{"abstract":"The spacecraft flies its orbit backwards in the radial direction.","category":"Orbital propagation","checks":7,"contract":"Input [p, e, i, raan, argp, nu, mu] (km, degrees). Perifocal position r=p/(1+e cos nu)[cos nu, sin nu, 0] and velocity sqrt(mu/p)[-sin nu, e+cos nu, 0] are rotated to the inertial frame by R3(-raan)R1(-i)R3(-argp). Return [r rounded 4, v rounded 7].","evaluation_group":"w2-orbital_propagation-coe2rv","failed_approach":"Replacing it with -k cos(nu) mixes the transverse term into the radial one.","family":"w2-orbital_propagation-coe2rv-perifocal-velocity","id":"FA-69501","implementations":{"attempt":{"sha256":"c4e8c1b45f21a26da136431d33ab33877a6fc90ec87b97f63a3521909c236142","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    p,e,i,raan,w,nu,mu=x\n    i,raan,w,nu=[math.radians(t) for t in (i,raan,w,nu)]\n    r=p/(1+e*math.cos(nu))\n    rp=[r*math.cos(nu),r*math.sin(nu),0.0]\n    k=math.sqrt(mu/p)\n    vp=[-k*math.cos(nu),k*(e+math.cos(nu)),0.0]\n    cO,sO,cw,sw,ci,si=math.cos(raan),math.sin(raan),math.cos(w),math.sin(w),math.cos(i),math.sin(i)\n    R=[[cO*cw-sO*sw*ci,-cO*sw-sO*cw*ci,sO*si],\n       [sO*cw+cO*sw*ci,-sO*sw+cO*cw*ci,-cO*si],\n       [sw*si,cw*si,ci]]\n    rv=[sum(R[j][q]*rp[q] for q in range(3)) for j in range(3)]\n    vv=[sum(R[j][q]*vp[q] for q in range(3)) for j in range(3)]\n    return [[round(c,4) for c in rv],[round(c,7) for c in vv]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('state vector from classical elements [7000, 0.01, 28.5, 40, 60, 30, 398600.4418]', [7000, 0.01, 28.5, 40, 60, 30, 398600.4418], [[-3920.2985, 4672.0298, 3311.4335], [-5.8519873, -4.8671157, 0.0180033]]), ('state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]', [8000, 0.2, 63.4, 200, 270, 120, 398600.4418], [[-6553.1233, -4502.8986, 3974.0188], [2.9260598, -1.8478178, 5.4659665]]), ('state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]', [12000, 0.4, 98.0, 300, 45, 250, 398600.4418], [[4456.1689, -4211.3181, -12476.7753], [1.3065909, -3.3947954, 4.0262806]]), ('state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]', [9000, 0.1, 51.6, 100, 190, 330, 398600.4418], [[-381.3488, -7970.4999, 2220.0855], [4.6015157, -1.3825381, -5.4145672]]), ('state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]', [26000, 0.7, 63.4, 270, 280, 10, 398600.4418], [[-6475.5994, -5263.8249, -12931.4731], [0.8127286, -6.3785031, 1.6229816]]), ('state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 398600.4418]', [7500, 0.05, 120.0, 10, 100, 200, 398600.4418], [[3283.3574, 4039.2189, -5902.3182], [6.1750334, -0.7296993, 3.1019243]]), ('state vector from classical elements [10000, 0.3, 30.0, 170, 340, 170, 398600.4418]', [10000, 0.3, 30.0, 170, 340, 170, 398600.4418], [[11037.7999, -8186.9522, 3548.3256], [3.0254103, 2.7095491, -1.8439078]])], [('state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]', [8000, 0.2, 63.4, 200, 270, 120, 398600.4418], [[-6553.1233, -4502.8986, 3974.0188], [2.9260598, -1.8478178, 5.4659665]]), ('state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]', [9000, 0.1, 51.6, 100, 190, 330, 398600.4418], [[-381.3488, -7970.4999, 2220.0855], [4.6015157, -1.3825381, -5.4145672]]), ('state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]', [26000, 0.7, 63.4, 270, 280, 10, 398600.4418], [[-6475.5994, -5263.8249, -12931.4731], [0.8127286, -6.3785031, 1.6229816]]), ('state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 398600.4418]', [7500, 0.05, 120.0, 10, 100, 200, 398600.4418], [[3283.3574, 4039.2189, -5902.3182], [6.1750334, -0.7296993, 3.1019243]]), ('state vector from classical elements [10000, 0.3, 30.0, 170, 340, 170, 