Calculadora lunar — versão científica

{
    "response_schema_version": "2.0",
    "computational_metadata": {
        "engine": {
            "name": "OC Scientific Lunar Engine",
            "version": "2.0.0",
            "ephemeris_model": "OCSE-Lite-2026A"
        },
        "computed_at_utc": "2026-04-28T06:36:37Z",
        "runtime_seconds": 0.4257,
        "preconditions": {
            "time_input_assumed_utc": true,
            "observer_input_assumed_wgs84": true,
            "output_legacy_v1_available": true
        }
    },
    "provenance": {
        "moon_ephemeris": {
            "algorithm": "ELP-2000/82B (Chapront-Touzé & Chapront 1983)",
            "truncation": "Meeus Astronomical Algorithms 1998 — main problem 60 terms",
            "reference": "Meeus J., Astronomical Algorithms (2nd ed.), Willmann-Bell 1998, ch. 47",
            "accuracy_class": "truncated-research-grade"
        },
        "sun_ephemeris": {
            "algorithm": "VSOP87D (Bretagnon & Francou 1988)",
            "truncation": "58 terms (35 L + 7 B + 16 R)",
            "reference": "Bretagnon P., Francou G., A&A 202, 309 (1988)",
            "accuracy_class": "truncated-research-grade"
        },
        "nutation_model": {
            "algorithm": "IAU 1980",
            "truncation": "63 terms",
            "reference": "Wahr 1981; Seidelmann 1982",
            "accuracy_class": "pre-2000"
        },
        "aberration_model": {
            "algorithm": "Annual aberration low-order",
            "reference": "Meeus 1998 ch. 23",
            "accuracy_class": "simplified"
        },
        "delta_t_model": {
            "algorithm": "Espenak-Meeus polynomial",
            "reference": "Espenak F., Meeus J., NASA TP-2009-214174",
            "range_years": "4000 BC to 3000 AD"
        },
        "refraction_model": {
            "algorithm": "Bennett 1982",
            "reference": "Bennett G.G., Journal of Navigation 35:255",
            "accuracy_class": "standard for visual altitudes"
        },
        "rise_set_solver": {
            "algorithm": "Adaptive scan + bisection root-finding",
            "description": "Adaptive step + bisection root-finding with dynamic threshold (upper-limb/center, dip, refraction, parallax)."
        },
        "phase_calculation": {
            "algorithm": "Phase-angle photometry (k = (1+cos i)/2)",
            "description": "Elongation + phase-angle photometry (k = (1 + cos(i)) / 2)."
        }
    },
    "input_echo": null,
    "normalized_input": {
        "latitude_deg": -23.5505,
        "longitude_deg": -46.6333,
        "altitude_m": 760,
        "pressure_hpa": 1013.25,
        "temperature_c": 10,
        "humidity_pct": 50,
        "timezone": "UTC",
        "ut1_minus_utc_seconds": 0,
        "observer_mode": "topocentric",
        "reference_frame": "ICRF/J2000",
        "use_refraction": true,
        "rise_set_disc": "upper_limb",
        "rise_set_refraction_deg": 0.5667,
        "event_step_seconds": 300,
        "tai_minus_utc_seconds": 37,
        "delta_t_mode": "auto",
        "delta_t_seconds": 69,
        "tracking_interval_seconds": 60,
        "birth_date_iso": "",
        "polar_motion_xp_arcsec": null,
        "polar_motion_yp_arcsec": null,
        "wavelength_nm": 590,
        "refraction_model": "bennett",
        "use_wgs84_parallax": false,
        "ephemeris_mode": "lite",
        "nutation_model": "iau1980",
        "hemisphere_override": "auto",
        "calendar_system": "gregorian",
        "display_mode": "standard"
    },
    "time_scales": {
        "utc_iso": "2026-04-28T06:36:00Z",
        "local_iso": "2026-04-28T06:36:00+00:00",
        "jd": {
            "utc": 2461158.775,
            "ut1": 2461158.775,
            "tai": 2461158.7754282407,
            "tt": 2461158.7758689187,
            "tdb": 2461158.7758689364
        },
        "mjd_utc": 61158.27499999991,
        "delta_t_seconds": 75.074584,
        "delta_t_mode": "auto",
        "ut1_minus_utc_seconds": 0,
        "tai_minus_utc_seconds": 37,
        "tdb_minus_tt_seconds": 0.0015176320704436766,
        "tdb_method": "Fairhead-Bretagnon (IAU 2006), ~10 µs accuracy",
        "leap_seconds_default": 37,
        "local_sidereal_deg": 268.619354,
        "local_sidereal_hms": "17:54:29"
    },
    "observer_geodetic": {
        "latitude_deg": -23.5505,
        "longitude_deg": -46.6333,
        "altitude_m": 760,
