{"abstract":"Critical inclination still shows perigee drift of the wrong direction.","category":"Orbital propagation","checks":7,"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].","contract_signature":"x","evaluation_group":"w2-orbital_propagation-j2_secular","failed_approach":"Mixing the sine form (4-5cos^2 i) into the cosine form shifts the critical inclination.","family":"w2-orbital_propagation-j2_secular-apsidal-factor","id":"FA-69581","implementations":{"attempt":{"sha256":"98c862c9668d30011594a5e18494107bda12a0418f99162f86ef82362ecb770e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    a,e,i,days=x\n    mu,Re,J2=398600.4418,6378.137,1.08263e-3\n    n=math.sqrt(mu/a**3)\n    p=a*(1-e*e)\n    ci=math.cos(math.radians(i))\n    fac=n*J2*(Re/p)**2\n    dO=-1.5*fac*ci\n    dw=0.75*fac*(4-5*ci*ci)\n    t=days*86400\n    sso=abs(math.degrees(dO)*86400-0.9856)<0.01\n    return [round(math.degrees(dO*t),4),round(math.degrees(dw*t),4),sso]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('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 [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 [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 [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 [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 [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 [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 [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, 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 [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])]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"b92b48aec73b3385a416b4b1584f49a303ffa6bc5866ed8e86e08a53450a51c5","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    a,e,i,days=x\n    mu,Re,J2=398600.4418,6378.137,1.08263e-3\n    n=math.sqrt(mu/a**3)\n    p=a*(1-e*e)\n    ci=math.cos(math.radians(i))\n    fac=n*J2*(Re/p)**2\n    dO=-1.5*fac*ci\n    dw=0.75*fac*(1-5*ci*ci)\n    t=days*86400\n    sso=abs(math.degrees(dO)*86400-0.9856)<0.01\n    return [round(math.degrees(dO*t),4),round(math.degrees(dw*t),4),sso]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('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 [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 [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 [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 [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 [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 [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 [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, 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 [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])]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"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.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-orbital_propagation-j2_secular-apsidal-factor","generated_at":"2026-09-29T14:48:12.758512+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Orbit determination and mission planning chain many small conversions; one wrong branch or unit silently moves a spacecraft by kilometres.","root_cause":"The apsidal term uses (1-5cos^2 i).","sha256":"8c5aa23035bcad48f2d871545458d5bcc076c80b4682b51e153f7031071d8ff1","title":"J2 secular node and perigee drift: Perigee drift factor has the wrong sign · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":42.325,"exit_code":1,"observations":[{"actual":[0.986,13.4912,true],"check":"j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1]","expected":[0.986,-3.1094,true],"passed":false},{"actual":[-4.2991,7.1664,false],"check":"j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]","expected":[-4.2991,3.2153,false],"passed":false},{"actual":[-1.4793,4.9517,false],"check":"j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]","expected":[-1.4793,0.004,false],"passed":false},{"actual":[-20.5825,1.6207,false],"check":"j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]","expected":[-20.5825,33.5103,false],"passed":false},{"actual":[1.971,29.9714,true],"check":"j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]","expected":[1.971,-7.0169,true],"passed":false},{"actual":[-3.9523,55.4217,false],"check":"j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]","expected":[-3.9523,-12.8241,false],"passed":false},{"actual":[4.6102,12.6779,false],"check":"j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]","expected":[4.6102,1.1525,false],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1]\", \"actual\": [0.986, 13.4912, true], \"expected\": [0.986, -3.1094, true], \"passed\": false}, {\"check\": \"j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]\", \"actual\": [-4.2991, 7.1664, false], \"expected\": [-4.2991, 3.2153, false], \"passed\": false}, {\"check\": \"j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]\", \"actual\": [-1.4793, 4.9517, false], \"expected\": [-1.4793, 0.004, false], \"passed\": false}, {\"check\": \"j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]\", \"actual\": [-20.5825, 1.6207, false], \"expected\": [-20.5825, 33.5103, false], \"passed\": false}, {\"check\": \"j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]\", \"actual\": [1.971, 29.9714, true], \"expected\": [1.971, -7.0169, true], \"passed\": false}, {\"check\": \"j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]\", \"actual\": [-3.9523, 55.4217, false], \"expected\": [-3.9523, -12.8241, false], \"passed\": false}, {\"check\": \"j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]\", \"actual\": [4.6102, 12.6779, false], \"expected\": [4.6102, 1.1525, false], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.126,"exit_code":1,"observations":[{"actual":[0.986,3.1094,true],"check":"j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1]","expected":[0.986,-3.1094,true],"passed":false},{"actual":[-4.2991,-3.2153,false],"check":"j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]","expected":[-4.2991,3.2153,false],"passed":false},{"actual":[-1.4793,-0.004,false],"check":"j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]","expected":[-1.4793,0.004,false],"passed":false},{"actual":[-20.5825,-33.5103,false],"check":"j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]","expected":[-20.5825,33.5103,false],"passed":false},{"actual":[1.971,7.0169,true],"check":"j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]","expected":[1.971,-7.0169,true],"passed":false},{"actual":[-3.9523,12.8241,false],"check":"j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]","expected":[-3.9523,-12.8241,false],"passed":false},{"actual":[4.6102,-1.1525,false],"check":"j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]","expected":[4.6102,1.1525,false],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"j2 secular node and perigee drift [7078.0, 0.001, 98.19, 1]\", \"actual\": [0.986, 3.1094, true], \"expected\": [0.986, -3.1094, true], \"passed\": false}, {\"check\": \"j2 secular node and perigee drift [7078.0, 0.001, 51.6, 1]\", \"actual\": [-4.2991, -3.2153, false], \"expected\": [-4.2991, 3.2153, false], \"passed\": false}, {\"check\": \"j2 secular node and perigee drift [26560.0, 0.74, 63.4, 10]\", \"actual\": [-1.4793, -0.004, false], \"expected\": [-1.4793, 0.004, false], \"passed\": false}, {\"check\": \"j2 secular node and perigee drift [7000.0, 0.2, 28.5, 3]\", \"actual\": [-20.5825, -33.5103, false], \"expected\": [-20.5825, 33.5103, false], \"passed\": false}, {\"check\": \"j2 secular node and perigee drift [6878.0, 0.0, 97.4, 2]\", \"actual\": [1.971, 7.0169, true], \"expected\": [1.971, -7.0169, true], \"passed\": false}, {\"check\": \"j2 secular node and perigee drift [7500.0, 0.05, 82.0, 5]\", \"actual\": [-3.9523, 12.8241, false], \"expected\": [-3.9523, -12.8241, false], \"passed\": false}, {\"check\": \"j2 secular node and perigee drift [12000.0, 0.3, 120.0, 7]\", \"actual\": [4.6102, -1.1525, false], \"expected\": [4.6102, 1.1525, false], \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}