398600.4418]', [10000, 0.3, 30.0, 170, 340, 170, 398600.4418], [[11037.7999, -8186.9522, 3548.3256], [3.0254103, 2.7095491, -1.8439078]]), ('state vector from classical elements [7200, 0.02, 85.0, 250, 20, 280, 398600.4418]', [7200, 0.02, 85.0, 250, 20, 280, 398600.4418], [[-1735.9191, -3185.9581, -6190.1572], [-1.8703175, -6.1223077, 3.8454015]]), ('state vector from classical elements [7000, 0.0, 0.0, 0, 0, 90, 398600.4418]', [7000, 0.0, 0.0, 0, 0, 90, 398600.4418], [[0.0, 7000.0, 0.0], [-7.5460533, 0.0, 0.0]])], [('state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]', [12000, 0.4, 98.0, 300, 45, 250, 398600.4418], [[4456.1689, -4211.3181, -12476.7753], [1.3065909, -3.3947954, 4.0262806]]), ('state vector from classical elements [10000, 0.3, 30.0, 170, 340, 170, 398600.4418]', [10000, 0.3, 30.0, 170, 340, 170, 398600.4418], [[11037.7999, -8186.9522, 3548.3256], [3.0254103, 2.7095491, -1.8439078]]), ('state vector from classical elements [7200, 0.02, 85.0, 250, 20, 280, 398600.4418]', [7200, 0.02, 85.0, 250, 20, 280, 398600.4418], [[-1735.9191, -3185.9581, -6190.1572], [-1.8703175, -6.1223077, 3.8454015]]), ('state vector from classical elements [7000, 0.0, 0.0, 0, 0, 90, 398600.4418]', [7000, 0.0, 0.0, 0, 0, 90, 398600.4418], [[0.0, 7000.0, 0.0], [-7.5460533, 0.0, 0.0]]), ('state vector from classical elements [6800, 0.001, 45, 0, 0, 0, 398600.4418]', [6800, 0.001, 45, 0, 0, 0, 398600.4418], [[6793.2068, 0.0, 0.0], [0.0, 5.4191792, 5.4191792]]), ('state vector from classical elements [7000, 0.01, 28.5, 40, 60, 30, 398600.4418]', [7000, 0.01, 28.5, 40, 60, 30, 398600.4418], [[-3920.2985, 4672.0298, 3311.4335], [-5.8519873, -4.8671157, 0.0180033]]), ('state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]', [8000, 0.2, 63.4, 200, 270, 120, 398600.4418], [[-6553.1233, -4502.8986, 3974.0188], [2.9260598, -1.8478178, 5.4659665]])], [('state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]', [9000, 0.1, 51.6, 100, 190, 330, 398600.4418], [[-381.3488, -7970.4999, 2220.0855], [4.6015157, -1.3825381, -5.4145672]]), ('state vector from classical elements [6800, 0.001, 45, 0, 0, 0, 398600.4418]', [6800, 0.001, 45, 0, 0, 0, 398600.4418], [[6793.2068, 0.0, 0.0], [0.0, 5.4191792, 5.4191792]]), ('state vector from classical elements [7000, 0.01, 28.5, 40, 60, 30, 398600.4418]', [7000, 0.01, 28.5, 40, 60, 30, 398600.4418], [[-3920.2985, 4672.0298, 3311.4335], [-5.8519873, -4.8671157, 0.0180033]]), ('state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]', [8000, 0.2, 63.4, 200, 270, 120, 398600.4418], [[-6553.1233, -4502.8986, 3974.0188], [2.9260598, -1.8478178, 5.4659665]]), ('state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]', [12000, 0.4, 98.0, 300, 45, 250, 398600.4418], [[4456.1689, -4211.3181, -12476.7753], [1.3065909, -3.3947954, 4.0262806]]), ('state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]', [26000, 0.7, 63.4, 270, 280, 10, 398600.4418], [[-6475.5994, -5263.8249, -12931.4731], [0.8127286, -6.3785031, 1.6229816]]), ('state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 398600.4418]', [7500, 0.05, 120.0, 10, 100, 200, 398600.4418], [[3283.3574, 4039.2189, -5902.3182], [6.1750334, -0.7296993, 3.1019243]])], [('state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]', [26000, 0.7, 63.4, 270, 280, 10, 398600.4418], [[-6475.5994, -5263.8249, -12931.4731], [0.8127286, -6.3785031, 1.6229816]]), ('state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]', [12000, 0.4, 98.0, 300, 45, 250, 398600.4418], [[4456.1689, -4211.3181, -12476.7753], [1.3065909, -3.3947954, 4.0262806]]), ('state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]', [9000, 0.1, 51.6, 100, 190, 330, 