FA-69531 / Orbital propagation / Open access

Fixed-step RK4 two-body propagation: Acceleration uses |r|^2 in the vector form · case 01

Gravity has the wrong falloff and scales with distance.

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ROOT CAUSE

The vector acceleration divides r by |r|^2 instead of |r|^3.

THE FAILURE

The vector acceleration divides r by |r|^2 instead of |r|^3.

Unsuccessful approach: Dividing by |r| gives a 1/r force law.

Case contract

Input [r0, v0, mu, T, steps] for a planar two-body orbit. Integrate state [x,y,vx,vy] with acceleration -mu r/|r|^3 using classical RK4 with h=T/steps for exactly steps steps. Return the final state rounded to 6 decimals.

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 f(s):
        px,py,vx,vy=s
        rr=(px*px+py*py)
        return [vx,vy,-mu*px/rr,-mu*py/rr]
    s=list(r0)+list(v0)
    for _ in range(steps):
        k1=f(s)
        k2=f([s[i]+h/2*k1[i] for i in range(4)])
        k3=f([s[i]+h/2*k2[i] for i in range(4)])
        k4=f([s[i]+h*k3[i] for i in range(4)])
        s=[s[i]+h/6*(k1[i]+2*k2[i]+2*k3[i]+k4[i]) for i in range(4)]
    return [round(c,6) for c in s]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('fixed-step rk4 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], [5586.092992, 4218.445527, -4.547562, 6.021804]), ('fixed-step rk4 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], [4101.15166, 6610.394483, -5.692596, 5.332573]), ('fixed-step rk4 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], [-6593.162659, 6759.502773, -4.170281, -4.18782]), ('fixed-step rk4 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], [-0.98999, 0.141112, -0.141113, -0.989997]), ('fixed-step rk4 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], [-2.095663, 1.089551, -0.384431, -0.37274]), ('fixed-step rk4 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], [-0.154684, -0.721678, 1.394034, 0.039166]), ('fixed-step rk4 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], [6111.623093, 3316.078893, -3.439749, 6.583115])], [('fixed-step rk4 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], [4101.15166, 6610.394483, -5.692596, 5.332573]), ('fixed-step rk4 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], [-0.98999, 0.141112, -0.141113, -0.989997]), ('fixed-step rk4 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], [-2.095663, 1.089551, -0.384431, -0.37274]), ('fixed-step rk4 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], [-0.154684, -0.721678, 1.394034, 0.039166]), ('fixed-step rk4 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], [6111.623093, 3316.078893, -3.439749, 6.583115]), ('fixed-step rk4 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], [-0.108631, 0.939625, -0.993051, -0.614991]), ('fixed-step rk4 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], [5586.092992, 4218.445527, -4.547562, 6.021804])], [('fixed-step rk4 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], [-6593.162659, 6759.502773, -4.170281, -4.18782]), ('fixed-step rk4 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], [6111.623093, 3316.078893, -3.439749, 6.583115]), ('fixed-step rk4 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], [-0.108631, 0.939625, -0.993051, -0.614991]), ('fixed-step rk4 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], [5586.092992, 4218.445527, -4.547562, 