FAILURE MAP
← Case archive

FA-69771 / Orbital propagation / Open access

Clohessy-Wiltshire relative motion: Radial velocity from a radial offset uses cosine · case 01

Radial velocity is out of phase with the radial displacement.

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

ROOT CAUSE

vx uses 3n cos(nt) x0 instead of 3n sin(nt) x0.

THE FAILURE

vx uses 3n cos(nt) x0 instead of 3n sin(nt) x0.

Unsuccessful approach: Dropping n from the sine term gives the wrong 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*c*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, 0.000264, -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, -0.001051, -0.000381, 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, -1.744977, -1.080605, 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 / 7d6a2a3c1f59ae943b5fa6e7ad1b14417cd2f29fe9377c21b9f855ef7dc2d68a

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*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, 0.188171, -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, -0.095047, -0.000381, 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 / 5f5f5e4f58f4ac6f66ea8d684d71093bff5b119630e872035d13f41d290b67c6

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.

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

Sign in to the archive ↗

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 2026-09-29T14:48:14.502798+00:00.

Case digest / 821325cf50ecd6dd684be78bee14d4133c0dfa27de438d7a61365d366f9594c4