{ "date": "2026-04-07", "daysFromEpoch": 309734, "sun": { "meanLongitude": 15.515370000000985, "trueLongitude": 17.479178118519485, "apogee": 99.65780555555557, "maslul": 275.8575644444454, "maslulCorrection": 1.9638081185185152, "constellation": { "index": 0, "hebrew": "טלה", "translit": "Taleh", "english": "Aries", "symbol": "♈", "positionInConstellation": 17.479178118519485, "degreesInto": 17.479178118519485, "ordinalDegree": 18, "normalized": 17.479178118519485 } }, "moon": { "meanLongitude": 249.4622222222224, "adjustedMeanLongitude": 249.7122222222224, "trueLongitude": 249.53168981481497, "maslul": 353.16638888888883, "doubleElongation": 108.39370444444285, "maslulHanachon": 2.1663888888888323, "maslulCorrection": 0.1805324074074027, "latitude": -4.9852822145061655, "nodePosition": 337.7655555555548, "constellation": { "index": 8, "hebrew": "קשת", "translit": "Keshet", "english": "Sagittarius", "symbol": "♐", "positionInConstellation": 9.531689814814968, "degreesInto": 9.531689814814968, "ordinalDegree": 10, "normalized": 249.53168981481497 }, "phase": "Waning Gibbous", "phaseHebrew": "גיבוס הולך ופוחת", "elongation": 232.05251169629548, "orechSheni": 231.4525116962955, "rochavSheni": -5.718615547839499, "orechShlishi": 230.4994091049889, "orechRevii": 230.4994091049889, "mnatGovahHaMedinah": 3.3235214763374437, "keshetHaReiyah": 227.17588762865145, "firstVisibilityAngle": 233.54809636064732, "isVisible": true, "visibilityVerdict": "visible", "visibilityPath": "Early exit (KH 17:4): אורך ראשון = 232.053° > 24° → ודאי יראה.", "illumination": 0.8074695017138505 }, "season": { "currentSeason": "Spring (אביב)", "daysUntilNextSeason": 90 }, "steps": [ { "id": "daysFromEpoch", "name": "Days from Epoch", "hebrewName": "ימים מתחילת המניין", "rambamRef": "KH 11:16", "formula": "HDate(date).abs() − HDate(3 Nisan 4938).abs()", "result": 309734, "unit": "days", "sourceNote": "Epoch date (3 Nisan 4938 AM, ליל חמישי) directly from the Rambam. This is an INTEGER civil-day count from the fixed calendar (KH 6-10) — NOT mean-synodic time. The two drift apart by ~0.13 day over 848 years. See \"Methodology notes\" link for the full writeup." }, { "id": "sunDailyMotion", "name": "Sun Daily Motion", "hebrewName": "מהלך אמצע השמש ליום", "rambamRef": "KH 12:1", "formula": "0° + 59'/60 + 8.333\"/3600", "result": 0.9856480555555555, "unit": "deg/day", "sourceNote": "Nun Tes Ches (59' 8\") — the combined motion of both the blue and red galgalim together.", "teachingNote": "This is NOT the motion of the red galgal alone, nor the blue alone. It is the sum total of both. The blue moves extremely slowly (~1°/70 years). The red carries the bulk of the motion. Together: 0° 59' 8 1/3\" per day." }, { "id": "sunMeanLongitude", "name": "Sun Mean Longitude", "hebrewName": "אמצע השמש", "rambamRef": "KH 12:1", "formula": "startPos + 30×10000d + 9×1000d + 7×100d + 3×10d + 4×1d (mod 360)", "result": 15.515370000000985, "formatted": "15° 30′ 55.3″", "unit": "degrees", "sourceNote": "Position at epoch = 7°3'32\" in Aries (KH 12:2). Computed via the Rambam's period-block method (KH 12:1) — decompose N days into 10,000 / 1,000 / 100 / 10 / remainder blocks and sum their motions from the published tables.", "teachingNote": "The emtzoi: where the sun appears in the mazalos if you were standing at the CENTER OF THE RED GALGAL. Since the red's center is not at Earth, this is NOT where we see the sun. But it is the essential first step — \"first know the sun's own language, then translate to ours.