{"abstract":"Multi-revolution phasing orbits are far too eccentric.","category":"Orbital propagation","checks":7,"contract":"Input [r, theta, k, mu, rmin]: circular radius, target lead angle in degrees (positive = target ahead), k phasing revolutions. Phasing period Tph=T-theta_rad/(k n). a_ph from Tph; total dv = 2|v_ph(r)-v_circ| with vis-viva at r. Return None if the phasing perigee 2a_ph-r is below rmin, else [a_ph rounded 3, dv rounded 6, k*Tph rounded 3].","contract_signature":"x","evaluation_group":"w2-orbital_propagation-phasing","failed_approach":"Dividing the whole shortened period by k shortens each orbit too much.","family":"w2-orbital_propagation-phasing-revolution-split","id":"FA-69801","implementations":{"attempt":{"sha256":"6f47a8f2178e3206e680ce95cc3969ab4d0d4b60617858d255ae85d9d522829b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    r,theta,k,mu,rmin=x\n    n=math.sqrt(mu/r**3)\n    T=2*math.pi/n\n    Tph=(T-math.radians(theta)/n)/k\n    aph=(mu*(Tph/(2*math.pi))**2)**(1/3)\n    if 2*aph-r<rmin: return None\n    vc=math.sqrt(mu/r)\n    vph=math.sqrt(mu*(2/r-1/aph))\n    dv=2*abs(vph-vc)\n    return [round(aph,3),round(dv,6),round(k*Tph,3)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('co-orbital phasing manoeuvre [6778.0, 20.0, 3, 398600.4418, 6478.0]', [6778.0, 20.0, 3, 398600.4418, 6478.0], [6694.061, 0.096463, 16351.842]), ('co-orbital phasing manoeuvre [6778.0, 20.0, 1, 398600.4418, 6478.0]', [6778.0, 20.0, 1, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]', [6778.0, -30.0, 2, 398600.4418, 6478.0], [6964.994, 0.204521, 11569.7]), ('co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]', [42164.0, 10.0, 1, 398600.4418, 6478.0], [41379.525, 0.058569, 83770.138]), ('co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]', [42164.0, -45.0, 4, 398600.4418, 6478.0], [43037.904, 0.062119, 355424.729]), ('co-orbital phasing manoeuvre [6778.0, 90.0, 1, 398600.4418, 6478.0]', [6778.0, 90.0, 1, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]', [6778.0, 90.0, 5, 398600.4418, 6478.0], None)], [('co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]', [6778.0, -30.0, 2, 398600.4418, 6478.0], [6964.994, 0.204521, 11569.7]), ('co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]', [42164.0, 10.0, 1, 398600.4418, 6478.0], [41379.525, 0.058569, 83770.138]), ('co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]', [42164.0, -45.0, 4, 398600.4418, 6478.0], [43037.904, 0.062119, 355424.729]), ('co-orbital phasing manoeuvre [6778.0, 90.0, 1, 398600.4418, 6478.0]', [6778.0, 90.0, 1, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]', [6778.0, 90.0, 5, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [1.0, 60.0, 2, 1.0, 0.5]', [1.0, 60.0, 2, 1.0, 0.5], [0.944, 0.060642, 11.519]), ('co-orbital phasing manoeuvre [1.0, -60.0, 2, 1.0, 0.5]', [1.0, -60.0, 2, 1.0, 0.5], [1.055, 0.051305, 13.614])], [('co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]', [42164.0, -45.0, 4, 398600.4418, 6478.0], [43037.904, 0.062119, 355424.729]), ('co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]', [6778.0, 90.0, 5, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [1.0, 60.0, 2, 1.0, 0.5]', [1.0, 60.0, 2, 1.0, 0.5], [0.944, 0.060642, 11.519]), ('co-orbital phasing manoeuvre [1.0, -60.0, 2, 1.0, 0.5]', [1.0, -60.0, 2, 1.0, 0.5], [1.055, 0.051305, 13.614]), ('co-orbital phasing manoeuvre [1.0, 170.0, 1, 1.0, 0.1]', [1.0, 170.0, 1, 1.0, 0.1], [0.653, 0.630624, 3.316]), ('co-orbital phasing manoeuvre [6778.0, 20.0, 1, 398600.4418, 6478.0]', [6778.0, 20.0, 1, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [6778.0, 20.0, 3, 