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FA-69576 / Orbital propagation / Open access

J2 secular node and perigee drift: Nodal rate sign ignores retrograde inclinations · case 01

Sun-synchronous retrograde orbits regress instead of precess.

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

ROOT CAUSE

The nodal rate uses |cos i|, so retrograde orbits keep the prograde sign.

VERIFIED REPAIR

Use the signed cos i.

Unsuccessful approach: Using sin i instead of cos i swaps polar and equatorial behaviour.

Case contract

Input [a km, e, i deg, days]. With mu=398600.4418, Re=6378.137, J2=1.08263e-3, n=sqrt(mu/a^3), p=a(1-e^2): dRAAN/dt=-1.5 n J2 (Re/p)^2 cos i, dargp/dt=0.75 n J2 (Re/p)^2 (5cos^2 i-1). Return [RAAN drift deg, argp drift deg over the interval (rounded 4), sun-synchronous flag: |RAAN rate in deg/day - 0.9856|<0.01].

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):
    a,e,i,days=x
    mu,Re,J2=398600.4418,6378.137,1.08263e-3
    n=math.sqrt(mu/a**3)
    p=a*(1-e*e)
    ci=math.cos(math.radians(i))
    fac=n*J2*(Re/p)**2
    dO=-1.5*fac*abs(ci)
    dw=0.75*fac*(5*ci*ci-1)
    t=days*86400
    sso=abs(math.degrees(dO)*86400-0.9856)<0.01
    return [round(math.degrees(dO*t),4),round(math.degrees(dw*t),4),sso]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1]', [7078.0, 0.001, 98.19, 1], [0.986, -3.1094, True]), ('j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]', [7078.0, 0.001, 51.6, 1], [-4.2991, 3.2153, False]), ('j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]', [26560.0, 0.74, 63.4, 10], [-1.4793, 0.004, False]), ('j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]', [7000.0, 0.2, 28.5, 3], [-20.5825, 33.5103, False]), ('j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]', [6878.0, 0.0, 97.4, 2], [1.971, -7.0169, True]), ('j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]', [7500.0, 0.05, 82.0, 5], [-3.9523, -12.8241, False]), ('j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]', [12000.0, 0.3, 120.0, 7], [4.6102, 1.1525, False])], [('j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]', [6878.0, 0.0, 97.4, 2], [1.971, -7.0169, True]), ('j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]', [7078.0, 0.001, 51.6, 1], [-4.2991, 3.2153, False]), ('j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]', [7000.0, 0.2, 28.5, 3], [-20.5825, 33.5103, False]), ('j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]', [7500.0, 0.05, 82.0, 5], [-3.9523, -12.8241, False]), ('j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]', [12000.0, 0.3, 120.0, 7], [4.6102, 1.1525, False]), ('j2 secular node and perigee drift [42164.0, 0.0, 0.1, 30]', [42164.0, 0.0, 0.1, 30], [-0.4024, 0.8049, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 81.81, 1]', [7078.0, 0.001, 81.81, 1], [-0.986, -3.1094, False])], [('j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]', [12000.0, 0.3, 120.0, 7], [4.6102, 1.1525, False]), ('j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]', [26560.0, 