        "datum": "WGS84",
        "flattening": 0.0033528106647474805,
        "semi_major_axis_km": 6378.137
    },
    "observer_geocentric": {
        "x_km": 4017.481522,
        "y_km": -4253.316605,
        "z_km": -2533.027841,
        "radius_km": 6375.507036,
        "geocentric_latitude_deg": -23.409877489,
        "derivation": "WGS84: N(φ) = a/√(1−e²sin²φ); X = (N+h)cosφcosλ; Y = (N+h)cosφsinλ; Z = (N(1−e²)+h)sinφ"
    },
    "earth_orientation": {
        "polar_motion_xp_arcsec": {
            "value": null,
            "explanation": "Polar motion not implemented; xp=0 assumed."
        },
        "polar_motion_yp_arcsec": {
            "value": null,
            "explanation": "Polar motion not implemented; yp=0 assumed."
        },
        "ut1_minus_utc_seconds": 0,
        "tai_minus_utc_seconds": 37
    },
    "reference_frames": {
        "primary": "ICRF/J2000",
        "epoch": "J2000.0",
        "mean_obliquity_deg": 23.435868272,
        "true_obliquity_deg": 23.438257212
    },
    "ephemeris_model": {
        "moon": {
            "engine": "ELP-2000/82B-truncated",
            "terms": 60,
            "version": "OCSE-Lite-2026A",
            "accuracy_class_documented": "truncated-research-grade"
        },
        "sun": {
            "engine": "VSOP87D-truncated",
            "terms": 58,
            "version": "OCSE-Lite-2026A",
            "accuracy_class_documented": "truncated-research-grade"
        },
        "nutation": {
            "engine": "IAU-1980",
            "terms": 63,
            "mode": "iau1980"
        }
    },
    "sun_state": {
        "apparent_geocentric": {
            "ra_deg": 35.630786,
            "dec_deg": 14.174074,
            "lambda_deg": 37.996948,
            "distance_au": 1.00669873,
            "distance_km": 150599986.407
        }
    },
    "moon_state": {
        "apparent_corrections": {
            "nutation_longitude_deg": 0.001612847,
            "nutation_obliquity_deg": 0.00238894,
            "annual_aberration_longitude_deg": -0.005653738,
            "true_obliquity_deg": 23.438257212
        },
        "orientation": {
            "colongitude_deg": 230.712215,
            "libration_longitude_deg_approx": 6.322885,
            "libration_latitude_deg_approx": -1.523224,
            "subsolar_lon_deg_approx": -39.287785,
            "subsolar_lat_deg_approx": 1.856299,
            "subobserver_lon_deg_approx": 140.712215,
            "subobserver_lat_deg_approx": 0.92815
        },
        "angular_diameter_arcmin": 30.4721,
        "horizontal_parallax_deg": 0.932261
    },
    "astrometric_coordinates": {
        "frame": "mean equator and equinox of date (no nutation, no aberration)",
        "note": "Engine ELP output before annual aberration and nutation corrections. For ICRF J2000 astrometric, apply precession from t to J2000 (Phase 3 deliverable).",
        "ra_deg": 178.081137,
        "dec_deg": -1.191476,
        "lambda_deg": 178.713201,
        "beta_deg": -1.856299,
        "distance_km": 392010.721
    },
    "apparent_coordinates": {
        "frame": "true equator and equinox of date (with nutation + annual aberration)",
        "ra_deg": 178.077384,
        "dec_deg": -1.189791,
        "lambda_deg": 178.709163,
        "beta_deg": -1.856299,
        "distance_km": 392010.721,
        "distance_earth_radii": 61.461634
    },
    "topocentric_coordinates": {
        "frame": "topocentric apparent (parallax + refraction applied where enabled)",
        "distance_km": 392064.994,
        "distance_earth_radii": 61.470143,
        "parallax_correction_deg": null,
        "horizontal_parallax_deg": 0.932261
    },
    "horizontal_coordinates": {
        "frame": "local horizon, observer-centered",
        "altitude_geometric_deg": -0.953731,
        "altitude_apparent_deg": -0.318994,
        "azimuth_deg": 268.692776,
        "hour_angle_deg": 90.54197,
        "refraction_deg": 0.634737,
        "azimuth_convention": "north=0, east=90 (clockwise)"
    },
    "state_vectors": {
        "moon_geocentric_equator_of_date_km": {
            "x": -391705.569,
            "y": 13149,
            "z": -8139.82,
            "magnitude_km": 392010.721
        },
        "moon_geocentric_velocity_km_s": {
            "value": null,
            "explanation": "Velocity not provided: caller must pass v1_at_plus_dt option (engine output at t+Δt) for finite-difference derivation."