398600.4418], [[-381.3488, -7970.4999, 2220.0855], [4.6015157, -1.3825381, -5.4145672]]), ('state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 398600.4418]', [7500, 0.05, 120.0, 10, 100, 200, 398600.4418], [[3283.3574, 4039.2189, -5902.3182], [6.1750334, -0.7296993, 3.1019243]]), ('state vector from classical elements [10000, 0.3, 30.0, 170, 340, 170, 398600.4418]', [10000, 0.3, 30.0, 170, 340, 170, 398600.4418], [[11037.7999, -8186.9522, 3548.3256], [3.0254103, 2.7095491, -1.8439078]]), ('state vector from classical elements [7200, 0.02, 85.0, 250, 20, 280, 398600.4418]', [7200, 0.02, 85.0, 250, 20, 280, 398600.4418], [[-1735.9191, -3185.9581, -6190.1572], [-1.8703175, -6.1223077, 3.8454015]]), ('state vector from classical elements [7000, 0.0, 0.0, 0, 0, 90, 398600.4418]', [7000, 0.0, 0.0, 0, 0, 90, 398600.4418], [[0.0, 7000.0, 0.0], [-7.5460533, 0.0, 0.0]])]]\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":"48142a5c23df47b4dbd24579bae6d2678c878e0b2d15bd8b57f045cc61166253","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    p,e,i,raan,w,nu,mu=x\n    i,raan,w,nu=[math.radians(t) for t in (i,raan,w,nu)]\n    r=p/(1+e*math.cos(nu))\n    rp=[r*math.cos(nu),r*math.sin(nu),0.0]\n    k=math.sqrt(mu/p)\n    vp=[k*math.sin(nu),k*(e+math.cos(nu)),0.0]\n    cO,sO,cw,sw,ci,si=math.cos(raan),math.sin(raan),math.cos(w),math.sin(w),math.cos(i),math.sin(i)\n    R=[[cO*cw-sO*sw*ci,-cO*sw-sO*cw*ci,sO*si],\n       [sO*cw+cO*sw*ci,-sO*sw+cO*cw*ci,-cO*si],\n       [sw*si,cw*si,ci]]\n    rv=[sum(R[j][q]*rp[q] for q in range(3)) for j in range(3)]\n    vv=[sum(R[j][q]*vp[q] for q in range(3)) for j in range(3)]\n    return [[round(c,4) for c in rv],[round(c,7) for c in vv]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('state vector from classical elements [7000, 0.01, 28.5, 40, 60, 30, 398600.4418]', [7000, 0.01, 28.5, 40, 60, 30, 398600.4418], [[-3920.2985, 4672.0298, 3311.4335], [-5.8519873, -4.8671157, 0.0180033]]), ('state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]', [8000, 0.2, 63.4, 200, 270, 120, 398600.4418], [[-6553.1233, -4502.8986, 3974.0188], [2.9260598, -1.8478178, 5.4659665]]), ('state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]', [12000, 0.4, 98.0, 300, 45, 250, 398600.4418], [[4456.1689, -4211.3181, -12476.7753], [1.3065909, -3.3947954, 4.0262806]]), ('state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]', [9000, 0.1, 51.6, 100, 190, 330, 398600.4418], [[-381.3488, -7970.4999, 2220.0855], [4.6015157, -1.3825381, -5.4145672]]), ('state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]', [26000, 0.7, 63.4, 270, 280, 10, 398600.4418], [[-6475.5994, -5263.8249, -12931.4731], [0.8127286, -6.3785031, 1.6229816]]), ('state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 398600.4418]', [7500, 0.05, 120.0, 10, 100, 200, 398600.4418], [[3283.3574, 4039.2189, -5902.3182], [6.1750334, -0.7296993, 3.1019243]]), ('state vector from classical elements [10000, 0.3, 30.0, 170, 340, 170, 398600.4418]', [10000, 0.3, 30.0, 170, 340, 170, 398600.4418], [[11037.7999, -8186.9522, 3548.3256], [3.0254103, 2.7095491, -1.8439078]])], [('state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]', [8000, 0.2, 63.4, 200, 270, 120, 398600.4418], [[-6553.1233, -4502.8986, 3974.0188], [2.9260598, -1.8478178, 5.4659665]]), ('state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]', [9000, 0.1, 51.6, 100, 190, 330, 398600.4418], [[-381.3488, -7970.4999, 2220.0855], [4.6015157, -1.3825381, -5.4145672]]), ('state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]', [26000, 0.7, 63.4, 270, 280, 10, 398600.4418], [[-6475.5994, -5263.8249, -12931.4731], [0.8127286, -6.3785031, 