6.021804]), ('fixed-step rk4 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], [4101.15166, 6610.394483, -5.692596, 5.332573]), ('fixed-step rk4 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], [-0.98999, 0.141112, -0.141113, -0.989997]), ('fixed-step rk4 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], [-2.095663, 1.089551, -0.384431, -0.37274])], [('fixed-step rk4 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], [-0.98999, 0.141112, -0.141113, -0.989997]), ('fixed-step rk4 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], [4101.15166, 6610.394483, -5.692596, 5.332573]), ('fixed-step rk4 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], [-6593.162659, 6759.502773, -4.170281, -4.18782]), ('fixed-step rk4 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], [-2.095663, 1.089551, -0.384431, -0.37274]), ('fixed-step rk4 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], [-0.154684, -0.721678, 1.394034, 0.039166]), ('fixed-step rk4 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], [6111.623093, 3316.078893, -3.439749, 6.583115]), ('fixed-step rk4 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], [-0.108631, 0.939625, -0.993051, -0.614991])], [('fixed-step rk4 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], [-2.095663, 1.089551, -0.384431, -0.37274]), ('fixed-step rk4 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], [-0.154684, -0.721678, 1.394034, 0.039166]), ('fixed-step rk4 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], [6111.623093, 3316.078893, -3.439749, 6.583115]), ('fixed-step rk4 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], [-0.108631, 0.939625, -0.993051, -0.614991]), ('fixed-step rk4 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], [5586.092992, 4218.445527, -4.547562, 6.021804]), ('fixed-step rk4 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], [4101.15166, 6610.394483, -5.692596, 5.332573]), ('fixed-step rk4 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], [-6593.162659, 6759.502773, -4.170281, -4.18782])]]
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
fixed-step rk4 two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]	`[-108816.050272, -2284.402005, 610.690326, 10.141135]`	`[5586.092992, 4218.445527, -4.547562, 6.021804]`	Failed
fixed-step rk4 two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]	`[-1098275.596222, -118313.469446, -2010.833068, -216.185802]`	`[4101.15166, 6610.394483, -5.692596, 5.332573]`	Failed
fixed-step rk4 two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]	`[18550.875826, -1065213.845329, 10.634364, -570.845461]`	`[-6593.162659, 6759.502773, -4.170281, -4.18782]`	Failed
fixed-step rk4 two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]	`[-0.989991, 0.141114, -0.141116, -0.989995]`	`[-0.98999, 0.141112, -0.141113, -0.989997]`	Failed
fixed-step rk4 two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]	`[-0.815839, -0.669205, 0.874403, -0.753624]`	`[-2.095663, 1.089551, -0.384431, -0.37274]`	Failed
fixed-step rk4 two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]	`[0.189969, -0.661306, 1.459708, 0.182418]`	`[-0.154684, -0.721678, 1.394034, 0.039166]`	Failed
fixed-step rk4 two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]	`[-176214.773483, -34221.841999, -216.671307, -43.785686]`	`[6111.623093, 3316.078893, -3.439749, 6.583115]`	Failed

