FA-69796 / Orbital propagation / Open access

Co-orbital phasing manoeuvre: Chaser raises its orbit to catch a target ahead · case 01

The target gets further ahead after the phasing orbit.

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

ROOT CAUSE

The lead angle is added to the period.

VERIFIED REPAIR

Shorten the period when the target is ahead.

Unsuccessful approach: Subtracting the lead angle in degrees mixes units.

Case 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].

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):
    r,theta,k,mu,rmin=x
    n=math.sqrt(mu/r**3)
    T=2*math.pi/n
    Tph=T+math.radians(theta)/(k*n)
    aph=(mu*(Tph/(2*math.pi))**2)**(1/3)
    if 2*aph-r<rmin: return None
    vc=math.sqrt(mu/r)
    vph=math.sqrt(mu*(2/r-1/aph))
    dv=2*abs(vph-vc)
    return [round(aph,3),round(dv,6),round(k*Tph,3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('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 [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, 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 [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 [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 [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 [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 [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, -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 [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, -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 [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])]]
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
co-orbital phasing manoeuvre [6778.0, 20.0, 1, 398600.4418, 6478.0]	`[7026.768, 0.269131, 5861.981]`	`None`	Failed
co-orbital phasing manoeuvre [6778.0, 20.0, 3, 398600.4418, 6478.0]	`[6861.423, 0.092955, 16968.893]`	`[6694.061, 0.096463, 16351.842]`	Failed
co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]	`None`	`[6964.994, 0.204521, 11569.7]`	Failed
co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]	`[42941.244, 0.055402, 88557.003]`	`[41379.525, 0.058569, 83770.138]`	Failed
co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]	`[41280.944, 0.066127, 333883.836]`	`[43037.904, 0.062119, 355424.729]`	Failed
co-orbital phasing manoeuvre [6778.0, 90.0, 1, 398600.4418, 6478.0]	`[7865.172, 1.025708, 6941.82]`	`None`	Failed
co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]	`[7002.091, 0.24349, 29155.643]`	`None`	Failed

SHA-256 / 9ce88adc36d0ead00aebd91c2f0b187a4be32a247ae95c87f3bce823692c8466

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    r,theta,k,mu,rmin=x
    n=math.sqrt(mu/r**3)
    T=2*math.pi/n
    Tph=T-theta/(k*n)
    aph=(mu*(Tph/(2*math.pi))**2)**(1/3)
    if 2*aph-r<rmin: return None
    vc=math.sqrt(mu/r)
    vph=math.sqrt(mu*(2/r-1/aph))
    dv=2*abs(vph-vc)
    return [round(aph,3),round(dv,6),round(k*Tph,3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('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 [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, 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 [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 [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 [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 [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 [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, -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 [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, -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 [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])]]
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
co-orbital phasing manoeuvre [6778.0, 20.0, 1, 398600.4418, 6478.0]	`[11406.45, 2.847422, -12123.743]`	`None`	Failed
co-orbital phasing manoeuvre [6778.0, 20.0, 3, 398600.4418, 6478.0]	`None`	`[6694.061, 0.096463, 16351.842]`	Failed
co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]	`[15287.603, 3.798298, 37622.711]`	`[6964.994, 0.204521, 11569.7]`	Failed
co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]	`[29712.27, 1.462416, -50970.011]`	`[41379.525, 0.058569, 83770.138]`	Failed
co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]	`[83572.317, 1.370672, 961755.4]`	`[43037.904, 0.062119, 355424.729]`	Failed
co-orbital phasing manoeuvre [6778.0, 90.0, 1, 398600.4418, 6478.0]	`[38094.018, 5.365612, -73993.94]`	`None`	Failed
co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]	`[10268.839, 2.416539, -51780.117]`	`None`	Failed

SHA-256 / ac7b7970b87ac776c1b4f61f0de173f60850bd7d8face289f13a0305384ee4f5

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    r,theta,k,mu,rmin=x
    n=math.sqrt(mu/r**3)
    T=2*math.pi/n
    Tph=T-math.radians(theta)/(k*n)
    aph=(mu*(Tph/(2*math.pi))**2)**(1/3)
    if 2*aph-r<rmin: return None
    vc=math.sqrt(mu/r)
    vph=math.sqrt(mu*(2/r-1/aph))
    dv=2*abs(vph-vc)
    return [round(aph,3),round(dv,6),round(k*Tph,3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('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 [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, 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 [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 [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 [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 [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 [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, -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 [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, -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 [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])]]
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
co-orbital phasing manoeuvre [6778.0, 20.0, 1, 398600.4418, 6478.0]	`None`	`None`	Passed
co-orbital phasing manoeuvre [6778.0, 20.0, 3, 398600.4418, 6478.0]	`[6694.061, 0.096463, 16351.842]`	`[6694.061, 0.096463, 16351.842]`	Passed
co-orbital phasing manoeuvre [6778.0, -30.0, 2, 398600.4418, 6478.0]	`[6964.994, 0.204521, 11569.7]`	`[6964.994, 0.204521, 11569.7]`	Passed
co-orbital phasing manoeuvre [42164.0, 10.0, 1, 398600.4418, 6478.0]	`[41379.525, 0.058569, 83770.138]`	`[41379.525, 0.058569, 83770.138]`	Passed
co-orbital phasing manoeuvre [42164.0, -45.0, 4, 398600.4418, 6478.0]	`[43037.904, 0.062119, 355424.729]`	`[43037.904, 0.062119, 355424.729]`	Passed
co-orbital phasing manoeuvre [6778.0, 90.0, 1, 398600.4418, 6478.0]	`None`	`None`	Passed
co-orbital phasing manoeuvre [6778.0, 90.0, 5, 398600.4418, 6478.0]	`None`	`None`	Passed

SHA-256 / b0e475801c0a1c4e99785f32e54073f9c8969b7740cd9b57a1e3dd7823814d1c

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 2026-09-29T14:48:14.679402+00:00.

Case digest / 35c45c04715c2eca1d5c61f257b5fef774db5578ffd7cf2737d0120bb89fc702