0.74, 63.4, 10], [-1.4793, 0.004, False]), ('j2 secular node and perigee drift [42164.0, 0.0, 0.1, 30]', [42164.0, 0.0, 0.1, 30], [-0.4024, 0.8049, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 81.81, 1]', [7078.0, 0.001, 81.81, 1], [-0.986, -3.1094, False]), ('j2 secular node and perigee drift [8000.0, 0.1, 45.0, 0.5]', [8000.0, 0.1, 45.0, 0.5], [-1.6264, 1.7251, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1]', [7078.0, 0.001, 98.19, 1], [0.986, -3.1094, True]), ('j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]', [7078.0, 0.001, 51.6, 1], [-4.2991, 3.2153, False])], [('j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1]', [7078.0, 0.001, 98.19, 1], [0.986, -3.1094, True]), ('j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]', [7000.0, 0.2, 28.5, 3], [-20.5825, 33.5103, False]), ('j2 secular node and perigee drift [8000.0, 0.1, 45.0, 0.5]', [8000.0, 0.1, 45.0, 0.5], [-1.6264, 1.7251, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]', [7078.0, 0.001, 51.6, 1], [-4.2991, 3.2153, False]), ('j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]', [26560.0, 0.74, 63.4, 10], [-1.4793, 0.004, False]), ('j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]', [6878.0, 0.0, 97.4, 2], [1.971, -7.0169, True]), ('j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]', [7500.0, 0.05, 82.0, 5], [-3.9523, -12.8241, False])], [('j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]', [6878.0, 0.0, 97.4, 2], [1.971, -7.0169, True]), ('j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]', [26560.0, 0.74, 63.4, 10], [-1.4793, 0.004, False]), ('j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]', [7000.0, 0.2, 28.5, 3], [-20.5825, 33.5103, False]), ('j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]', [7500.0, 0.05, 82.0, 5], [-3.9523, -12.8241, False]), ('j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]', [12000.0, 0.3, 120.0, 7], [4.6102, 1.1525, False]), ('j2 secular node and perigee drift [42164.0, 0.0, 0.1, 30]', [42164.0, 0.0, 0.1, 30], [-0.4024, 0.8049, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 81.81, 1]', [7078.0, 0.001, 81.81, 1], [-0.986, -3.1094, False])]]
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
j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1][-0.986, -3.1094, False][0.986, -3.1094, True]Failed
j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1][-4.2991, 3.2153, False][-4.2991, 3.2153, False]Passed
j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10][-1.4793, 0.004, False][-1.4793, 0.004, False]Passed
j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3][-20.5825, 33.5103, False][-20.5825, 33.5103, False]Passed
j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2][-1.971, -7.0169, False][1.971, -7.0169, True]Failed
j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5][-3.9523, -12.8241, False][-3.9523, -12.8241, False]Passed
j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7][-4.6102, 1.1525, False][4.6102, 1.1525, False]Failed

