{ "schemaVersion": 1, "verifiedAt": "2026-09-10T01:45:07.786298+00:00", "method": "Tropical apparent geocentric Sun/Moon longitude returns", "reference": { "software": { "skyfield": "1.55", "jplephem": "2.24", "numpy": "2.5.3", "sgp4": "2.27" }, "kernel": "JPL DE421", "kernelSHA256": "a20a7139da04cbc462454634918e9a9ca69127044e2cc9d4f9c16e238d2deedc", "method": { "direction": "Earth-center observe(body).apparent(): light-time, aberration and gravitational light deflection", "frame": "ecliptic_frame: true ecliptic and equinox of each position date; default IAU 2000A nutation", "target": "Natal body longitude measured at natal epoch; moving body longitude measured at candidate epoch", "root": "First forward signed-longitude zero in [startUTC,endUTC); antipode discontinuity explicitly discarded; all roots also recorded", "algorithm": "Independent mesh/bracket/bisection; daily Sun mesh, hourly Moon mesh; half-step cross-check; 0.001 s final bracket", "time": "UTC parsed with Skyfield builtin leap-second table; solve in TT Julian days; JPL evaluation uses TDB internally; output UTC. UT1 not used for geocentric direction.", "historical": "Skyfield proleptic UTC extends TAI−UTC=10 s before 1972; 1950 is explicitly a diagnostic, not historical civil UTC.", "excluded": [ "sidereal returns", "houses", "topocentric parallax", "atmospheric refraction", "interpretation validity" ] }, "rootToleranceSeconds": 2, "declaredBeforeComparison": true }, "summary": { "independentCases": 30, "rootComparisons": 20, "noCrossingCases": 10, "modernUtcCases": 24, "historicalUt1Cases": 6, "maximumRootDifferenceSeconds": 0.08536887168884277, "allPassed": true }, "comparisons": [ { "id": "synthetic-1975-sun-first", "body": "Sun", "classification": "strict-comparison", "expectedUtc": "2026-07-10T23:35:31.770923Z", "actualUtc": "2026-07-10T23:35:31.691Z", "statusMatches": true, "differenceSeconds": 0.07992291450500488, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -0.002157541166525334, "passed": true, "input": { "natalUTC": "1975-07-11T15:37:00Z", "startUTC": "2026-01-01T00:00:00Z", "endUTC": "2027-02-05T00:00:00Z", "body": "Sun" }, "natalReferenceTTJulianDate": 2442605.1512289816 }, { "id": "synthetic-1975-sun-subsequent", "body": "Sun", "classification": "strict-comparison", "expectedUtc": "2027-07-11T05:16:12.259369Z", "actualUtc": "2027-07-11T05:16:12.174Z", "statusMatches": true, "differenceSeconds": 0.08536887168884277, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -0.002157541166525334, "passed": true, "input": { "natalUTC": "1975-07-11T15:37:00Z", "startUTC": "2026-07-11T23:35:31.770923Z", "endUTC": "2027-08-15T23:35:31.770923Z", "body": "Sun" }, "natalReferenceTTJulianDate": 2442605.1512289816 }, { "id": "synthetic-1975-sun-no-crossing", "body": "Sun", "classification": "strict-comparison", "expectedUtc": null, "actualUtc": null, "statusMatches": true, "differenceSeconds": null, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -0.002157541166525334, "passed": true, "input": { "natalUTC": "1975-07-11T15:37:00Z", "startUTC": "2026-07-11T00:35:31.770923Z", "endUTC": "2026-07-11T01:35:31.770923Z", "body": "Sun" }, "natalReferenceTTJulianDate": 2442605.1512289816 }, { "id": "synthetic-1975-moon-first", "body": "Moon", "classification": "strict-comparison", "expectedUtc": "2026-01-06T03:44:01.042458Z", "actualUtc": "2026-01-06T03:44:01.036Z", "statusMatches": true, "differenceSeconds": 0.0064580440521240234, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -0.001508378727521631, "passed": true, "input": { "natalUTC": "1975-07-11T15:37:00Z", "startUTC": "2026-01-01T00:00:00Z", "endUTC": "2026-02-05T00:00:00Z", "body": "Moon" }, "natalReferenceTTJulianDate": 2442605.1512289816 }, { "id": "synthetic-1975-moon-subsequent", "body": "Moon", "classification": "strict-comparison", "expectedUtc": "2026-02-02T14:15:03.671851Z", "actualUtc": "2026-02-02T14:15:03.663Z", "statusMatches": true, "differenceSeconds": 0.008850812911987305, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -0.001508378727521631, "passed": true, "input": { "natalUTC": "1975-07-11T15:37:00Z", "startUTC": "2026-01-07T03:44:01.042458Z", "endUTC": "2026-02-11T03:44:01.042458Z", "body": "Moon" }, "natalReferenceTTJulianDate": 2442605.1512289816 }, { "id": "synthetic-1975-moon-no-crossing", "body": "Moon", "classification": "strict-comparison", "expectedUtc": null, "actualUtc": null, "statusMatches": true, "differenceSeconds": null, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -0.001508378727521631, "passed": true, "input": { "natalUTC": "1975-07-11T15:37:00Z", "startUTC": "2026-01-06T04:44:01.042458Z", "endUTC": "2026-01-06T05:44:01.042458Z", "body": "Moon" }, "natalReferenceTTJulianDate": 2442605.1512289816 }, { "id": "synthetic-1988-sun-first", "body": "Sun", "classification": "strict-comparison", "expectedUtc": "2026-09-22T22:36:21.268194Z", "actualUtc": "2026-09-22T22:36:21.284Z", "statusMatches": true, "differenceSeconds": 0.015805959701538086, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": 0.0008258712114184164, "passed": true, "input": { "natalUTC": "1988-09-22T18:00:00Z", "startUTC": "2026-01-01T00:00:00Z", "endUTC": "2027-02-05T00:00:00Z", "body": "Sun" }, "natalReferenceTTJulianDate": 2447427.250650278 }, { "id": "synthetic-1988-sun-subsequent", "body": "Sun", "classification": "strict-comparison", "expectedUtc": "2027-09-23T04:32:52.913017Z", "actualUtc": "2027-09-23T04:32:52.935Z", "statusMatches": true, "differenceSeconds": 0.021982908248901367, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": 0.0008258712114184164, "passed": true, "input": { "natalUTC": "1988-09-22T18:00:00Z", "startUTC": "2026-09-23T22:36:21.268194Z", "endUTC": "2027-10-28T22:36:21.268194Z", "body": "Sun" }, "natalReferenceTTJulianDate": 2447427.250650278 }, { "id": "synthetic-1988-sun-no-crossing", "body": "Sun", "classification": "strict-comparison", "expectedUtc": null, "actualUtc": null, "statusMatches": true, "differenceSeconds": null, 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"2026-02-16T14:27:25.095Z", "statusMatches": true, "differenceSeconds": 0.00049591064453125, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": 0.0031220993150782306, "passed": true, "input": { "natalUTC": "1988-09-22T18:00:00Z", "startUTC": "2026-01-21T06:45:55.581809Z", "endUTC": "2026-02-25T06:45:55.581809Z", "body": "Moon" }, "natalReferenceTTJulianDate": 2447427.250650278 }, { "id": "synthetic-1988-moon-no-crossing", "body": "Moon", "classification": "strict-comparison", "expectedUtc": null, "actualUtc": null, "statusMatches": true, "differenceSeconds": null, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": 0.0031220993150782306, "passed": true, "input": { "natalUTC": "1988-09-22T18:00:00Z", "startUTC": "2026-01-20T07:45:55.581809Z", "endUTC": "2026-01-20T08:45:55.581809Z", "body": "Moon" }, "natalReferenceTTJulianDate": 2447427.250650278 }, { "id": "synthetic-2000-sun-first", "body": "Sun", "classification": "strict-comparison", "expectedUtc": 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}, "natalReferenceTTJulianDate": 2451711.0007428704 }, { "id": "equinox-2024-sun-first", "body": "Sun", "classification": "strict-comparison", "expectedUtc": "2026-03-20T14:45:33.306506Z", "actualUtc": "2026-03-20T14:45:33.314Z", "statusMatches": true, "differenceSeconds": 0.0074939727783203125, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": 