398600.4418, 6478.0]', [6778.0, 20.0, 3, 398600.4418, 6478.0], [6694.061, 0.096463, 16351.842])], [('co-orbital phasing manoeuvre [1.0, 60.0, 2, 1.0, 0.5]', [1.0, 60.0, 2, 1.0, 0.5], [0.944, 0.060642, 11.519]), ('co-orbital phasing manoeuvre [1.0, 170.0, 1, 1.0, 0.1]', [1.0, 170.0, 1, 1.0, 0.1], [0.653, 0.630624, 3.316]), ('co-orbital phasing manoeuvre [6778.0, 20.0, 1, 398600.4418, 6478.0]', [6778.0, 20.0, 1, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [6778.0, 20.0, 3, 398600.4418, 6478.0]', [6778.0, 20.0, 3, 398600.4418, 6478.0], [6694.061, 0.096463, 16351.842]), ('co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]', [6778.0, -30.0, 2, 398600.4418, 6478.0], [6964.994, 0.204521, 11569.7]), ('co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]', [42164.0, 10.0, 1, 398600.4418, 6478.0], [41379.525, 0.058569, 83770.138]), ('co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]', [42164.0, -45.0, 4, 398600.4418, 6478.0], [43037.904, 0.062119, 355424.729])], [('co-orbital phasing manoeuvre [1.0, -60.0, 2, 1.0, 0.5]', [1.0, -60.0, 2, 1.0, 0.5], [1.055, 0.051305, 13.614]), ('co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]', [6778.0, -30.0, 2, 398600.4418, 6478.0], [6964.994, 0.204521, 11569.7]), ('co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]', [42164.0, 10.0, 1, 398600.4418, 6478.0], [41379.525, 0.058569, 83770.138]), ('co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]', [42164.0, -45.0, 4, 398600.4418, 6478.0], [43037.904, 0.062119, 355424.729]), ('co-orbital phasing manoeuvre [6778.0, 90.0, 1, 398600.4418, 6478.0]', [6778.0, 90.0, 1, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]', [6778.0, 90.0, 5, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [1.0, 60.0, 2, 1.0, 0.5]', [1.0, 60.0, 2, 1.0, 0.5], [0.944, 0.060642, 11.519])]]\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":"e1ddc6197702c86dea0d9b3a0aca5bccd907d136ac828c552333fbe1af14fd3f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    r,theta,k,mu,rmin=x\n    n=math.sqrt(mu/r**3)\n    T=2*math.pi/n\n    Tph=T-math.radians(theta)/n\n    aph=(mu*(Tph/(2*math.pi))**2)**(1/3)\n    if 2*aph-r<rmin: return None\n    vc=math.sqrt(mu/r)\n    vph=math.sqrt(mu*(2/r-1/aph))\n    dv=2*abs(vph-vc)\n    return [round(aph,3),round(dv,6),round(k*Tph,3)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('co-orbital phasing manoeuvre [6778.0, 20.0, 3, 398600.4418, 6478.0]', [6778.0, 20.0, 3, 398600.4418, 6478.0], [6694.061, 0.096463, 16351.842]), ('co-orbital phasing manoeuvre [6778.0, 20.0, 1, 398600.4418, 6478.0]', [6778.0, 20.0, 1, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]', [6778.0, -30.0, 2, 398600.4418, 6478.0], [6964.994, 0.204521, 11569.7]), ('co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]', [42164.0, 10.0, 1, 398600.4418, 6478.0], [41379.525, 0.058569, 83770.138]), ('co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]', [42164.0, -45.0, 4, 398600.4418, 6478.0], [43037.904, 0.062119, 355424.729]), ('co-orbital phasing manoeuvre [6778.0, 90.0, 1, 398600.4418, 6478.0]', [6778.0, 90.0, 1, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]', [6778.0, 90.0, 5, 398600.4418, 6478.0], None)], [('co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]', [6778.0, -30.0, 2, 398600.4418, 6478.0], [6964.994, 0.204521, 11569.7]), ('co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]', [42164.0, 10.0, 1, 398600.4418, 6478.0], [41379.525, 0.058569, 83770.138]), ('co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]', [42164.0, -45.0, 4, 398600.4418, 6478.0], [43037.904, 0.062119, 355424.729]), ('co-orbital phasing manoeuvre [6778.0, 90.0, 1, 398600.4418, 6478.0]', [6778.0, 90.0, 1, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]', [6778.0, 90.0, 5, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [1.0, 60.0, 2, 1.0, 0.5]', [1.0, 60.0, 2, 1.0, 0.5], [0.944, 0.060642, 11.519]), ('co-orbital phasing manoeuvre [1.0, -60.0, 2, 1.0, 0.5]', [1.0, -60.0, 2, 1.0, 0.5], [1.055, 0.051305, 13.614])], [('co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]', [42164.0, -45.0, 4, 398600.4418, 6478.0], [43037.904, 0.062119, 355424.729]), ('co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]', [6778.0, 90.0, 5, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [1.0, 60.0, 2, 1.0, 0.5]', [1.0, 60.0, 2, 1.0, 0.5], [0.944, 0.060642, 11.519]), ('co-orbital phasing manoeuvre [1.0, -60.0, 2, 1.0, 0.5]', [1.0, -60.0, 2, 1.0, 0.5], [1.055, 0.051305, 13.614]), ('co-orbital phasing manoeuvre [1.0, 170.0, 1, 1.0, 0.1]', [1.0, 170.0, 1, 1.0, 0.1], [0.653, 0.630624, 3.316]), ('co-orbital phasing manoeuvre [6778.0, 20.0, 1, 398600.4418, 6478.0]', [6778.0, 20.0, 1, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [6778.0, 20.0, 3, 398600.4418, 6478.0]', [6778.0, 20.0, 3, 398600.4418, 6478.0], [6694.061, 0.096463, 16351.842])], [('co-orbital phasing manoeuvre [1.0, 60.0, 2, 1.0, 0.5]', [1.0, 60.0, 2, 1.0, 0.5], [0.944, 0.060642, 11.519]), ('co-orbital phasing manoeuvre [1.0, 170.0, 1, 1.0, 0.1]', [1.0, 170.0, 1, 1.0, 0.1], [0.653, 0.630624, 3.316]), ('co-orbital phasing manoeuvre [6778.0, 20.0, 1, 398600.4418, 6478.0]', [6778.0, 20.0, 1, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [6778.0, 20.0, 3, 398600.4418, 6478.0]', [6778.0, 20.0, 3, 398600.4418, 6478.0], [6694.061, 0.096463, 16351.842]), ('co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]', [6778.0, -30.0, 2, 398600.4418, 6478.0], [6964.994, 0.204521, 11569.7]), ('co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]', [42164.0, 10.0, 1, 398600.4418, 6478.0], [41379.525, 0.058569, 83770.138]), ('co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]', [42164.0, -45.0, 4, 398600.4418, 6478.0], [43037.904, 0.062119, 355424.729])], [('co-orbital phasing manoeuvre [1.0, -60.0, 2, 1.0, 0.5]', [1.0, -60.0, 2, 1.0, 0.5], [1.055, 0.051305, 13.614]), ('co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]', [6778.0, -30.0, 2, 398600.4418, 6478.0], [6964.994, 0.204521, 11569.7]), ('co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]', [42164.0, 10.0, 1, 398600.4418, 6478.0], [41379.525, 0.058569, 83770.138]), ('co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]', [42164.0, -45.0, 4, 398600.4418, 6478.0], [43037.904, 0.062119, 355424.729]), ('co-orbital phasing manoeuvre [6778.0, 90.0, 1, 398600.4418, 6478.0]', [6778.0, 90.0, 1, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]', [6778.0, 90.0, 5, 398600.4418, 6478.0], None), ('co-orbital phasing manoeuvre [1.0, 60.0, 2, 1.0, 0.5]', [1.0, 60.0, 2, 1.0, 0.5], [0.944, 0.060642, 11.519])]]\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-phasing-revolution-split","generated_at":"2026-09-29T14:48:14.720160+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 period change uses theta/n without dividing by k.","sha256":"88975beb259c33fb3ba3164e3615729581c14f736e8677d4f3028bb27bc61071","title":"Co-orbital phasing manoeuvre: The lead angle is not split across phasing revolutions · 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":38.308,"exit_code":1,"observations":[{"actual":null,"check":"co-orbital phasing manoeuvre [6778.0, 20.0, 3, 398600.4418, 6478.0]","expected":[6694.061,0.096463,16351.842],"passed":false},{"actual":null,"check":"co-orbital phasing