FA-69691 / Orbital propagation / Open access

Cylindrical Earth shadow test: Sun direction is not normalized · case 01

Shadow geometry scales with the length of the sun vector.

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

ROOT CAUSE

The sun vector is used directly as the shadow axis.

VERIFIED REPAIR

Normalize the sun vector.

Unsuccessful approach: Dividing by the component sum is not a normalization.

Case contract

Input [r, s, R]: satellite position, sun direction (any length) and body radius. With u=s/|s| and d=r.u, the satellite is sunlit when d>=0; otherwise it is in umbra when the distance of r from the shadow axis |r-d u| is <= R. Return "umbra" or "sunlit".

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,s,R=x
    sn=math.sqrt(sum(c*c for c in s))
    u=list(s)
    d=sum(a*b for a,b in zip(r,u))
    if d>=0: return 'sunlit'
    perp=[a-d*b for a,b in zip(r,u)]
    return 'umbra' if math.sqrt(sum(c*c for c in perp))<=R else 'sunlit'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'sunlit')], [('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-5000.0, -5000.0, 1000.0], [3.0, 4.0, 0.0], 6378.0]', [[-5000.0, -5000.0, 1000.0], [3.0, 4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit')], [('cylindrical earth shadow test [[-5000.0, -5000.0, 1000.0], [3.0, 4.0, 0.0], 6378.0]', [[-5000.0, -5000.0, 1000.0], [3.0, 4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-42164.0, 0.0, 6000.0], [0.0, 0.0, 0.0001], 6378.0]', [[-42164.0, 0.0, 6000.0], [0.0, 0.0, 0.0001], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[3000.0, -7000.0, 0.0], [0.0, 0.5, 0.5], 6378.0]', [[3000.0, -7000.0, 0.0], [0.0, 0.5, 0.5], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra')], [('cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-42164.0, 0.0, 6000.0], [0.0, 0.0, 0.0001], 6378.0]', [[-42164.0, 0.0, 6000.0], [0.0, 0.0, 0.0001], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[3000.0, -7000.0, 0.0], [0.0, 0.5, 0.5], 6378.0]', [[3000.0, -7000.0, 0.0], [0.0, 0.5, 0.5], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit')], [('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'sunlit')]]
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
cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]	`sunlit`	`umbra`	Failed
cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]	`sunlit`	`umbra`	Failed
cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]	`umbra`	`umbra`	Passed
cylindrical earth shadow test [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]	`sunlit`	`sunlit`	Passed
cylindrical earth shadow test [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0]	`umbra`	`umbra`	Passed
cylindrical earth shadow test [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0]	`sunlit`	`sunlit`	Passed
cylindrical earth shadow test [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]	`sunlit`	`sunlit`	Passed

SHA-256 / 8f83d52a6896909244621be59234dd30ed8fcd1f84d59300ba910f3481fb2654

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,s,R=x
    sn=math.sqrt(sum(c*c for c in s))
    u=[c/sum(s) for c in s] if sum(s) else list(s)
    d=sum(a*b for a,b in zip(r,u))
    if d>=0: return 'sunlit'
    perp=[a-d*b for a,b in zip(r,u)]
    return 'umbra' if math.sqrt(sum(c*c for c in perp))<=R else 'sunlit'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'sunlit')], [('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-5000.0, -5000.0, 1000.0], [3.0, 4.0, 0.0], 6378.0]', [[-5000.0, -5000.0, 1000.0], [3.0, 4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit')], [('cylindrical earth shadow test [[-5000.0, -5000.0, 1000.0], [3.0, 4.0, 0.0], 6378.0]', [[-5000.0, -5000.0, 1000.0], [3.0, 4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-42164.0, 0.0, 6000.0], [0.0, 0.0, 0.0001], 6378.0]', [[-42164.0, 0.0, 6000.0], [0.0, 0.0, 0.0001], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[3000.0, -7000.0, 0.0], [0.0, 0.5, 0.5], 6378.0]', [[3000.0, -7000.0, 0.0], [0.0, 0.5, 0.5], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra')], [('cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-42164.0, 0.0, 6000.0], [0.0, 0.0, 0.0001], 6378.0]', [[-42164.0, 0.0, 6000.0], [0.0, 0.0, 0.0001], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[3000.0, -7000.0, 0.0], [0.0, 0.5, 0.5], 6378.0]', [[3000.0, -7000.0, 0.0], [0.0, 0.5, 0.5], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit')], [('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'sunlit')]]
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
cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]	`umbra`	`umbra`	Passed
cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]	`sunlit`	`umbra`	Failed
cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]	`umbra`	`umbra`	Passed
cylindrical earth shadow test [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]	`sunlit`	`sunlit`	Passed
cylindrical earth shadow test [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0]	`umbra`	`umbra`	Passed
cylindrical earth shadow test [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0]	`sunlit`	`sunlit`	Passed
cylindrical earth shadow test [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]	`sunlit`	`sunlit`	Passed