0.0005814400992676383, "passed": true, "input": { "natalUTC": "2024-03-20T03:06:00Z", "startUTC": "2026-01-01T00:00:00Z", "endUTC": "2027-02-05T00:00:00Z", "body": "Sun" }, "natalReferenceTTJulianDate": 2460389.6299674073 }, { "id": "equinox-2024-sun-subsequent", "body": "Sun", "classification": "strict-comparison", "expectedUtc": "2027-03-20T20:24:17.172289Z", "actualUtc": "2027-03-20T20:24:17.190Z", "statusMatches": true, "differenceSeconds": 0.017711162567138672, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": 0.0005814400992676383, "passed": true, "input": { "natalUTC": "2024-03-20T03:06:00Z", "startUTC": "2026-03-21T14:45:33.306506Z", "endUTC": "2027-04-25T14:45:33.306506Z", "body": "Sun" }, "natalReferenceTTJulianDate": 2460389.6299674073 }, { "id": "equinox-2024-sun-no-crossing", "body": "Sun", "classification": "strict-comparison", "expectedUtc": null, "actualUtc": null, "statusMatches": true, "differenceSeconds": null, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": 0.0005814400992676383, "passed": true, "input": { "natalUTC": "2024-03-20T03:06:00Z", "startUTC": "2026-03-20T15:45:33.306506Z", "endUTC": "2026-03-20T16:45:33.306506Z", "body": "Sun" }, "natalReferenceTTJulianDate": 2460389.6299674073 }, { "id": "equinox-2024-moon-first", "body": "Moon", "classification": "strict-comparison", "expectedUtc": "2026-01-04T20:03:12.887776Z", "actualUtc": "2026-01-04T20:03:12.888Z", "statusMatches": true, "differenceSeconds": 0.00022411346435546875, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": 0.0030390398933377583, "passed": true, "input": { "natalUTC": "2024-03-20T03:06:00Z", "startUTC": "2026-01-01T00:00:00Z", "endUTC": "2026-02-05T00:00:00Z", "body": "Moon" }, "natalReferenceTTJulianDate": 2460389.6299674073 }, { "id": "equinox-2024-moon-subsequent", "body": "Moon", "classification": "strict-comparison", "expectedUtc": "2026-02-01T06:32:22.034381Z", "actualUtc": "2026-02-01T06:32:22.032Z", "statusMatches": true, "differenceSeconds": 0.002380847930908203, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": 0.0030390398933377583, "passed": true, "input": { "natalUTC": "2024-03-20T03:06:00Z", "startUTC": "2026-01-05T20:03:12.887776Z", "endUTC": "2026-02-09T20:03:12.887776Z", "body": "Moon" }, "natalReferenceTTJulianDate": 2460389.6299674073 }, { "id": "equinox-2024-moon-no-crossing", "body": "Moon", "classification": "strict-comparison", "expectedUtc": null, "actualUtc": null, "statusMatches": true, "differenceSeconds": null, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": 0.0030390398933377583, "passed": true, "input": { "natalUTC": "2024-03-20T03:06:00Z", "startUTC": "2026-01-04T21:03:12.887776Z", "endUTC": "2026-01-04T22:03:12.887776Z", "body": "Moon" }, "natalReferenceTTJulianDate": 2460389.6299674073 }, { "id": "historical-1950-ut1-sun-first", "body": "Sun", "classification": "strict-historical-ut1", "expectedUtc": "2026-03-20T10:11:02.434509Z", "actualUtc": "2026-03-20T10:11:02.383Z", "statusMatches": true, "differenceSeconds": 0.05150914192199707, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -0.0020001087250420824, "passed": true, "input": { "natalUTC": "1950-03-21T00:00:00Z", "natalTimeScale": "UT1", "natalUT1Calendar": "1950-03-21T00:00:00", "natalUTCFieldMeaning": "Nominal calendar label only; interpret as UT1, not UTC", "startUTC": "2026-01-01T00:00:00Z", "endUTC": "2027-02-05T00:00:00Z", "body": "Sun" }, "natalReferenceTTJulianDate": 2433361.5003358135 }, { "id": "historical-1950-ut1-sun-subsequent", "body": "Sun", "classification": "strict-historical-ut1", "expectedUtc": "2027-03-20T15:49:34.996390Z", "actualUtc": "2027-03-20T15:49:34.952Z", "statusMatches": true, "differenceSeconds": 