SHA-256 / 373a45a98aeaf50984c8dc1456633e06fb7d7dd39609c3a60dcbd0e977ced381

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 f(s):
        px,py,vx,vy=s
        rr=(px*px+py*py)**0.5
        return [vx,vy,-mu*px/rr,-mu*py/rr]
    s=list(r0)+list(v0)
    for _ in range(steps):
        k1=f(s)
        k2=f([s[i]+h/2*k1[i] for i in range(4)])
        k3=f([s[i]+h/2*k2[i] for i in range(4)])
        k4=f([s[i]+h*k3[i] for i in range(4)])
        s=[s[i]+h/6*(k1[i]+2*k2[i]+2*k3[i]+k4[i]) for i in range(4)]
    return [round(c,6) for c in s]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('fixed-step rk4 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], [5586.092992, 4218.445527, -4.547562, 6.021804]), ('fixed-step rk4 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], [4101.15166, 6610.394483, -5.692596, 5.332573]), ('fixed-step rk4 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], [-6593.162659, 6759.502773, -4.170281, -4.18782]), ('fixed-step rk4 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], [-0.98999, 0.141112, -0.141113, -0.989997]), ('fixed-step rk4 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], [-2.095663, 1.089551, -0.384431, -0.37274]), ('fixed-step rk4 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], [-0.154684, -0.721678, 1.394034, 0.039166]), ('fixed-step rk4 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], [6111.623093, 3316.078893, -3.439749, 6.583115])], [('fixed-step rk4 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], [4101.15166, 6610.394483, -5.692596, 5.332573]), ('fixed-step rk4 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], [-0.98999, 0.141112, -0.141113, -0.989997]), ('fixed-step rk4 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], [-2.095663, 1.089551, -0.384431, -0.37274]), ('fixed-step rk4 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], [-0.154684, -0.721678, 1.394034, 0.039166]), ('fixed-step rk4 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], [6111.623093, 3316.078893, -3.439749, 6.583115]), ('fixed-step rk4 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], [-0.108631, 0.939625, -0.993051, -0.614991]), ('fixed-step rk4 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], [5586.092992, 4218.445527, -4.547562, 6.021804])], [('fixed-step rk4 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], [-6593.162659, 6759.502773, -4.170281, -4.18782]), ('fixed-step rk4 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], [6111.623093, 3316.078893, -3.439749, 6.583115]), ('fixed-step rk4 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], [-0.108631, 0.939625, -0.993051, -0.614991]), ('fixed-step rk4 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], [5586.092992, 4218.445527, -4.547562, 6.021804]), ('fixed-step rk4 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], [4101.15166, 6610.394483, -5.692596, 5.332573]), ('fixed-step rk4 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], [-0.98999, 0.141112, -0.141113, -0.989997]), ('fixed-step rk4 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], [-2.095663, 1.089551, -0.384431, -0.37274])], [('fixed-step rk4 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], [-0.98999, 0.141112, -0.141113, -0.989997]), ('fixed-step rk4 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], [4101.15166, 6610.394483, -5.692596, 5.332573]), ('fixed-step rk4 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], [-6593.162659, 6759.502773, -4.170281, -4.18782]), ('fixed-step rk4 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], [-2.095663, 1.089551, -0.384431, -0.37274]), ('fixed-step rk4 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], [-0.154684, -0.721678, 1.394034, 0.039166]), ('fixed-step rk4 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], [6111.623093, 3316.078893, -3.439749, 6.583115]), ('fixed-step rk4 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], [-0.108631, 0.939625, -0.993051, -0.614991])], [('fixed-step rk4 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], [-2.095663, 1.089551, -0.384431, -0.37274]), ('fixed-step rk4 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], [-0.154684, -0.721678, 1.394034, 0.039166]), ('fixed-step rk4 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], [6111.623093, 3316.078893, -3.439749, 6.583115]), ('fixed-step rk4 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], [-0.108631, 0.939625, -0.993051, -0.614991]), ('fixed-step rk4 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], [5586.092992, 4218.445527, -4.547562, 6.021804]), ('fixed-step rk4 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], [4101.15166, 6610.394483, -5.692596, 5.332573]), ('fixed-step rk4 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], [-6593.162659, 6759.502773, -4.170281, -4.18782])]]
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
fixed-step rk4 two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]	`[61793243.471592, 57152847.380241, 676402.855493, -389828.169621]`	`[5586.092992, 4218.445527, -4.547562, 6.021804]`	Failed
fixed-step rk4 two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]	`[-36044949.624155, -40807419.065776, -1504022.952532, 1015430.83679]`	`[4101.15166, 6610.394483, -5.692596, 5.332573]`	Failed
fixed-step rk4 two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]	`[-43413847.04234, -136710411.023683, -2132272.526462, 360989.841671]`	`[-6593.162659, 6759.502773, -4.170281, -4.18782]`	Failed
fixed-step rk4 two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]	`[-0.989992, 0.141119, -0.141119, -0.989993]`	`[-0.98999, 0.141112, -0.141113, -0.989997]`	Failed
fixed-step rk4 two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]	`[0.106517, -1.18055, 1.027189, -0.118921]`	`[-2.095663, 1.089551, -0.384431, -0.37274]`	Failed
fixed-step rk4 two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]	`[0.472245, -0.710786, 1.398322, 0.012865]`	`[-0.154684, -0.721678, 1.394034, 0.039166]`	Failed
fixed-step rk4 two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]	`[-3678208.41082, 33534739.974537, 91157.639268, 173319.328584]`	`[6111.623093, 3316.078893, -3.439749, 6.583115]`	Failed

SHA-256 / e48969e7f155b70ef30b4cf4fa94df919657a84386773de20501673616b947c9

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 2026-09-29T14:48:12.457957+00:00.

Case digest / fddd028b42c38b927b3d18c404bb3a4ff3c69328c6d387869da4aaeb05872231