Astronomical Twilight Duration mechanism

Model scope

The four vectors are deterministic provisional checks for the standard geometric hour-angle method, not definitive checks of the unspecified lookup-table implementation. The instrument needs a named algorithm, explicit UTC/local-time behavior, longitude convention, atmospheric/elevation assumptions, and documented polar/no-crossing outputs before it can receive PASS.

• The specification names depression-angle thresholds but does not define the solar-position algorithm, so the result is not uniquely reproducible.
• The implementation must explicitly use solar zenith angles of 96° (civil), 102° (nautical), and 108° (astronomical), equivalent to solar-center altitudes of -6°, -12°, and -18°; whether atmospheric refraction and the solar disk are included is unspecified.
• The input date is insufficiently defined: a timezone, time scale, and timestamp/date convention are required. Longitude alone does not determine displayed local clock times.
• No behavior is specified for locations or dates where one or more twilight crossings do not occur, including polar day, polar night, and continuous twilight.
• The stated lookup-table engine is ambiguous because no table source, interpolation rule, or solar-position equations are supplied.
• The claimed approximately 1-minute accuracy cannot be verified without specifying the algorithm, reference ephemeris, refraction model, elevation, and validity range.

Units and conventions

• Latitude and longitude are assumed to be decimal degrees, with latitude positive north and longitude positive east.
• Depression angles are degrees below the ideal geometric horizon; zenith angles are 90° plus the depression angle.
• Test-vector times are UTC, at sea level, with longitude interpreted using the conventional east-positive sign.
• The provisional hand checks below use the idealized hour-angle model: solar declination is explicitly set to the stated value, equation of time is zero, and solar noon is 12:00 UTC minus longitude divided by 15° per hour.
• The provisional model ignores atmospheric refraction, observer elevation, solar-radius correction, and terrain obstruction.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "lat_deg": 0,
    "lon_deg": 0,
    "date": "idealized_equinox",
    "solar_declination_deg": 0,
    "timezone": "UTC",
    "model": "geometric hour-angle check"
  },
  "expected_outputs": {
    "civil": {
      "begin": "05:36:00 UTC",
      "end": "18:24:00 UTC",
      "hour_angle_deg": 96
    },
    "nautical": {
      "begin": "05:12:00 UTC",
      "end": "18:48:00 UTC",
      "hour_angle_deg": 102
    },
    "astronomical": {
      "begin": "04:48:00 UTC",
      "end": "19:12:00 UTC",
      "hour_angle_deg": 108
    }
  },
  "working": "For latitude 0° and declination 0°, sin(phi)sin(delta)=0 and cos(phi)cos(delta)=1, so cos(H)=cos(Z). Therefore H=Z. Civil: Z=90°+6°=96°; 96°/15=6.4 h=6 h 24 min, so 12:00-06:24=05:36 and 12:00+06:24=18:24. Nautical: Z=102°; 102/15=6.8 h=6 h 48 min, so 05:12 and 18:48. Astronomical: Z=108°; 108/15=7.2 h=7 h 12 min, so 04:48 and 19:12."
}

Failure boundary

• Missing timezone or explicit UTC output can shift every displayed time by hours.
• Longitude sign convention and degree-versus-radian handling must be validated; a 180° longitude is an especially important wraparound case.
• The hour-angle formula divides by cos(latitude)cos(declination); it becomes singular or numerically unstable near the poles and must use an explicit no-event/continuous-event policy.
• Each threshold requires checking whether the computed acos argument lies in [-1,1]. Outside that interval, the corresponding twilight event does not occur rather than producing NaN or a fabricated time.
• Near the poles and near threshold boundaries, floating-point rounding can incorrectly switch between an event and no event.
• Atmospheric refraction, elevation above sea level, solar radius, and terrain horizon can change event times by more than the claimed one-minute accuracy.
• Date handling must include leap years, UTC date boundaries, and equation-of-time/date conversion. A date without timezone and calendar specification is not sufficient.
• The honest label should say approximately one minute only after the exact solar-position algorithm and environmental assumptions are documented; otherwise the accuracy claim is unsupported.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json