1.6229816]]), ('state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 398600.4418]', [7500, 0.05, 120.0, 10, 100, 200, 398600.4418], [[3283.3574, 4039.2189, -5902.3182], [6.1750334, -0.7296993, 3.1019243]]), ('state vector from classical elements [10000, 0.3, 30.0, 170, 340, 170, 398600.4418]', [10000, 0.3, 30.0, 170, 340, 170, 398600.4418], [[11037.7999, -8186.9522, 3548.3256], [3.0254103, 2.7095491, -1.8439078]]), ('state vector from classical elements [7200, 0.02, 85.0, 250, 20, 280, 398600.4418]', [7200, 0.02, 85.0, 250, 20, 280, 398600.4418], [[-1735.9191, -3185.9581, -6190.1572], [-1.8703175, -6.1223077, 3.8454015]]), ('state vector from classical elements [7000, 0.0, 0.0, 0, 0, 90, 398600.4418]', [7000, 0.0, 0.0, 0, 0, 90, 398600.4418], [[0.0, 7000.0, 0.0], [-7.5460533, 0.0, 0.0]])], [('state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]', [12000, 0.4, 98.0, 300, 45, 250, 398600.4418], [[4456.1689, -4211.3181, -12476.7753], [1.3065909, -3.3947954, 4.0262806]]), ('state vector from classical elements [10000, 0.3, 30.0, 170, 340, 170, 398600.4418]', [10000, 0.3, 30.0, 170, 340, 170, 398600.4418], [[11037.7999, -8186.9522, 3548.3256], [3.0254103, 2.7095491, -1.8439078]]), ('state vector from classical elements [7200, 0.02, 85.0, 250, 20, 280, 398600.4418]', [7200, 0.02, 85.0, 250, 20, 280, 398600.4418], [[-1735.9191, -3185.9581, -6190.1572], [-1.8703175, -6.1223077, 3.8454015]]), ('state vector from classical elements [7000, 0.0, 0.0, 0, 0, 90, 398600.4418]', [7000, 0.0, 0.0, 0, 0, 90, 398600.4418], [[0.0, 7000.0, 0.0], [-7.5460533, 0.0, 0.0]]), ('state vector from classical elements [6800, 0.001, 45, 0, 0, 0, 398600.4418]', [6800, 0.001, 45, 0, 0, 0, 398600.4418], [[6793.2068, 0.0, 0.0], [0.0, 5.4191792, 5.4191792]]), ('state vector from classical elements [7000, 0.01, 28.5, 40, 60, 30, 398600.4418]', [7000, 0.01, 28.5, 40, 60, 30, 398600.4418], [[-3920.2985, 4672.0298, 3311.4335], [-5.8519873, -4.8671157, 0.0180033]]), ('state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]', [8000, 0.2, 63.4, 200, 270, 120, 398600.4418], [[-6553.1233, -4502.8986, 3974.0188], [2.9260598, -1.8478178, 5.4659665]])], [('state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]', [9000, 0.1, 51.6, 100, 190, 330, 398600.4418], [[-381.3488, -7970.4999, 2220.0855], [4.6015157, -1.3825381, -5.4145672]]), ('state vector from classical elements [6800, 0.001, 45, 0, 0, 0, 398600.4418]', [6800, 0.001, 45, 0, 0, 0, 398600.4418], [[6793.2068, 0.0, 0.0], [0.0, 5.4191792, 5.4191792]]), ('state vector from classical elements [7000, 0.01, 28.5, 40, 60, 30, 398600.4418]', [7000, 0.01, 28.5, 40, 60, 30, 398600.4418], [[-3920.2985, 4672.0298, 3311.4335], [-5.8519873, -4.8671157, 0.0180033]]), ('state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]', [8000, 0.2, 63.4, 200, 270, 120, 398600.4418], [[-6553.1233, -4502.8986, 3974.0188], [2.9260598, -1.8478178, 5.4659665]]), ('state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]', [12000, 0.4, 98.0, 300, 45, 250, 398600.4418], [[4456.1689, -4211.3181, -12476.7753], [1.3065909, -3.3947954, 4.0262806]]), ('state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]', [26000, 0.7, 63.4, 270, 280, 10, 398600.4418], [[-6475.5994, -5263.8249, -12931.4731], [0.8127286, -6.3785031, 1.6229816]]), ('state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 398600.4418]', [7500, 0.05, 120.0, 10, 100, 200, 398600.4418], [[3283.3574, 4039.2189, -5902.3182], [6.1750334, -0.7296993, 3.1019243]])], [('state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]', [26000, 0.7, 63.4, 270, 280, 10, 398600.4418], [[-6475.5994, -5263.8249, -12931.4731], [0.8127286, -6.3785031, 