\" (Rabbi Losh)" }, { "id": "sunApogee", "name": "Sun's Apogee (Govah)", "hebrewName": "גובה השמש", "rambamRef": "KH 12:2", "formula": "apogeeStart + 30×10000d + 9×1000d + 7×100d + 3×10d + 4×1d (mod 360)", "result": 99.65780555555557, "formatted": "99° 39′ 28.1″", "unit": "degrees", "sourceNote": "Starting position at epoch (26° 45' 8\" in Gemini). Motion per the Rambam's period-block tables (KH 12:2): 1.5\" per 10 days, 15\" per 100 days, 2'30\" per 1000 days, 25' per 10000 days.", "teachingNote": "The govah is the point on the red galgal that is FURTHEST from Earth (because the red is off-center in the blue). It moves very slowly — about 1° every 70 years. This is the motion of the BLUE galgal. When the sun is at the govah, it appears to us to move slower (covering fewer degrees per day) because it is further away. Rabbi Losh's airplane mashal: a plane at high altitude seems to crawl, but at low altitude the same speed looks blazing fast." }, { "id": "sunMaslul", "name": "Sun Maslul (Course)", "hebrewName": "מסלול השמש", "rambamRef": "KH 13:1-3", "formula": "(meanLongitude − apogee + 360) mod 360", "result": 275.8575644444454, "formatted": "275° 51′ 27.2″", "unit": "degrees", "sourceNote": "Maslul = distance of the sun from the govah (apogee). Directly from the Rambam.", "teachingNote": "How far is the sun from the govah? This distance determines how much the emtzoi differs from the amiti. At 0° or 360° (sun at govah) there is NO difference. At 180° (sun opposite govah, closest to Earth) there is also no difference. The maximum difference (~2°) occurs around 90°, where the viewing angle between Earth and the red's center diverges most." }, { "id": "sunMaslulCorrection", "name": "Sun Maslul Correction", "hebrewName": "מנת המסלול של השמש", "rambamRef": "KH 13:4", "formula": "Linear interpolation from Rambam's SUN correction table (KH 13:4)", "result": 1.9638081185185152, "formatted": "1° 57′ 49.7″", "unit": "degrees", "sourceNote": "Interpolated between table entries. The Rambam instructs to interpolate proportionally (KH 13:7-8).", "teachingNote": "The menaseh hamaslul: the portion we add or subtract to translate the emtzoi to the amiti. If maslul < 180° the correction is SUBTRACTED (sun appears behind where its emtzoi says). If > 180° it is ADDED. Maximum correction: ~2° near 90° maslul." }, { "id": "sunTrueLongitude", "name": "Sun True Longitude", "hebrewName": "מקום השמש האמיתי", "rambamRef": "KH 13:2-6", "formula": "meanLongitude + correction", "result": 17.479178118519485, "formatted": "17° 28′ 45.0″", "unit": "degrees", "sourceNote": "Direction rule (subtract if < 180°, add if > 180°) directly from the Rambam.", "teachingNote": "The amiti: where the sun ACTUALLY appears in the mazalos from our perspective on Earth. This is the \"lashon kodesh\" — the common language that both sun and moon must be translated into before we can compare them. This is what Beis Din needs to know for the molad calculation." }, { "id": "moonMeanLongitude", "name": "Moon Mean Longitude", "hebrewName": "אמצע הירח", "rambamRef": "KH 14:1-2", "formula": "startPos + 30×10000d + 9×1000d + 7×100d + 3×10d + 4×1d (mod 360)", "result": 249.4622222222224, "formatted": "249° 27′ 44.0″", "unit": "degrees", "sourceNote": "Daily motion of 13°10'35\" (KH 14:1) and starting position (1°14'43\" in Taurus, KH 14:4) from the Rambam. Computed via his period-block tables (KH 14:2).", "teachingNote": "The emtza hayareach is the center point of the galgal katan — where the small epicycle's center is, NOT where the moon actually is. The moon sits on the edge of the galgal katan." }, { "id": "moonSeasonCorrection", "name": "Season Correction", "hebrewName": "תיקון עונתי", "rambamRef": "KH 14:5", "formula": "Lookup from season table based on sun position in zodiac", "result": 0.25, "formatted": "0° 15′ 0.0″", "unit": "degrees", "sourceNote": "The Rambam specifies this adjustment to account for the difference between 6:00 PM and actual sunset. The