0, 7.5, 0.0], [7000.0, 5.0, 0.0]][0.0, -5.0, 0.0][0.0, 5.0, 0.0]Failed
radial in-track cross-track projection [[0.0, 7000.0, 0.0], [-7.0, 0.0, 1.0], [10.0, 7010.0, -4.0]][10.0, 10.46518, 2.545584][10.0, -10.46518, -2.545584]Failed
radial in-track cross-track projection [[5000.0, 5000.0, 1000.0], [-5.0, 5.0, 1.0], [5003.0, 4998.0, 1002.0]][0.980196, 3.240487, -2.353394][0.980196, -3.240487, 2.353394]Failed
radial in-track cross-track projection [[6778.0, 0.0, 0.0], [0.0, 5.3, 5.3], [6778.0, 1.0, 1.0]][0.0, -1.414214, 0.0][0.0, 1.414214, 0.0]Failed
radial in-track cross-track projection [[1.0, 0.0, 0.0], [0.5, 1.0, 0.0], [1.1, 0.2, -0.3]][0.1, -0.2, 0.3][0.1, 0.2, -0.3]Failed
radial in-track cross-track projection [[7000.0, 0.0, 0.0], [0.0, 7.5, 0.0], [7000.0, 0.0, 0.0]][0.0, 0.0, 0.0][0.0, 0.0, 0.0]Passed

SHA-256 / fe0c058570d27f86e0362500a1c1d98a2ffce17a193c523c7415c86043a4cac3

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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Verification & scope

A deterministic toy two-body model with stipulated constants and conventions; not flight dynamics software or a validated SGP4 implementation. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:48:14.636702+00:00.

Case digest / 13d57cf71a957c4e979f060ba698ec6161770034d93bb0f8696dabd58f01eda8