1.6229816]]), ('state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]', [12000, 0.4, 98.0, 300, 45, 250, 398600.4418], [[4456.1689, -4211.3181, -12476.7753], [1.3065909, -3.3947954, 4.0262806]]), ('state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]', [9000, 0.1, 51.6, 100, 190, 330, 398600.4418], [[-381.3488, -7970.4999, 2220.0855], [4.6015157, -1.3825381, -5.4145672]]), ('state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 398600.4418]', [7500, 0.05, 120.0, 10, 100, 200, 398600.4418], [[3283.3574, 4039.2189, -5902.3182], [6.1750334, -0.7296993, 3.1019243]]), ('state vector from classical elements [10000, 0.3, 30.0, 170, 340, 170, 398600.4418]', [10000, 0.3, 30.0, 170, 340, 170, 398600.4418], [[11037.7999, -8186.9522, 3548.3256], [3.0254103, 2.7095491, -1.8439078]]), ('state vector from classical elements [7200, 0.02, 85.0, 250, 20, 280, 398600.4418]', [7200, 0.02, 85.0, 250, 20, 280, 398600.4418], [[-1735.9191, -3185.9581, -6190.1572], [-1.8703175, -6.1223077, 3.8454015]]), ('state vector from classical elements [7000, 0.0, 0.0, 0, 0, 90, 398600.4418]', [7000, 0.0, 0.0, 0, 0, 90, 398600.4418], [[0.0, 7000.0, 0.0], [-7.5460533, 0.0, 0.0]])]]\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"},"fixed":{"sha256":"20cfeb349e6cc6241a263f39c2f17ccb5233a06d4f7c8349815abe11d51a493e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    p,e,i,raan,w,nu,mu=x\n    i,raan,w,nu=[math.radians(t) for t in (i,raan,w,nu)]\n    r=p/(1+e*math.cos(nu))\n    rp=[r*math.cos(nu),r*math.sin(nu),0.0]\n    k=math.sqrt(mu/p)\n    vp=[-k*math.sin(nu),k*(e+math.cos(nu)),0.0]\n    cO,sO,cw,sw,ci,si=math.cos(raan),math.sin(raan),math.cos(w),math.sin(w),math.cos(i),math.sin(i)\n    R=[[cO*cw-sO*sw*ci,-cO*sw-sO*cw*ci,sO*si],\n       [sO*cw+cO*sw*ci,-sO*sw+cO*cw*ci,-cO*si],\n       [sw*si,cw*si,ci]]\n    rv=[sum(R[j][q]*rp[q] for q in range(3)) for j in range(3)]\n    vv=[sum(R[j][q]*vp[q] for q in range(3)) for j in range(3)]\n    return [[round(c,4) for c in rv],[round(c,7) for c in vv]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('state vector from classical elements [7000, 0.01, 28.5, 40, 60, 30, 398600.4418]', [7000, 0.01, 28.5, 40, 60, 30, 398600.4418], [[-3920.2985, 4672.0298, 3311.4335], [-5.8519873, -4.8671157, 0.0180033]]), ('state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]', [8000, 0.2, 63.4, 200, 270, 120, 398600.4418], [[-6553.1233, -4502.8986, 3974.0188], [2.9260598, -1.8478178, 5.4659665]]), ('state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]', [12000, 0.4, 98.0, 300, 45, 250, 398600.4418], [[4456.1689, -4211.3181, -12476.7753], [1.3065909, -3.3947954, 4.0262806]]), ('state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]', [9000, 0.1, 51.6, 100, 190, 330, 398600.4418], [[-381.3488, -7970.4999, 2220.0855], [4.6015157, -1.3825381, -5.4145672]]), ('state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]', [26000, 0.7, 63.4, 270, 280, 10, 398600.4418], [[-6475.5994, -5263.8249, -12931.4731], [0.8127286, -6.3785031, 1.6229816]]), ('state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 398600.4418]', [7500, 0.05, 120.0, 10, 100, 200, 398600.4418], [[3283.3574, 4039.2189, -5902.3182], [6.1750334, -0.7296993, 3.1019243]]), ('state vector from classical elements [10000, 0.3, 30.0, 170, 340, 170, 398600.4418]', [10000, 0.3, 30.0, 170, 340, 170, 398600.4418], [[11037.7999, -8186.9522, 3548.3256], [3.0254103, 2.7095491, -1.8439078]])], [('state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]', [8000, 0.2, 63.4, 200, 270, 120, 398600.4418], [[-6553.1233, -4502.8986, 3974.0188], [2.9260598, -1.8478178, 5.4659665]]), ('state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]', [9000, 0.1, 