        },
        "moon_topocentric_enu_km": {
            "east_km": -391956.881,
            "north_km": -8944.19,
            "up_km": -2182.809,
            "range_km": 392064.994,
            "range_rate_km_s": {
                "value": null,
                "explanation": "Topocentric range-rate requires Δt sample of distance + observer rotation; deferred to Phase 2 TopocentricTransformer service."
            },
            "frame": "local horizon ENU (east, north, up) at observer position",
            "azimuth_convention": "north=0, east=90 (clockwise)"
        },
        "frame_note": "Position vector referred to equator and equinox of date (mean equinox + nutation already in apparent RA/Dec). For ICRF J2000 conversion, apply precession from t to J2000 — Phase 3 deliverable."
    },
    "phase_geometry": {
        "name": "Crescente Gibosa",
        "fraction_0_1": 0.39086726,
        "age_days": 11.54254,
        "elongation_deg": 140.675476,
        "phase_angle_deg": 39.230202,
        "illumination_pct": 88.730561,
        "bright_limb_position_angle_deg": 291.169901,
        "parallactic_angle_deg": 113.556371
    },
    "rise_set_transit": {
        "moonrise_local": "18:46:48",
        "moonset_local": "06:36:12",
        "transit_local": "23:59:59",
        "transit_altitude_deg": 65.989361,
        "transit_local_sidereal_deg": 170.32977,
        "transit_local_sidereal_hms": "11:21:19",
        "event_timezone": "UTC",
        "rise_set_status": "normal",
        "rise_set_method": "adaptive-scan+binary-root",
        "horizon_threshold_deg": -0.696007,
        "horizon_components": {
            "disc_mode": "upper_limb",
            "semi_diameter_deg": 0.253934,
            "dip_deg": 0.807745,
            "refraction_deg": 0.5667,
            "parallax_deg": 0.932372
        }
    },
    "tracking_rates": {
        "interval_seconds": 60,
        "dra_deg_per_min": 0.00775913,
        "ddec_deg_per_min": -0.004153246,
        "dalt_deg_per_min": -0.855691858,
        "daz_deg_per_min": -0.100881915,
        "dra_arcsec_per_sec": 0.465547787,
        "ddec_arcsec_per_sec": -0.249194746,
        "dalt_arcsec_per_sec": -51.341511492,
        "daz_arcsec_per_sec": -6.052914922
    },
    "uncertainty_budget": {
        "components": {
            "model_truncation": {
                "ra_arcsec": {
                    "value": 23.04,
                    "method": "JPL Horizons benchmark P95 (mean=18.453, max=53.654)."
                },
                "dec_arcsec": {
                    "value": 8.2188,
                    "method": "JPL Horizons benchmark P95 (mean=4.911, max=24.696)."
                },
                "distance_km": {
                    "value": 39.837,
                    "method": "JPL Horizons benchmark P95 (mean=25.341, max=45.568)."
                },
                "illumination_pp": {
                    "value": 0.0112,
                    "method": "JPL Horizons benchmark P95 (mean=0.024, max=0.673)."