moon moves ~0.5° per hour.", "teachingNote": "We compute positions for 6 PM, but we can only SEE the moon after sunset. In summer, sunset is later, so the moon has moved further by then. In winter, sunset is earlier. This correction brings the mean longitude to the actual sunset moment." }, { "id": "moonMaslul", "name": "Moon Maslul (Anomaly)", "hebrewName": "אמצע המסלול", "rambamRef": "KH 14:3", "formula": "maslulStart + 30×10000d + 9×1000d + 7×100d + 3×10d + 4×1d (mod 360)", "result": 353.16638888888883, "formatted": "353° 9′ 59.0″", "unit": "degrees", "sourceNote": "Daily motion of 13°3'54\" (KH 14:3, Sefaria reading) and starting position (84°28'42\", KH 14:4). Computed via the Rambam's period-block tables (KH 14:3).", "teachingNote": "The emtza hamaslul tells us where the moon is on the galgal katan (small epicycle). At 0°/360° the moon is at the top (furthest from Earth = govah). At 180° it is closest to Earth. The galgal katan moves at 13° 3' but appears to move faster due to the nekudah hanichaches (prosneusis point)." }, { "id": "doubleElongation", "name": "Double Elongation", "hebrewName": "מרחק כפול", "rambamRef": "KH 15:1-2", "formula": "2 × (emtza hayareach − emtza hashemesh) mod 360", "result": 108.39370444444285, "formatted": "108° 23′ 37.3″", "unit": "degrees", "sourceNote": "The Rambam instructs: subtract emtza hashemesh from emtza hayareach, then double the result.", "teachingNote": "Why double? Because the moon's three outer galgalim move in OPPOSITE directions: the red+blue go 11°12'/day mi'mizrach l'maarav, while the green goes 24°23'/day mi'maarav l'mizrach. The sun also goes ~1°/day mi'maarav l'mizrach. So the effective separation has components in both directions — doubling captures the full angular effect. Rabbi Losh: \"It's like money owed to the bank — you think you owe 12, before you blink you owe 24.\"" }, { "id": "maslulHanachon", "name": "Corrected Course (Maslul Hanachon)", "hebrewName": "המסלול הנכון", "rambamRef": "KH 15:3", "formula": "emtza hamaslul + adjustment(merchak kaful)", "result": 2.1663888888888323, "formatted": "2° 9′ 59.0″", "unit": "degrees", "sourceNote": "The Rambam only specifies adjustments for merchak kaful 0-63°. Values beyond that are extrapolated.", "teachingNote": "The nekudah hanichaches (prosneusis point) shifts the effective center from which the galgal katan's motion is measured. Instead of measuring from the green's center, or from Earth's center, the reference point is on the OPPOSITE side of Earth from the green's center. This is why the moon appears to move faster than 13° 3' after the molad — and this table corrects for that effect." }, { "id": "moonMaslulCorrection", "name": "Moon Maslul Correction", "hebrewName": "מנת המסלול של הירח", "rambamRef": "KH 15:4-6", "formula": "Linear interpolation from Rambam's MOON correction table (KH 15:4-6)", "result": 0.1805324074074027, "formatted": "0° 10′ 49.9″", "unit": "degrees", "sourceNote": "Value interpolated between two entries in the Rambam's table. The Rambam instructs to interpolate linearly (KH 15:7).", "teachingNote": "This table is DIFFERENT from the sun's table! The sun's max correction is ~2° at 90°. The moon's max is ~5° 8' at 100°. This is because the galgal katan's diameter is 10° — the moon can be up to 5° away from the emtza hayareach on each side. The asymmetry (peak at 100° not 90°) comes from the nekudah hanichaches shifting the effective center." }, { "id": "moonTrueLongitude", "name": "Moon True Longitude", "hebrewName": "מקום הירח האמיתי", "rambamRef": "KH 15:4", "formula": "adjustedMeanLon − correction", "result": 249.53168981481497, "formatted": "249° 31′ 54.1″", "unit": "degrees", "sourceNote": "Direction rule from the Rambam: if maslul hanachon < 