51.6, 100, 190, 330, 398600.4418], [[-381.3488, -7970.4999, 2220.0855], [4.6015157, -1.3825381, -5.4145672]]), ('state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]', [26000, 0.7, 63.4, 270, 280, 10, 398600.4418], [[-6475.5994, -5263.8249, -12931.4731], [0.8127286, -6.3785031, 1.6229816]]), ('state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 398600.4418]', [7500, 0.05, 120.0, 10, 100, 200, 398600.4418], [[3283.3574, 4039.2189, -5902.3182], [6.1750334, -0.7296993, 3.1019243]]), ('state vector from classical elements [10000, 0.3, 30.0, 170, 340, 170, 398600.4418]', [10000, 0.3, 30.0, 170, 340, 170, 398600.4418], [[11037.7999, -8186.9522, 3548.3256], [3.0254103, 2.7095491, -1.8439078]]), ('state vector from classical elements [7200, 0.02, 85.0, 250, 20, 280, 398600.4418]', [7200, 0.02, 85.0, 250, 20, 280, 398600.4418], [[-1735.9191, -3185.9581, -6190.1572], [-1.8703175, -6.1223077, 3.8454015]]), ('state vector from classical elements [7000, 0.0, 0.0, 0, 0, 90, 398600.4418]', [7000, 0.0, 0.0, 0, 0, 90, 398600.4418], [[0.0, 7000.0, 0.0], [-7.5460533, 0.0, 0.0]])], [('state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]', [12000, 0.4, 98.0, 300, 45, 250, 398600.4418], [[4456.1689, -4211.3181, -12476.7753], [1.3065909, -3.3947954, 4.0262806]]), ('state vector from classical elements [10000, 0.3, 30.0, 170, 340, 170, 398600.4418]', [10000, 0.3, 30.0, 170, 340, 170, 398600.4418], [[11037.7999, -8186.9522, 3548.3256], [3.0254103, 2.7095491, -1.8439078]]), ('state vector from classical elements [7200, 0.02, 85.0, 250, 20, 280, 398600.4418]', [7200, 0.02, 85.0, 250, 20, 280, 398600.4418], [[-1735.9191, -3185.9581, -6190.1572], [-1.8703175, -6.1223077, 3.8454015]]), ('state vector from classical elements [7000, 0.0, 0.0, 0, 0, 90, 398600.4418]', [7000, 0.0, 0.0, 0, 0, 90, 398600.4418], [[0.0, 7000.0, 0.0], [-7.5460533, 0.0, 0.0]]), ('state vector from classical elements [6800, 0.001, 45, 0, 0, 0, 398600.4418]', [6800, 0.001, 45, 0, 0, 0, 398600.4418], [[6793.2068, 0.0, 0.0], [0.0, 5.4191792, 5.4191792]]), ('state vector from classical elements [7000, 0.01, 28.5, 40, 60, 30, 398600.4418]', [7000, 0.01, 28.5, 40, 60, 30, 398600.4418], [[-3920.2985, 4672.0298, 3311.4335], [-5.8519873, -4.8671157, 0.0180033]]), ('state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]', [8000, 0.2, 63.4, 200, 270, 120, 398600.4418], [[-6553.1233, -4502.8986, 3974.0188], [2.9260598, -1.8478178, 5.4659665]])], [('state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]', [9000, 0.1, 51.6, 100, 190, 330, 398600.4418], [[-381.3488, -7970.4999, 2220.0855], [4.6015157, -1.3825381, -5.4145672]]), ('state vector from classical elements [6800, 0.001, 45, 0, 0, 0, 398600.4418]', [6800, 0.001, 45, 0, 0, 0, 398600.4418], [[6793.2068, 0.0, 0.0], [0.0, 5.4191792, 5.4191792]]), ('state vector from classical elements [7000, 0.01, 28.5, 40, 60, 30, 398600.4418]', [7000, 0.01, 28.5, 40, 60, 30, 398600.4418], [[-3920.2985, 4672.0298, 3311.4335], [-5.8519873, -4.8671157, 0.0180033]]), ('state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]', [8000, 0.2, 63.4, 200, 270, 120, 398600.4418], [[-6553.1233, -4502.8986, 3974.0188], [2.9260598, -1.8478178, 5.4659665]]), ('state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]', [12000, 0.4, 98.0, 300, 45, 250, 398600.4418], [[4456.1689, -4211.3181, -12476.7753], [1.3065909, -3.3947954, 4.0262806]]), ('state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]', [26000, 0.7, 63.4, 270, 280, 10, 398600.4418], [[-6475.5994, -5263.8249, -12931.4731], [0.8127286, -6.3785031, 1.6229816]]), ('state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 398600.4418]', [7500, 0.05, 120.0, 10, 