{"id":"vidhyamitra:day:1641-12-04:en","page_class":"VM-1-day","url":"https://vidhyamitra.com/day/1641-12-04","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"1641-12-04","date_display":"December 4, 1641 CE","panchanga":{"method":"Sūrya Siddhānta + Bhāskara-II iterative manda + Kerala-school (Mādhava-Nīlakaṇṭha) evection + variation + annual equation","engine_version":"2.0 (Kerala-school enhanced)","accuracy_note":"Sub-degree on Moon at any Kali-Yuga date (~2-5° residual max)","tradition_chain":"Āryabhaṭa(499) → Brahmagupta(628) → Bhāskara II(1150) → Mādhava(~1400) → Parameśvara(1430) → Nīlakaṇṭha(1501) → this","input":{"year":1641,"month":12,"day":4,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2320760.770833,"kali_year":4743,"ahargana":1732295.2708,"sun":{"sidereal_longitude":233.8871,"rashi":8,"rashi_name":"Vṛścika"},"moon":{"sidereal_longitude":251.4243,"rashi":9,"rashi_name":"Dhanu"},"tithi":{"number":2,"name":"Dvitīyā","paksha":"Śukla","full_name":"Śukla Dvitīyā","elongation_degrees":17.5372,"elapsed_within_tithi_degrees":5.5372},"nakshatra":{"number":19,"name":"Mūla","pada":4,"moon_longitude":251.4243,"elapsed_within_degrees":11.4243},"yoga":{"number":10,"name":"Gaṇḍa","sum_longitude":125.3114},"karana":{"half_tithi_index":2,"name":"Bālava"},"vara":{"number":5,"name":"Budhavāra (Wednesday)"}},"sky":{"method":"Sūrya-Siddhāntic Bhāskara-II 4-step iteration with atan2-based śīghra + varying peripheries + lunar latitude","engine_version":"3.0 (Pūrṇa — complete SS implementation)","tradition_sources":"Āryabhaṭīya 499 CE → SS Ch.1-5 Burgess 1860 → Siddhānta-Śiromaṇi Bhāskara II 1150 → Tantrasaṅgraha Nīlakaṇṭha 1501","input":{"year":1641,"month":12,"day":4,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2320760.770833,"ahargana":1732295.2708,"kali_year":4743,"ayanamsa_lahiri":18.851,"grahas":{"sun":{"sidereal_longitude":233.47052899999994,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":3},"retrograde":false},"moon":{"sidereal_longitude":252.624229,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":4},"retrograde":false,"latitude":3.7627},"mars":{"sidereal_longitude":209.40612899999996,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":16,"name":"Viśākhā","pada":3},"retrograde":false},"mercury":{"sidereal_longitude":257.93422899999996,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":2},"retrograde":false},"jupiter":{"sidereal_longitude":294.6928290000001,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":1},"retrograde":false},"venus":{"sidereal_longitude":202.84492899999998,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":16,"name":"Viśākhā","pada":1},"retrograde":false},"saturn":{"sidereal_longitude":322.0240289999999,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":25,"name":"Pūrva Bhādrapadā","pada":1},"retrograde":false},"rahu":{"sidereal_longitude":194.6602,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":15,"name":"Svātī","pada":3},"retrograde":false},"ketu":{"sidereal_longitude":14.6602,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":2,"name":"Bharaṇī","pada":1},"retrograde":false}},"panchang":{"method":"Sūrya Siddhānta + Bhāskara-II iterative manda + Kerala-school (Mādhava-Nīlakaṇṭha) evection + variation + annual equation","engine_version":"2.0 (Kerala-school enhanced)","accuracy_note":"Sub-degree on Moon at any Kali-Yuga date (~2-5° residual max)","tradition_chain":"Āryabhaṭa(499) → Brahmagupta(628) → Bhāskara II(1150) → Mādhava(~1400) → Parameśvara(1430) → Nīlakaṇṭha(1501) → this","input":{"year":1641,"month":12,"day":4,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2320760.770833,"kali_year":4743,"ahargana":1732295.2708,"sun":{"sidereal_longitude":233.8871,"rashi":8,"rashi_name":"Vṛścika"},"moon":{"sidereal_longitude":251.4243,"rashi":9,"rashi_name":"Dhanu"},"tithi":{"number":2,"name":"Dvitīyā","paksha":"Śukla","full_name":"Śukla Dvitīyā","elongation_degrees":17.5372,"elapsed_within_tithi_degrees":5.5372},"nakshatra":{"number":19,"name":"Mūla","pada":4,"moon_longitude":251.4243,"elapsed_within_degrees":11.4243},"yoga":{"number":10,"name":"Gaṇḍa","sum_longitude":125.3114},"karana":{"half_tithi_index":2,"name":"Bālava"},"vara":{"number":5,"name":"Budhavāra (Wednesday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":3.763,"elongation":17.537},"lunar":{"type":"lunar","occurs":false,"moon_latitude":3.763,"opposition_distance":162.463}},"eclipse_window_40days":[]},"calendars":{"vikram_samvat":1698,"vikram_samvatsara":"Jaya","saka_samvat":1563,"saka_samvatsara":"Vṛṣa","bengali_samvat":1048,"malayalam_era":817,"nanakshahi_year":172,"lunar_month":"Mārgaśīrṣa","lunar_month_paksha_full":"Mārgaśīrṣa Śukla Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Mārgaśīrṣa","lunar_month_amanta":"Mārgaśīrṣa","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Vṛścika (Kārttikai)","ritu":"Hemanta (Pre-winter)","display_summary":"Mārgaśīrṣa Śukla Dvitīyā · Vikram 1698 Jaya · Śaka 1563 Vṛṣa"},"festivals":[],"todays_walk":{"walk":{"id":"budha-walk","name":"Budha Walk","name_sanskrit":"बुध यात्रा","type":"graha","description":"Discrimination + BG 2.41 (vyavasāyātmikā buddhi).","step_count":6,"url":"/walk/budha-walk"},"reason":"Budhavāra (Wednesday) — its presiding graha's walk."},"cosmic_resonances":[]},"validity":{"eternal":false,"valid_from":"1641-12-04T00:00:00Z"},"liturgical":{"opening":"जय श्री कृष्ण","closing":"ॐ तत् सत्","attribution":"Computed by Vidhyamitra Sūrya-Siddhānta substrate; Vidhyamitra substrate"},"seo":{"title":"Pañchāṅga December 4, 1641 CE · Vidhyamitra","description":"Vedic pañchāṅga for December 4, 1641 CE: Śukla Dvitīyā · Mūla.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/day/1641-12-04","hreflang_alternates":{"en":"https://vidhyamitra.com/day/1641-12-04","sa":"https://sa.vidhyamitra.com/day/1641-12-04","hi":"https://hi.vidhyamitra.com/day/1641-12-04","x-default":"https://vidhyamitra.com/day/1641-12-04"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-06-09T16:45:32.440Z","verification":{"type":"multi-marker","confidence":"canonical"}}],"meta":{"generated_at":"2026-06-09T16:45:32.440Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa"}}}