SHA-256 / f424e7de8c931992793b23f7229dda56dffc3f43ebe2b9f556bc01ccc6bccb83

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    a,e,i,days=x
    mu,Re,J2=398600.4418,6378.137,1.08263e-3
    n=math.sqrt(mu/a**3)
    p=a*(1-e*e)
    ci=math.cos(math.radians(i))
    fac=n*J2*(Re/p)**2
    dO=-1.5*fac*math.sin(math.radians(i))
    dw=0.75*fac*(5*ci*ci-1)
    t=days*86400
    sso=abs(math.degrees(dO)*86400-0.9856)<0.01
    return [round(math.degrees(dO*t),4),round(math.degrees(dw*t),4),sso]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1]', [7078.0, 0.001, 98.19, 1], [0.986, -3.1094, True]), ('j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]', [7078.0, 0.001, 51.6, 1], [-4.2991, 3.2153, False]), ('j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]', [26560.0, 0.74, 63.4, 10], [-1.4793, 0.004, False]), ('j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]', [7000.0, 0.2, 28.5, 3], [-20.5825, 33.5103, False]), ('j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]', [6878.0, 0.0, 97.4, 2], [1.971, -7.0169, True]), ('j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]', [7500.0, 0.05, 82.0, 5], [-3.9523, -12.8241, False]), ('j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]', [12000.0, 0.3, 120.0, 7], [4.6102, 1.1525, False])], [('j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]', [6878.0, 0.0, 97.4, 2], [1.971, -7.0169, True]), ('j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]', [7078.0, 0.001, 51.6, 1], [-4.2991, 3.2153, False]), ('j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]', [7000.0, 0.2, 28.5, 3], [-20.5825, 33.5103, False]), ('j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]', [7500.0, 0.05, 82.0, 5], [-3.9523, -12.8241, False]), ('j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]', [12000.0, 0.3, 120.0, 7], [4.6102, 1.1525, False]), ('j2 secular node and perigee drift [42164.0, 0.0, 0.1, 30]', [42164.0, 0.0, 0.1, 30], [-0.4024, 0.8049, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 81.81, 1]', [7078.0, 0.001, 81.81, 1], [-0.986, -3.1094, False])], [('j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]', [12000.0, 0.3, 120.0, 7], [4.6102, 1.1525, False]), ('j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]', [26560.0, 0.74, 63.4, 10], [-1.4793, 0.004, False]), ('j2 secular node and perigee drift [42164.0, 0.0, 0.1, 30]', [42164.0, 0.0, 0.1, 30], [-0.4024, 0.8049, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 81.81, 1]', [7078.0, 0.001, 81.81, 1], [-0.986, -3.1094, False]), ('j2 secular node and perigee drift [8000.0, 0.1, 45.0, 0.5]', [8000.0, 0.1, 45.0, 0.5], [-1.6264, 1.7251, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1]', [7078.0, 0.001, 98.19, 1], [0.986, -3.1094, True]), ('j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]', [7078.0, 0.001, 51.6, 1], [-4.2991, 3.2153, False])], [('j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1]', [7078.0, 0.001, 98.19, 1], [0.986, -3.1094, True]), ('j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]', [7000.0, 0.2, 28.5, 3], [-20.5825, 33.5103, False]), ('j2 secular node and perigee drift [8000.0, 0.1, 45.0, 0.5]', [8000.0, 0.1, 45.0, 0.5], [-1.6264, 1.7251, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]', [7078.0, 0.001, 51.6, 1], [-4.2991, 3.2153, False]), ('j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]', [26560.0, 0.74, 63.4, 10], [-1.4793, 0.004, False]), ('j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]', [6878.0, 0.0, 97.4, 2], [1.971, -7.0169, True]), ('j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]', [7500.0, 0.05, 82.0, 5], [-3.9523, -12.8241, False])], [('j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]', [6878.0, 0.0, 97.4, 2], [1.971, -7.0169, True]), ('j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]', [26560.0, 0.74, 63.4, 10], [-1.4793, 0.004, False]), ('j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]', [7000.0, 0.2, 28.5, 3], [-20.5825, 33.5103, False]), ('j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]', [7500.0, 0.05, 82.0, 5], [-3.9523, -12.8241, False]), ('j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]', [12000.0, 0.3, 120.0, 7], [4.6102, 1.1525, False]), ('j2 secular node and perigee drift [42164.0, 0.0, 0.1, 30]', [42164.0, 0.0, 0.1, 30], [-0.4024, 0.8049, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 81.81, 1]', [7078.0, 0.001, 81.81, 1], [-0.986, -3.1094, False])]]
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
j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1][-6.8506, -3.1094, False][0.986, -3.1094, True]Failed
j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1][-5.4241, 3.2153, False][-4.2991, 3.2153, False]Failed
j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10][-2.9542, 0.004, False][-1.4793, 0.004, False]Failed
j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3][-11.1754, 33.5103, False][-20.5825, 33.5103, False]Failed
j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2][-15.1755, -7.0169, False][1.971, -7.0169, True]Failed
j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5][-28.122, -12.8241, False][-3.9523, -12.8241, False]Failed
j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7][-7.985, 1.1525, False][4.6102, 1.1525, False]Failed