100, 200, 398600.4418], [[3283.3574, 4039.2189, -5902.3182], [6.1750334, -0.7296993, 3.1019243]])], [('state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]', [26000, 0.7, 63.4, 270, 280, 10, 398600.4418], [[-6475.5994, -5263.8249, -12931.4731], [0.8127286, -6.3785031, 1.6229816]]), ('state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]', [12000, 0.4, 98.0, 300, 45, 250, 398600.4418], [[4456.1689, -4211.3181, -12476.7753], [1.3065909, -3.3947954, 4.0262806]]), ('state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]', [9000, 0.1, 51.6, 100, 190, 330, 398600.4418], [[-381.3488, -7970.4999, 2220.0855], [4.6015157, -1.3825381, -5.4145672]]), ('state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 398600.4418]', [7500, 0.05, 120.0, 10, 100, 200, 398600.4418], [[3283.3574, 4039.2189, -5902.3182], [6.1750334, -0.7296993, 3.1019243]]), ('state vector from classical elements [10000, 0.3, 30.0, 170, 340, 170, 398600.4418]', [10000, 0.3, 30.0, 170, 340, 170, 398600.4418], [[11037.7999, -8186.9522, 3548.3256], [3.0254103, 2.7095491, -1.8439078]]), ('state vector from classical elements [7200, 0.02, 85.0, 250, 20, 280, 398600.4418]', [7200, 0.02, 85.0, 250, 20, 280, 398600.4418], [[-1735.9191, -3185.9581, -6190.1572], [-1.8703175, -6.1223077, 3.8454015]]), ('state vector from classical elements [7000, 0.0, 0.0, 0, 0, 90, 398600.4418]', [7000, 0.0, 0.0, 0, 0, 90, 398600.4418], [[0.0, 7000.0, 0.0], [-7.5460533, 0.0, 0.0]])]]\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-coe2rv-perifocal-velocity","generated_at":"2026-09-29T14:48:11.934008+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.","repair":"Use -k sin(nu).","root_cause":"The P component of velocity is +k sin(nu).","sha256":"29766c7fb552425765530c87d234af4cceedafae2418092fef2fc34de78e12f3","title":"State vector from classical elements: Perifocal radial velocity has the wrong sign · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.4,"exit_code":1,"observations":[{"actual":[[-3920.2985,4672.0298,3311.4335],[-5.5586876,-7.365148,-1.1233619]],"check":"state vector from classical elements [7000, 0.01, 28.5, 40, 60, 30, 398600.4418]","expected":[[-3920.2985,4672.0298,3311.4335],[-5.8519873,-4.8671157,0.0180033]],"passed":false},{"actual":[[-6553.1233,-4502.8986,3974.0188],[1.4494058,2.2092559,-3.1557772]],"check":"state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]","expected":[[-6553.1233,-4502.8986,3974.0188],[2.9260598,-1.8478178,5.4659665]],"passed":false},{"actual":[[4456.1689,-4211.3181,-12476.7753],[0.3823037,-1.1159111,1.6142695]],"check":"state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]","expected":[[4456.1689,-4211.3181,-12476.7753],[1.3065909,-3.3947954,4.0262806]],"passed":false},{"actual":[[-381.3488,-7970.4999,2220.0855],[2.0812246,7.2639567,-4.1774158]],"check":"state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]","expected":[[-381.3488,-7970.4999,2220.0855],[4.6015157,-1.3825381,-5.4145672]],"passed":false},{"actual":[[-6475.5994,-5263.8249,-12931.4731],[2.2132327,-5.8269863,4.4197237]],"check":"state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]","expected":[[-6475.5994,-5263.8249,-12931.4731],[0.8127286,-6.3785031,1.6229816]],"passed":false},{"actual":[[3283.3574,4039.2189,-5902.3182],[5.802476,-2.9739612,6.8179919]],"check":"state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 398600.4418]","expected":[[3283.3574,4039.2189,-5902.3182],[6.1750334,-0.7296993,3.1019243]],"passed":false},{"actual":[[11037.7999,-8186.9522,3548.3256],[-3.3667999,6.0364483,-3.0946566]],"check":"state vector from classical elements [10000, 0.3, 30.0, 170, 340, 170, 