FAILURE MAP
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FA-69766 / Orbital propagation / Open access

Clohessy-Wiltshire relative motion: Radial offset drives along-track velocity with the wrong sign · case 01

A lower chaser appears to fall behind.

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

ROOT CAUSE

vy uses 6n(1-cos nt) x0.

VERIFIED REPAIR

Use 6n(cos nt - 1) x0.

Unsuccessful approach: Dropping n gives an along-track velocity in position units.

Case contract

Input [x0,y0,z0,vx0,vy0,vz0,n,t] with x radial, y along-track, z cross-track about a circular reference orbit of mean motion n. Return [x,y,z,vx,vy,vz] from the closed-form HCW solution, 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):
    x0,y0,z0,vx,vy,vz,n,t=x
    s=math.sin(n*t); c=math.cos(n*t)
    X=(4-3*c)*x0+s/n*vx+2/n*(1-c)*vy
    Y=6*(s-n*t)*x0+y0-2/n*(1-c)*vx+(4*s-3*n*t)/n*vy
    Z=c*z0+s/n*vz
    VX=3*n*s*x0+c*vx+2*s*vy
    VY=6*n*(1-c)*x0-2*s*vx+(4*c-3)*vy
    VZ=-n*s*z0+c*vz
    return [round(q,6) for q in (X,Y,Z,VX,VY,VZ)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0]', [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0], [0.0, 0.0, -0.181368, 0.0, -0.0, -0.000563]), ('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0]', [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0], [0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]), ('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0]', [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0])], [('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0]', [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0], [0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]), ('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0]', [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), ('clohessy-wiltshire relative motion [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0]', [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0], [-0.571404, 9.834915, -0.062542, 0.000589, 0.000851, -0.000249]), ('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0])], [('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]), ('clohessy-wiltshire relative motion [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0]', [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0], [-0.571404, 9.834915, -0.062542, 0.000589, 0.000851, -0.000249]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0]', [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), ('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0]', [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0], [0.0, 0.0, -0.181368, 0.0, -0.0, -0.000563]), ('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05])], [('clohessy-wiltshire relative motion [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0]', [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0], [-0.571404, 9.834915, -0.062542, 0.000589, 0.000851, -0.000249]), ('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0]', [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0], [0.0, 0.0, -0.181368, 0.0, -0.0, -0.000563]), ('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0]', [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0], [0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]), ('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0])], [('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0]', [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0], [0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]), ('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0]', [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), ('clohessy-wiltshire relative motion [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0]', [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0], [-0.571404, 9.834915, -0.062542, 0.000589, 0.000851, -0.000249]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0])]]
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
clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0][0.166351, -0.030458, 0.0, 0.000213, 0.00015, 0.0][0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]Failed
clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0][1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0][1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0]Passed
clohessy-wiltshire relative motion [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0][0.0, 0.0, -0.181368, 0.0, 0.0, -0.000563][0.0, 0.0, -0.181368, 0.0, -0.0, -0.000563]Passed
clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0][0.236705, -4.084008, -0.098748, -0.000503, 0.004866, 1.7e-05][0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]Failed
clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0][0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0][0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]Passed
clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0][0.540302, -1.682942, 0.0, -0.841471, 4.435768, 0.0][0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]Failed
clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0]Passed

SHA-256 / b48eebf85f4952945e33ceb31bd8fad0916623daf8b58460acc4bbf4524b2b7c

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    x0,y0,z0,vx,vy,vz,n,t=x
    s=math.sin(n*t); c=math.cos(n*t)
    X=(4-3*c)*x0+s/n*vx+2/n*(1-c)*vy
    Y=6*(s-n*t)*x0+y0-2/n*(1-c)*vx+(4*s-3*n*t)/n*vy
    Z=c*z0+s/n*vz
    VX=3*n*s*x0+c*vx+2*s*vy
    VY=6*(c-1)*x0-2*s*vx+(4*c-3)*vy
    VZ=-n*s*z0+c*vz
    return [round(q,6) for q in (X,Y,Z,VX,VY,VZ)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0]', [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0], [0.0, 0.0, -0.181368, 0.0, -0.0, -0.000563]), ('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0]', [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0], [0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]), ('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0]', [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0])], [('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0]', [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0], [0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]), ('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0]', [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), ('clohessy-wiltshire relative motion [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0]', [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0], [-0.571404, 9.834915, -0.062542, 0.000589, 0.000851, -0.000249]), ('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0])], [('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]), ('clohessy-wiltshire relative motion [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0]', [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0], [-0.571404, 9.834915, -0.062542, 0.000589, 0.000851, -0.000249]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0]', [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), ('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0]', [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0], [0.0, 0.0, -0.181368, 0.0, -0.0, -0.000563]), ('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05])], [('clohessy-wiltshire relative motion [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0]', [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0], [-0.571404, 9.834915, -0.062542, 0.000589, 0.000851, -0.000249]), ('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0]', [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0], [0.0, 0.0, -0.181368, 0.0, -0.0, -0.000563]), ('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0]', [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0], [0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]), ('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0])], [('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0]', [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0], [0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]), ('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0]', [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), ('clohessy-wiltshire relative motion [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0]', [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0], [-0.571404, 9.834915, -0.062542, 0.000589, 0.000851, -0.000249]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0])]]
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
clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0][0.166351, -0.030458, 0.0, 0.000213, -0.132703, 0.0][0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]Failed
clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0][1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0][1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0]Passed
clohessy-wiltshire relative motion [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0][0.0, 0.0, -0.181368, 0.0, -0.0, -0.000563][0.0, 0.0, -0.181368, 0.0, -0.0, -0.000563]Passed
clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0][0.236705, -4.084008, -0.098748, -0.000503, -2.382733, 1.7e-05][0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]Failed
clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0][0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0][0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]Passed
clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0][0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0][0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]Passed
clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0]Passed