SHA-256 / 5995691a1c6dc8208ea351385fbc148eb3803e2fbed81c1a39cb3d5647fbe138

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    a,e,i,days=x
    mu,Re,J2=398600.4418,6378.137,1.08263e-3
    n=math.sqrt(mu/a**3)
    p=a*(1-e*e)
    ci=math.cos(math.radians(i))
    fac=n*J2*(Re/p)**2
    dO=-1.5*fac*ci
    dw=0.75*fac*(5*ci*ci-1)
    t=days*86400
    sso=abs(math.degrees(dO)*86400-0.9856)<0.01
    return [round(math.degrees(dO*t),4),round(math.degrees(dw*t),4),sso]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1]', [7078.0, 0.001, 98.19, 1], [0.986, -3.1094, True]), ('j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]', [7078.0, 0.001, 51.6, 1], [-4.2991, 3.2153, False]), ('j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]', [26560.0, 0.74, 63.4, 10], [-1.4793, 0.004, False]), ('j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]', [7000.0, 0.2, 28.5, 3], [-20.5825, 33.5103, False]), ('j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]', [6878.0, 0.0, 97.4, 2], [1.971, -7.0169, True]), ('j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]', [7500.0, 0.05, 82.0, 5], [-3.9523, -12.8241, False]), ('j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]', [12000.0, 0.3, 120.0, 7], [4.6102, 1.1525, False])], [('j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]', [6878.0, 0.0, 97.4, 2], [1.971, -7.0169, True]), ('j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]', [7078.0, 0.001, 51.6, 1], [-4.2991, 3.2153, False]), ('j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]', [7000.0, 0.2, 28.5, 3], [-20.5825, 33.5103, False]), ('j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]', [7500.0, 0.05, 82.0, 5], [-3.9523, -12.8241, False]), ('j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]', [12000.0, 0.3, 120.0, 7], [4.6102, 1.1525, False]), ('j2 secular node and perigee drift [42164.0, 0.0, 0.1, 30]', [42164.0, 0.0, 0.1, 30], [-0.4024, 0.8049, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 81.81, 1]', [7078.0, 0.001, 81.81, 1], [-0.986, -3.1094, False])], [('j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]', [12000.0, 0.3, 120.0, 7], [4.6102, 1.1525, False]), ('j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]', [26560.0, 0.74, 63.4, 10], [-1.4793, 0.004, False]), ('j2 secular node and perigee drift [42164.0, 0.0, 0.1, 30]', [42164.0, 0.0, 0.1, 30], [-0.4024, 0.8049, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 81.81, 1]', [7078.0, 0.001, 81.81, 1], [-0.986, -3.1094, False]), ('j2 secular node and perigee drift [8000.0, 0.1, 45.0, 0.5]', [8000.0, 0.1, 45.0, 0.5], [-1.6264, 1.7251, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1]', [7078.0, 0.001, 98.19, 1], [0.986, -3.1094, True]), ('j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]', [7078.0, 0.001, 51.6, 1], [-4.2991, 3.2153, False])], [('j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1]', [7078.0, 0.001, 98.19, 1], [0.986, -3.1094, True]), ('j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]', [7000.0, 0.2, 28.5, 3], [-20.5825, 33.5103, False]), ('j2 secular node and perigee drift [8000.0, 0.1, 45.0, 0.5]', [8000.0, 0.1, 45.0, 0.5], [-1.6264, 1.7251, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]', [7078.0, 0.001, 51.6, 1], [-4.2991, 3.2153, False]), ('j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]', [26560.0, 0.74, 63.4, 10], [-1.4793, 0.004, False]), ('j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]', [6878.0, 0.0, 97.4, 2], [1.971, -7.0169, True]), ('j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]', [7500.0, 0.05, 82.0, 5], [-3.9523, -12.8241, False])], [('j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]', [6878.0, 0.0, 97.4, 2], [1.971, -7.0169, True]), ('j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]', [26560.0, 0.74, 63.4, 10], [-1.4793, 0.004, False]), ('j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]', [7000.0, 0.2, 28.5, 3], [-20.5825, 33.5103, False]), ('j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]', [7500.0, 0.05, 82.0, 5], [-3.9523, -12.8241, False]), ('j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]', [12000.0, 0.3, 120.0, 7], [4.6102, 1.1525, False]), ('j2 secular node and perigee drift [42164.0, 0.0, 0.1, 30]', [42164.0, 0.0, 0.1, 30], [-0.4024, 0.8049, False]), ('j2 secular node and perigee drift [7078.0, 0.001, 81.81, 1]', [7078.0, 0.001, 81.81, 1], [-0.986, -3.1094, False])]]
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
j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1][0.986, -3.1094, True][0.986, -3.1094, True]Passed
j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1][-4.2991, 3.2153, False][-4.2991, 3.2153, False]Passed
j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10][-1.4793, 0.004, False][-1.4793, 0.004, False]Passed
j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3][-20.5825, 33.5103, False][-20.5825, 33.5103, False]Passed
j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2][1.971, -7.0169, True][1.971, -7.0169, True]Passed
j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5][-3.9523, -12.8241, False][-3.9523, -12.8241, False]Passed
j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7][4.6102, 1.1525, False][4.6102, 1.1525, False]Passed

SHA-256 / df04985343316dbd193e4b0263a0b3711cd3e7c5f20657d6281ddaec700b7075

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 2026-09-29T14:48:12.640127+00:00.

Case digest / 6d0671b0014bfaf07b2fad174471b428dfb5f9044e39662b59b3955484d4541a