398600.4418]","expected":[[11037.7999,-8186.9522,3548.3256],[3.0254103,2.7095491,-1.8439078]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"state vector from classical elements [7000, 0.01, 28.5, 40, 60, 30, 398600.4418]\", \"actual\": [[-3920.2985, 4672.0298, 3311.4335], [-5.5586876, -7.365148, -1.1233619]], \"expected\": [[-3920.2985, 4672.0298, 3311.4335], [-5.8519873, -4.8671157, 0.0180033]], \"passed\": false}, {\"check\": \"state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]\", \"actual\": [[-6553.1233, -4502.8986, 3974.0188], [1.4494058, 2.2092559, -3.1557772]], \"expected\": [[-6553.1233, -4502.8986, 3974.0188], [2.9260598, -1.8478178, 5.4659665]], \"passed\": false}, {\"check\": \"state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]\", \"actual\": [[4456.1689, -4211.3181, -12476.7753], [0.3823037, -1.1159111, 1.6142695]], \"expected\": [[4456.1689, -4211.3181, -12476.7753], [1.3065909, -3.3947954, 4.0262806]], \"passed\": false}, {\"check\": \"state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]\", \"actual\": [[-381.3488, -7970.4999, 2220.0855], [2.0812246, 7.2639567, -4.1774158]], \"expected\": [[-381.3488, -7970.4999, 2220.0855], [4.6015157, -1.3825381, -5.4145672]], \"passed\": false}, {\"check\": \"state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]\", \"actual\": [[-6475.5994, -5263.8249, -12931.4731], [2.2132327, -5.8269863, 4.4197237]], \"expected\": [[-6475.5994, -5263.8249, -12931.4731], [0.8127286, -6.3785031, 1.6229816]], \"passed\": false}, {\"check\": \"state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 398600.4418]\", \"actual\": [[3283.3574, 4039.2189, -5902.3182], [5.802476, -2.9739612, 6.8179919]], \"expected\": [[3283.3574, 4039.2189, -5902.3182], [6.1750334, -0.7296993, 3.1019243]], \"passed\": false}, {\"check\": \"state vector from classical elements [10000, 0.3, 30.0, 170, 340, 170, 398600.4418]\", \"actual\": [[11037.7999, -8186.9522, 3548.3256], [-3.3667999, 6.0364483, -3.0946566]], \"expected\": [[11037.7999, -8186.9522, 3548.3256], [3.0254103, 2.7095491, -1.8439078]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.914,"exit_code":1,"observations":[{"actual":[[-3920.2985,4672.0298,3311.4335],[-6.6532971,1.9576355,3.1362711]],"check":"state vector from classical elements [7000, 0.01, 28.5, 40, 60, 30, 398600.4418]","expected":[[-3920.2985,4672.0298,3311.4335],[-5.8519873,-4.8671157,0.0180033]],"passed":false},{"actual":[[-6553.1233,-4502.8986,3974.0188],[1.0537375,3.2963455,-5.4659665]],"check":"state vector from classical elements [8000, 0.2, 63.4, 200, 270, 120, 398600.4418]","expected":[[-6553.1233,-4502.8986,3974.0188],[2.9260598,-1.8478178,5.4659665]],"passed":false},{"actual":[[4456.1689,-4211.3181,-12476.7753],[-1.5998364,3.7711722,-3.558305]],"check":"state vector from classical elements [12000, 0.4, 98.0, 300, 45, 250, 398600.4418]","expected":[[4456.1689,-4211.3181,-12476.7753],[1.3065909,-3.3947954,4.0262806]],"passed":false},{"actual":[[-381.3488,-7970.4999,2220.0855],[2.7565346,4.9471354,-4.5089095]],"check":"state vector from classical elements [9000, 0.1, 51.6, 100, 190, 330, 398600.4418]","expected":[[-381.3488,-7970.4999,2220.0855],[4.6015157,-1.3825381,-5.4145672]],"passed":false},{"actual":[[-6475.5994,-5263.8249,-12931.4731],[0.2131056,-6.614634,0.4255621]],"check":"state vector from classical elements [26000, 0.7, 63.4, 270, 280, 10, 398600.4418]","expected":[[-6475.5994,-5263.8249,-12931.4731],[0.8127286,-6.3785031,1.6229816]],"passed":false},{"actual":[[3283.3574,4039.2189,-5902.3182],[6.601428,1.838874,-1.1511407]],"check":"state vector from classical elements [7500, 0.05, 120.0, 10, 100, 200, 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