FA-69546 / Orbital propagation / Open access

Velocity Verlet two-body propagation: Position drift omits the one-half acceleration factor · case 01

Positions overshoot toward the central body every step.

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

ROOT CAUSE

The drift uses h^2 a instead of h^2 a/2.

VERIFIED REPAIR

Use 0.5*h*h*a.

Unsuccessful approach: Using 0.5*h*a has the wrong dimension for a position update.

Case contract

Input [r0, v0, mu, T, steps]; planar two-body. Velocity Verlet with h=T/steps: p += h v + h^2 a/2; a_new = a(p); v += h (a + a_new)/2; carry a_new. Return final [x,y,vx,vy] rounded to 6 plus specific energy v^2/2-mu/|r| 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):
    r0,v0,mu,T,steps=x
    h=T/steps
    def acc(q):
        rr=(q[0]**2+q[1]**2)**1.5
        return [-mu*q[0]/rr,-mu*q[1]/rr]
    p=list(r0); v=list(v0)
    a=acc(p)
    for _ in range(steps):
        p=[p[i]+h*v[i]+h*h*a[i] for i in range(2)]
        an=acc(p)
        v=[v[i]+0.5*h*(a[i]+an[i]) for i in range(2)]
        a=an
    en=(v[0]**2+v[1]**2)/2-mu/math.sqrt(p[0]**2+p[1]**2)
    return [round(c,6) for c in p+v]+[round(en,6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489])], [('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856])], [('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826])], [('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049])], [('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038])]]
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 fixture	Actual	Expected	Outcome
velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]	`[5453.637556, 4177.262982, -4.621184, 5.974317, -29.499746]`	`[5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]`	Failed
velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]	`[3931.40996, 6513.089214, -5.786309, 5.219849, -22.030603]`	`[4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]`	Failed
velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]	`[-6489.974993, 6502.627983, -4.081661, -4.298127, -25.81975]`	`[-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]`	Failed
velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]	`[-0.496093, -0.374943, 0.867143, -0.913719, -0.814709]`	`[-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]`	Failed
velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]	`[-1.263526, -0.22052, 0.347844, -0.667586, -0.496317]`	`[-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]`	Failed
velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]	`[0.064076, -0.549877, 1.425104, 0.47201, -0.679507]`	`[-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]`	Failed
velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]	`[6049.735426, 3297.220983, -3.459482, 6.573078, -30.266028]`	`[6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]`	Failed

SHA-256 / 49d792cc3fac70d8fd211030a4d1c9759aebb60dc9acca6548b8755a0edd0303

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    r0,v0,mu,T,steps=x
    h=T/steps
    def acc(q):
        rr=(q[0]**2+q[1]**2)**1.5
        return [-mu*q[0]/rr,-mu*q[1]/rr]
    p=list(r0); v=list(v0)
    a=acc(p)
    for _ in range(steps):
        p=[p[i]+h*v[i]+0.5*h*a[i] for i in range(2)]
        an=acc(p)
        v=[v[i]+0.5*h*(a[i]+an[i]) for i in range(2)]
        a=an
    en=(v[0]**2+v[1]**2)/2-mu/math.sqrt(p[0]**2+p[1]**2)
    return [round(c,6) for c in p+v]+[round(en,6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489])], [('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856])], [('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826])], [('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049])], [('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038])]]
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 fixture	Actual	Expected	Outcome
velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]	`[5711.537898, 4260.468281, -4.475625, 6.065216, -27.530685]`	`[5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]`	Failed
velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]	`[4260.757337, 6703.776146, -5.601079, 5.436802, -19.715795]`	`[4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]`	Failed
velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]	`[-6693.93796, 7000.084916, -4.249688, -4.083833, -23.785338]`	`[-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]`	Failed
velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]	`[-1.58811, -1.314714, -0.535358, -0.259116, -0.308164]`	`[-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]`	Failed
velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]	`[-0.485751, -4.115111, -0.132602, -1.05214, 0.32096]`	`[-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]`	Failed
velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]	`[-1.129637, 1.756435, -0.809542, 2.398682, 2.725668]`	`[-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]`	Failed
velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]	`[6170.769208, 3336.240484, -3.419715, 6.592828, -29.242012]`	`[6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]`	Failed

SHA-256 / 1506bfe65eddfc4fa74e8210f2270674ef2bf2742f43d59bbbf5e0ff96d44b38

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    r0,v0,mu,T,steps=x
    h=T/steps
    def acc(q):
        rr=(q[0]**2+q[1]**2)**1.5
        return [-mu*q[0]/rr,-mu*q[1]/rr]
    p=list(r0); v=list(v0)
    a=acc(p)
    for _ in range(steps):
        p=[p[i]+h*v[i]+0.5*h*h*a[i] for i in range(2)]
        an=acc(p)
        v=[v[i]+0.5*h*(a[i]+an[i]) for i in range(2)]
        a=an
    en=(v[0]**2+v[1]**2)/2-mu/math.sqrt(p[0]**2+p[1]**2)
    return [round(c,6) for c in p+v]+[round(en,6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489])], [('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856])], [('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826])], [('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049])], [('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038])]]
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 fixture	Actual	Expected	Outcome
velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]	`[5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]`	`[5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]`	Passed
velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]	`[4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]`	`[4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]`	Passed
velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]	`[-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]`	`[-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]`	Passed
velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]	`[-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]`	`[-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]`	Passed
velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]	`[-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]`	`[-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]`	Passed
velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]	`[-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]`	`[-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]`	Passed
velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]	`[6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]`	`[6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]`	Passed

SHA-256 / 1f28a6014b215676f2f2a79a2e1707b4fc1e7dcaa1cf29a1bf9e877a2fdbeb0c

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 2026-09-29T14:48:12.493982+00:00.

Case digest / 9b655b95dc5851d341b94a447c457b2b877a7e864682c1fbd34f9b13e0114a12