SHA-256 / 9ad5609ff95d8b435493ec29ba08c3830b004c9d7d77a3db3643008dad2b295a

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,s,R=x
    sn=math.sqrt(sum(c*c for c in s))
    u=[c/sn for c in s]
    d=sum(a*b for a,b in zip(r,u))
    if d>=0: return 'sunlit'
    perp=[a-d*b for a,b in zip(r,u)]
    return 'umbra' if math.sqrt(sum(c*c for c in perp))<=R else 'sunlit'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'sunlit')], [('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-5000.0, -5000.0, 1000.0], [3.0, 4.0, 0.0], 6378.0]', [[-5000.0, -5000.0, 1000.0], [3.0, 4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit')], [('cylindrical earth shadow test [[-5000.0, -5000.0, 1000.0], [3.0, 4.0, 0.0], 6378.0]', [[-5000.0, -5000.0, 1000.0], [3.0, 4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-42164.0, 0.0, 6000.0], [0.0, 0.0, 0.0001], 6378.0]', [[-42164.0, 0.0, 6000.0], [0.0, 0.0, 0.0001], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[3000.0, -7000.0, 0.0], [0.0, 0.5, 0.5], 6378.0]', [[3000.0, -7000.0, 0.0], [0.0, 0.5, 0.5], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra')], [('cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-100.0, 7000.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-42164.0, 0.0, 6000.0], [0.0, 0.0, 0.0001], 6378.0]', [[-42164.0, 0.0, 6000.0], [0.0, 0.0, 0.0001], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[3000.0, -7000.0, 0.0], [0.0, 0.5, 0.5], 6378.0]', [[3000.0, -7000.0, 0.0], [0.0, 0.5, 0.5], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit')], [('cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]', [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0]', [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0], 'sunlit'), ('cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'umbra'), ('cylindrical earth shadow test [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]', [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0], 'sunlit')]]
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
cylindrical earth shadow test [[0.0, -8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]	`umbra`	`umbra`	Passed
cylindrical earth shadow test [[5000.0, 5000.0, 0.0], [-3.0, -4.0, 0.0], 6378.0]	`umbra`	`umbra`	Passed
cylindrical earth shadow test [[-7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]	`umbra`	`umbra`	Passed
cylindrical earth shadow test [[7000.0, 100.0, 0.0], [1.0, 0.0, 0.0], 6378.0]	`sunlit`	`sunlit`	Passed
cylindrical earth shadow test [[-7000.0, 6378.0, 0.0], [1.0, 0.0, 0.0], 6378.0]	`umbra`	`umbra`	Passed
cylindrical earth shadow test [[-7000.0, 6400.0, 0.0], [1.0, 0.0, 0.0], 6378.0]	`sunlit`	`sunlit`	Passed
cylindrical earth shadow test [[0.0, 8000.0, 500.0], [0.0, 2.0, 0.0], 6378.0]	`sunlit`	`sunlit`	Passed

SHA-256 / 14ab844d2f98a82614abf669ca88c417eb37fab0224f92199a8bf447349e4af3

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 2026-09-29T14:48:13.831237+00:00.

Case digest / f4ca937019763daec207a6625e6adf1e1fbd23971897c258d4ef3417bbd99ec9