0.044390201568603516, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -0.0020001087250420824, "passed": true, "input": { "natalUTC": "1950-03-21T00:00:00Z", "natalTimeScale": "UT1", "natalUT1Calendar": "1950-03-21T00:00:00", "natalUTCFieldMeaning": "Nominal calendar label only; interpret as UT1, not UTC", "startUTC": "2026-03-21T10:11:02.434509Z", "endUTC": "2027-04-25T10:11:02.434509Z", "body": "Sun" }, "natalReferenceTTJulianDate": 2433361.5003358135 }, { "id": "historical-1950-ut1-sun-no-crossing", "body": "Sun", "classification": "strict-historical-ut1", "expectedUtc": null, "actualUtc": null, "statusMatches": true, "differenceSeconds": null, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -0.0020001087250420824, "passed": true, "input": { "natalUTC": "1950-03-21T00:00:00Z", "natalTimeScale": "UT1", "natalUT1Calendar": "1950-03-21T00:00:00", "natalUTCFieldMeaning": "Nominal calendar label only; interpret as UT1, not UTC", "startUTC": "2026-03-20T11:11:02.434509Z", "endUTC": "2026-03-20T12:11:02.434509Z", "body": "Sun" }, "natalReferenceTTJulianDate": 2433361.5003358135 }, { "id": "historical-1950-ut1-moon-first", "body": "Moon", "classification": "strict-historical-ut1", "expectedUtc": "2026-01-25T10:48:30.600629Z", "actualUtc": "2026-01-25T10:48:30.596Z", "statusMatches": true, "differenceSeconds": 0.0046291351318359375, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -0.00032509465199836995, "passed": true, "input": { "natalUTC": "1950-03-21T00:00:00Z", "natalTimeScale": "UT1", "natalUT1Calendar": "1950-03-21T00:00:00", "natalUTCFieldMeaning": "Nominal calendar label only; interpret as UT1, not UTC", "startUTC": "2026-01-01T00:00:00Z", "endUTC": "2026-02-05T00:00:00Z", "body": "Moon" }, "natalReferenceTTJulianDate": 2433361.5003358135 }, { "id": "historical-1950-ut1-moon-subsequent", "body": "Moon", "classification": "strict-historical-ut1", "expectedUtc": "2026-02-21T16:17:59.754394Z", "actualUtc": "2026-02-21T16:17:59.749Z", "statusMatches": true, "differenceSeconds": 0.00539398193359375, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -0.00032509465199836995, "passed": true, "input": { "natalUTC": "1950-03-21T00:00:00Z", "natalTimeScale": "UT1", "natalUT1Calendar": "1950-03-21T00:00:00", "natalUTCFieldMeaning": "Nominal calendar label only; interpret as UT1, not UTC", "startUTC": "2026-01-26T10:48:30.600629Z", "endUTC": "2026-03-02T10:48:30.600629Z", "body": "Moon" }, "natalReferenceTTJulianDate": 2433361.5003358135 }, { "id": "historical-1950-ut1-moon-no-crossing", "body": "Moon", "classification": "strict-historical-ut1", "expectedUtc": null, "actualUtc": null, "statusMatches": true, "differenceSeconds": null, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -0.00032509465199836995, "passed": true, "input": { "natalUTC": "1950-03-21T00:00:00Z", "natalTimeScale": "UT1", "natalUT1Calendar": "1950-03-21T00:00:00", "natalUTCFieldMeaning": "Nominal calendar label only; interpret as UT1, not UTC", "startUTC": "2026-01-25T11:48:30.600629Z", "endUTC": "2026-01-25T12:48:30.600629Z", "body": "Moon" }, "natalReferenceTTJulianDate": 2433361.5003358135 } ], "historicalClockDiagnostics": [ { "id": "historical-1950-sun-first", "body": "Sun", "classification": "historical-timescale-diagnostic", "expectedUtc": "2026-03-20T10:11:15.594928Z", "actualUtc": "2026-03-20T10:11:02.383Z", "statusMatches": true, "differenceSeconds": 13.211928129196167, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -0.547124657259701, "passed": false, "swissNatalTT": 2433361.500335812, "referenceNatalTT": 2433361.5004882407, "natalTTDifferenceSeconds": -13.169834017753601, "matchedTTTargetDifferenceArcseconds": -0.00200655067601474, "scope": "Diagnostic only: different pre-1972 calendar clock conventions. 