180° → subtract correction; if > 180° → add correction.", "teachingNote": "This is WHERE THE MOON ACTUALLY APPEARS in the mazalos from our perspective on Earth. Unlike the emtza hayareach (which is the galgal katan's center position), this accounts for the moon's actual position ON the galgal katan, adjusted for the off-center viewing angle (govah effect)." }, { "id": "nodePosition", "name": "Ascending Node (Rosh)", "hebrewName": "ראש התלי", "rambamRef": "KH 16:2-4", "formula": "(360 − (startPos + 30×10000d + 9×1000d + 7×100d + 3×10d + 4×1d)) mod 360", "result": 337.7655555555548, "formatted": "337° 45′ 56.0″", "unit": "degrees", "sourceNote": "Starting position (180°57'28\", KH 16:3) and daily motion (3'11\", KH 16:2) directly from the Rambam. Moves achoranim (backwards) through the zodiac. Computed via his period-block tables (KH 16:2), then reflected (360 − result) for makom rosh.", "teachingNote": "The rosh is where the moon's tilted orbital plane (galgal noteh / blue) crosses the ecliptic going north. The zanav (tail) is exactly 180° opposite — where the moon crosses going south. The rosh/zanav move backwards through the zodiac, completing a full cycle in ~18.6 years. This is caused by the red galgal (domeh) slowly rotating. When the moon is at the rosh or zanav, a solar or lunar eclipse is possible." }, { "id": "moonLatitude", "name": "Moon Latitude", "hebrewName": "רוחב הירח", "rambamRef": "KH 16:9-10", "formula": "latitude table lookup(|distance from rosh| reduced to 0-90°)", "result": -4.9852822145061655, "formatted": "4° 59′ 7.0″ South (דרום)", "unit": "degrees", "sourceNote": "Value interpolated between entries in the Rambam's latitude table.", "teachingNote": "The moon's orbit (galgal noteh / blue) is tilted 5° from the ecliptic. The maximum latitude of 5° is reached 90° from the rosh (ascending node). The rosh is where the moon crosses the ecliptic going north; the zanav (180° opposite) is where it crosses going south. This is called rochav — width or latitude." }, { "id": "elongation", "name": "First Longitude (Elongation)", "hebrewName": "אורך ראשון", "rambamRef": "KH 17:1", "formula": "(moonTrueLon − sunTrueLon + 360) mod 360", "result": 232.05251169629548, "formatted": "232° 3′ 9.0″", "unit": "degrees" }, { "id": "moonPhase", "name": "Moon Phase", "hebrewName": "מופע הירח", "rambamRef": "KH 17", "formula": "Phase determined by elongation angle ranges", "result": "Waning Gibbous", "unit": "", "sourceNote": "Phase names are modern terminology. The Rambam discusses visibility thresholds (9°-24°) but does not name phases." }, { "id": "orechSheni", "name": "Second Longitude (after parallax in longitude)", "hebrewName": "אורך שני", "rambamRef": "KH 17:5", "formula": "orechRishon − (chalakim / 60)", "result": 231.4525116962955, "formatted": "231° 27′ 9.0″", "unit": "degrees", "sourceNote": "Moon in מזל קשת → subtract 36′ (KH 17:5 table)." }, { "id": "rochavSheni", "name": "Second Latitude (after parallax in latitude)", "hebrewName": "רוחב שני", "rambamRef": "KH 17:7-9", "formula": "rochavRishon − (chalakim/60) [signed: north +, south −]", "result": -5.718615547839499, "formatted": "5° 43′ 7.0″ דרומי", "unit": "degrees", "sourceNote": "Moon in מזל קשת → add 44′ (KH 17:7-8)." }, { "id": "orechShlishi", "name": "Third Longitude (after מעגל הירח)", "hebrewName": "אורך שלישי", "rambamRef": "KH 17:10-11", "formula": "orechSheni + signedMaagal (sign per KH 17:11)", "result": 230.4994091049889, "formatted": "230° 29′ 57.9″", "unit": "degrees", "sourceNote": "Moon in [240°, 250°): take שתותו of |רוחב שני|; סרטן-קשת half, רוחב דרומי → subtract." }, { "id": "orechRevii", "name": "Fourth Longitude (after long/short setting correction)", "hebrewName": "אורך רביעי", "rambamRef": "KH 