SHA-256 / c558b6b6e363aaa795925c08ee693d687b6a90680006dad5c0fb0ef0f0f17244

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    x0,y0,z0,vx,vy,vz,n,t=x
    s=math.sin(n*t); c=math.cos(n*t)
    X=(4-3*c)*x0+s/n*vx+2/n*(1-c)*vy
    Y=6*(s-n*t)*x0+y0-2/n*(1-c)*vx+(4*s-3*n*t)/n*vy
    Z=c*z0+s/n*vz
    VX=3*n*s*x0+c*vx+2*s*vy
    VY=6*n*(c-1)*x0-2*s*vx+(4*c-3)*vy
    VZ=-n*s*z0+c*vz
    return [round(q,6) for q in (X,Y,Z,VX,VY,VZ)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0]', [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0], [0.0, 0.0, -0.181368, 0.0, -0.0, -0.000563]), ('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0]', [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0], [0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]), ('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0]', [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0])], [('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0]', [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0], [0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]), ('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0]', [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), ('clohessy-wiltshire relative motion [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0]', [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0], [-0.571404, 9.834915, -0.062542, 0.000589, 0.000851, -0.000249]), ('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0])], [('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]), ('clohessy-wiltshire relative motion [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0]', [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0], [-0.571404, 9.834915, -0.062542, 0.000589, 0.000851, -0.000249]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0]', [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), ('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0]', [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0], [0.0, 0.0, -0.181368, 0.0, -0.0, -0.000563]), ('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05])], [('clohessy-wiltshire relative motion [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0]', [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0], [-0.571404, 9.834915, -0.062542, 0.000589, 0.000851, -0.000249]), ('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0]', [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0], [0.0, 0.0, -0.181368, 0.0, -0.0, -0.000563]), ('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0]', [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0], [0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]), ('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0])], [('clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0]', [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0], [0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]), ('clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0]', [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0], [0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0]', [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0], [0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]), ('clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0]', [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0], [0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]), ('clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0]', [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), ('clohessy-wiltshire relative motion [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0]', [-0.3, 2.0, -0.2, 0.0001, 0.0002, -0.0001, 0.0012, 4500.0], [-0.571404, 9.834915, -0.062542, 0.000589, 0.000851, -0.000249]), ('clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0]', [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0], [1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0])]]
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
clohessy-wiltshire relative motion [0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 600.0][0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0][0.166351, -0.030458, 0.0, 0.000213, -0.00015, 0.0]Passed
clohessy-wiltshire relative motion [0.0, 1.0, 0.0, 0.0, 0.001, 0.0, 0.00113, 1200.0][1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0][1.392658, 0.858477, 0.0, 0.001954, -0.002147, 0.0]Passed
clohessy-wiltshire relative motion [0.0, 0.0, 0.5, 0.0, 0.0, 0.0002, 0.00113, 2000.0][0.0, 0.0, -0.181368, 0.0, -0.0, -0.000563][0.0, 0.0, -0.181368, 0.0, -0.0, -0.000563]Passed
clohessy-wiltshire relative motion [0.2, -1.0, 0.1, 0.0005, -0.0003, 0.0, 0.0011, 3000.0][0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05][0.236705, -4.084008, -0.098748, -0.000503, -0.000381, 1.7e-05]Passed
clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.00113, 900.0][0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0][0.752685, -0.83908, 0.0, 0.000526, -0.001701, 0.0]Passed
clohessy-wiltshire relative motion [1.0, 0.0, 0.0, 0.0, -2.0, 0.0, 1.0, 1.0][0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0][0.540302, -1.682942, 0.0, -0.841471, -1.080605, 0.0]Passed
clohessy-wiltshire relative motion [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00113, 500.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0][0.0, 0.0, 0.0, 0.0, 0.0, 0.0]Passed

SHA-256 / 350e6dd881428264133f5d04560cc8a613d424e44e73add60309b524c1ea36d7

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 2026-09-29T14:48:14.460363+00:00.

Case digest / b26e0a59e7c8a33ec2d2fc53279dfd8533d59ae2d9ac3a5d5bb7c84b55317f4a