manoeuvre [6778.0, 20.0, 1, 398600.4418, 6478.0]","expected":null,"passed":true},{"actual":null,"check":"co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]","expected":[6964.994,0.204521,11569.7],"passed":false},{"actual":[41379.525,0.058569,83770.138],"check":"co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]","expected":[41379.525,0.058569,83770.138],"passed":true},{"actual":null,"check":"co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]","expected":[43037.904,0.062119,355424.729],"passed":false},{"actual":null,"check":"co-orbital phasing manoeuvre [6778.0, 90.0, 1, 398600.4418, 6478.0]","expected":null,"passed":true},{"actual":null,"check":"co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"co-orbital phasing manoeuvre [6778.0, 20.0, 3, 398600.4418, 6478.0]\", \"actual\": null, \"expected\": [6694.061, 0.096463, 16351.842], \"passed\": false}, {\"check\": \"co-orbital phasing manoeuvre [6778.0, 20.0, 1, 398600.4418, 6478.0]\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]\", \"actual\": null, \"expected\": [6964.994, 0.204521, 11569.7], \"passed\": false}, {\"check\": \"co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]\", \"actual\": [41379.525, 0.058569, 83770.138], \"expected\": [41379.525, 0.058569, 83770.138], \"passed\": true}, {\"check\": \"co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]\", \"actual\": null, \"expected\": [43037.904, 0.062119, 355424.729], \"passed\": false}, {\"check\": \"co-orbital phasing manoeuvre [6778.0, 90.0, 1, 398600.4418, 6478.0]\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.003,"exit_code":1,"observations":[{"actual":null,"check":"co-orbital phasing manoeuvre [6778.0, 20.0, 3, 398600.4418, 6478.0]","expected":[6694.061,0.096463,16351.842],"passed":false},{"actual":null,"check":"co-orbital phasing manoeuvre [6778.0, 20.0, 1, 398600.4418, 6478.0]","expected":null,"passed":true},{"actual":[7149.51,0.393439,12032.488],"check":"co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]","expected":[6964.994,0.204521,11569.7],"passed":false},{"actual":[41379.525,0.058569,83770.138],"check":"co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]","expected":[41379.525,0.058569,83770.138],"passed":true},{"actual":[45608.258,0.227968,387736.067],"check":"co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]","expected":[43037.904,0.062119,355424.729],"passed":false},{"actual":null,"check":"co-orbital phasing manoeuvre [6778.0, 90.0, 1, 398600.4418, 6478.0]","expected":null,"passed":true},{"actual":null,"check":"co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"co-orbital phasing manoeuvre [6778.0, 20.0, 3, 398600.4418, 6478.0]\", \"actual\": null, \"expected\": [6694.061, 0.096463, 16351.842], \"passed\": false}, {\"check\": \"co-orbital phasing manoeuvre [6778.0, 20.0, 1, 398600.4418, 6478.0]\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]\", \"actual\": [7149.51, 0.393439, 12032.488], \"expected\": [6964.994, 0.204521, 11569.7], \"passed\": false}, {\"check\": \"co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]\", \"actual\": [41379.525, 0.058569, 83770.138], \"expected\": [41379.525, 0.058569, 83770.138], \"passed\": true}, {\"check\": \"co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]\", \"actual\": [45608.258, 0.227968, 387736.067], \"expected\": [43037.904, 0.062119, 355424.729], \"passed\": false}, {\"check\": \"co-orbital phasing manoeuvre [6778.0, 90.0, 1, 398600.4418, 6478.0]\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]\", \"actual\": null, \"expected\": null, \"passed\": true}], \"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."}}