17:12", "formula": "orechShlishi (unchanged)", "result": 230.4994091049889, "formatted": "230° 29′ 57.9″", "unit": "degrees", "sourceNote": "Moon in מזל קשת: leave unchanged of אורך שלישי." }, { "id": "mnatGovahHaMedinah", "name": "Country-Elevation Portion", "hebrewName": "מנת גובה המדינה", "rambamRef": "KH 17:12-14", "formula": "(2/3) × |רוחב ראשון|", "result": 3.3235214763374437, "formatted": "3° 19′ 24.7″", "unit": "degrees", "sourceNote": "Always 2/3 of |רוחב ראשון|; Rambam fixes this for ארץ ישראל (\"שני שלישיו לעולם\")." }, { "id": "keshetHaReiyah", "name": "Arc of Vision", "hebrewName": "קשת הראיה", "rambamRef": "KH 17:12 (final), 17:15", "formula": "orechRevii − mnatGovahHaMedinah", "result": 227.17588762865145, "formatted": "227° 10′ 33.2″", "unit": "degrees", "sourceNote": "רוחב דרומי → SUBTRACT מנת גובה המדינה from אורך רביעי." }, { "id": "moonVisibility", "name": "Moon Visibility Verdict", "hebrewName": "ראיית הירח", "rambamRef": "KH 17:3-4, 17:15-21", "formula": "KH 17:3-4 early exit, else קשת ≤9°/>14° gates, else KH 17:16-21 table", "result": true, "unit": "boolean", "sourceNote": "Early exit (KH 17:4): אורך ראשון = 232.053° > 24° → ודאי יראה." }, { "id": "firstVisibilityAngle", "name": "First Visibility Angle (DEPRECATED heuristic)", "hebrewName": "זווית הראייה הראשונה (היוריסטיקה ישנה)", "rambamRef": "— (heuristic; see KH 17:12 for the canonical קשת הראיה)", "formula": "elongation + 0.3 × |latitude| (heuristic, NOT in Rambam)", "result": 233.54809636064732, "formatted": "233° 32′ 53.1″", "unit": "degrees", "sourceNote": "DEPRECATED: superseded by the full KH 17 chain. Do not use as a visibility input." }, { "id": "seasonalInfo", "name": "Season", "hebrewName": "תקופה", "rambamRef": "KH 9:3", "result": { "currentSeason": "Spring (אביב)", "daysUntilNextSeason": 90 }, "unit": "" }, { "id": "baharadAnchor", "name": "BaHaRaD Anchor", "hebrewName": "בהר״ד", "rambamRef": "KH 6:8", "formula": "BaHaRaD = Day 2 (Monday), 5h, 204 parts", "result": 31524, "formatted": "ב״ה״רד (Monday, 5h, 204p)", "unit": "parts from start of week", "sourceNote": "Molad Tishrei of year 1 of creation — the Rambam fixes this as the spine of the fixed Hebrew calendar.", "teachingNote": "BaHaRaD = ב (day 2, Monday) ה (5 hours into the day) רד (204 parts into that hour). Hebrew days begin at 6 PM the previous civil evening, so BaHaRaD is Sunday evening 11:11 PM civil → Monday morning 5h 204p. Every future molad is computed as BaHaRaD + N × (mean synodic month)." }, { "id": "monthsSinceBaharad", "name": "Months Since BaHaRaD", "hebrewName": "חדשים מאז בהר״ד", "rambamRef": "KH 6:11, 11:4", "formula": "monthsFromYear1ToTishrei(year) + monthPositionInYear(month, year)", "result": 71557, "formatted": "71,557 months", "unit": "months", "sourceNote": "Count of mean moladot from BaHaRaD (molad Tishrei year 1) to the molad of the given date's month. Uses the 19-year cycle of 235 months (12 years of 12 months + 7 leap years of 13 months).", "teachingNote": "Every molad after BaHaRaD is just BaHaRaD + (this number) × (synodic interval). The whole fixed calendar rides on this integer." }, { "id": "meanMoladOfMonth", "name": "Mean Molad of Month", "hebrewName": "מולד אמצעי", "rambamRef": "KH 6:3, 6:8", "formula": "BaHaRaD + months × 29d 12h 793p (mod 7 days for weekday)", "result": 102145, "formatted": "Wednesday 22h 625p (Nisan)", "unit": "parts within week", "sourceNote": "Mean molad = BaHaRaD + (months since BaHaRaD) × (29d 12h 793p). Reduced mod 7 days for weekday display.", "teachingNote": "This is the MEAN molad only — not the astronomical true conjunction, which can be up to ~14 hours off. The fixed calendar uses this mean molad (plus dehiyot) to determine Rosh Chodesh, not the actual sighted new moon." } ] }