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Matched-TT target comparison is separately recorded." }, { "id": "historical-1950-sun-no-crossing", "body": "Sun", "classification": "historical-timescale-diagnostic", "expectedUtc": null, "actualUtc": null, "statusMatches": true, "differenceSeconds": null, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -0.547124657259701, "passed": true, "swissNatalTT": 2433361.500335812, "referenceNatalTT": 2433361.5004882407, "natalTTDifferenceSeconds": -13.169834017753601, "matchedTTTargetDifferenceArcseconds": -0.00200655067601474, "scope": "Diagnostic only: different pre-1972 calendar clock conventions. Matched-TT target comparison is separately recorded." }, { "id": "historical-1950-moon-first", "body": "Moon", "classification": "historical-timescale-diagnostic", "expectedUtc": "2026-01-25T10:48:41.877936Z", "actualUtc": "2026-01-25T10:48:30.596Z", "statusMatches": true, "differenceSeconds": 11.281935930252075, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -6.511323306403938, "passed": false, "swissNatalTT": 2433361.500335812, "referenceNatalTT": 2433361.5004882407, "natalTTDifferenceSeconds": -13.169834017753601, "matchedTTTargetDifferenceArcseconds": -0.0004097043984074844, "scope": "Diagnostic only: different pre-1972 calendar clock conventions. Matched-TT target comparison is separately recorded." }, { "id": "historical-1950-moon-subsequent", "body": "Moon", "classification": "historical-timescale-diagnostic", "expectedUtc": "2026-02-21T16:18:10.917520Z", "actualUtc": "2026-02-21T16:17:59.749Z", "statusMatches": true, "differenceSeconds": 11.168519973754883, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -6.511323306403938, "passed": false, "swissNatalTT": 2433361.500335812, "referenceNatalTT": 2433361.5004882407, "natalTTDifferenceSeconds": -13.169834017753601, "matchedTTTargetDifferenceArcseconds": -0.0004097043984074844, "scope": "Diagnostic only: different pre-1972 calendar clock conventions. Matched-TT target comparison is separately recorded." }, { "id": "historical-1950-moon-no-crossing", "body": "Moon", "classification": "historical-timescale-diagnostic", "expectedUtc": null, "actualUtc": null, "statusMatches": true, "differenceSeconds": null, "toleranceSeconds": 2, "natalTargetDifferenceArcseconds": -6.511323306403938, "passed": true, "swissNatalTT": 2433361.500335812, "referenceNatalTT": 2433361.5004882407, "natalTTDifferenceSeconds": -13.169834017753601, "matchedTTTargetDifferenceArcseconds": -0.0004097043984074844, "scope": "Diagnostic only: different pre-1972 calendar clock conventions. Matched-TT target comparison is separately recorded." } ], "endpointChecks": { "independentMarginChecks": 40, "sameEngineMillisecondBoundaryPairs": 20, "scope": "Independent ±5-second root margins; separate same-engine exact rounded end inclusion and start exclusion. Reference and product endpoint intervals differ, so exact endpoint checks are not independent accuracy evidence." }, "limitations": [ "Synthetic samples, not all supported dates. Modern births1975–2024 plus a1950UT1 sample; searches start2026.", "Tropical only. Sidereal frames, houses, relocation and interpretive validity are outside this reference check.", "Two astronomy implementations with related JPL ephemeris ancestry; agreement is model comparison, not observational certification.", "Original1950 proleptic-UTC diagnostics differ because their input physical instants differ; they remain separate from matched-UT1 acceptance." ], "sources": [ { "title": "Swiss Ephemeris · UTC and Julian days, §9.3", "url": "https://www.astro.com/swisseph/swephprg.htm" }, { "title": "Skyfield · ecliptic coordinates", "url": "https://rhodesmill.org/skyfield/coordinates.html#ecliptic-coordinates" }, { "title": "Skyfield · time scales", "url": "https://rhodesmill.org/skyfield/time.html" } ] }