                }
            },
            "delta_t_contribution": {
                "ra_arcsec": {
                    "value": null,
                    "explanation": "ΔT (TT−UT1) computed via Espenak-Meeus polynomial. Uncertainty depends on date: ±1s for 1900-2030, ±10s for 1700-1900, larger before 1700. Translates to ~0.5 arcsec/s through Moon mean motion."
                }
            },
            "ut1_contribution": {
                "ra_arcsec": {
                    "value": null,
                    "explanation": "No IERS Bulletin A integration. UT1−UTC accepted as manual override only; defaults to 0. Real-world value can be ±0.5s, contributing ~0.25 arcsec to RA via Earth rotation."
                }
            },
            "polar_motion_contribution": {
                "altitude_arcsec": {
                    "value": 0.3,
                    "method": "Polar motion (xp, yp) wired in TopocentricTransformer but defaulted to zero. Residual error ±0.3 arcsec corresponds to typical IERS Bulletin A magnitude. Provide xp_arcsec/yp_arcsec to reduce."
                },
                "azimuth_arcsec": {
                    "value": 0.3,
                    "method": "Same magnitude as altitude component near horizon (zero at zenith)."
                }
            },
            "observer_location_contribution": {
                "altitude_arcsec": {
                    "value": 0.5,
                    "method": "WGS84 ellipsoid, lat/lon precision ±0.0001° (~11 m). Geocentric radius computed from N(φ) = a/√(1−e²sin²φ)."
                }
            },
            "refraction_contribution": {
                "altitude_arcsec": {
                    "value": 30.64,
                    "method": "Bennett 1982 atmospheric refraction; uncertainty ~31 arcsec at altitude -0.3°. Driven by atmospheric model assumptions (T=20°C, P=1013 hPa, RH=60%)."
                }
            },
            "horizon_model_contribution": {
                "rise_set_seconds": {
                    "value": 60,
                    "method": "Upper-limb (default) vs center contributes ~30s; no local horizon profile contributes ~30s for hilly terrain."
                }
            },
            "numerical_solver_contribution": {
                "rise_set_seconds": {
                    "value": 5,
                    "method": "Bisection root-finder, 24 iterations — converges to ~0.01s on a smooth altitude curve. Adaptive scan step is 300s."
                }
            },
            "parallax_geocentric_topocentric": {
                "distance_km": {
                    "value": null,
                    "explanation": "Topocentric mode: parallax already applied; no additional uncertainty."
                }
            }
        },
        "totals_p95": {
            "ra_arcsec": 23.04,
            "dec_arcsec": 8.2188,
            "distance_km": 39.837,
            "illumination_pp": 0.0112,
            "altitude_arcsec_estimate": 38.34,
            "azimuth_arcsec_estimate": 23.04,
            "rise_set_seconds_estimate": 90.2
        },
        "methodology_note": "Components are summed in quadrature only when independent. Total RA/Dec uses the measured benchmark P95 directly (already a real-world envelope).",
        "benchmark_provenance": {
            "available": true,
            "snapshot_path": null,
            "rows_evaluated": 322,
            "engine_version_at_measurement": "2.0.0",
            "measured_at_utc": "2026-04-28T00:49:20Z",
            "measurement_method": "JPL Horizons DE441 ephemeris, observer_apparent of date, 322 epoch points 1969-2030"
        }
    },
    "validation": {
        "measurement_method": "JPL Horizons DE441 ephemeris, observer_apparent of date, 322 epoch points 1969-2030",
        "benchmark_available": true,
        "benchmark_snapshot_path": null,
        "benchmark_rows_evaluated": 322,
        "benchmark_measured_at_utc": "2026-04-28T00:49:20Z",
        "engine_version_at_measurement": "2.0.0",
        "measured_p95": {
            "ra_arcsec": 23.04,
            "dec_arcsec": 8.2188,
            "distance_km": 39.837,
            "illumination_pp": 0.0112
        }
    },
    "warnings": [],
    "data_quality_flags": {
        "benchmark_snapshot_loaded": true,
        "polar_motion_assumed_zero": true,
        "ut1_minus_utc_assumed_zero": true,
        "refraction_applied": true,
        "topocentric_mode": true
    }
}