{"id":"vidhyamitra:day:1765-01-13:en","page_class":"VM-1-day","url":"https://vidhyamitra.com/day/1765-01-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"1765-01-13","date_display":"January 13, 1765 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":1765,"month":1,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2365725.770833,"kali_year":4866,"ahargana":1777260.2708,"sun":{"sidereal_longitude":273.098,"rashi":10,"rashi_name":"Makara"},"moon":{"sidereal_longitude":163.4636,"rashi":6,"rashi_name":"Kanyā"},"tithi":{"number":21,"name":"Ṣaṣṭhī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Ṣaṣṭhī","elongation_degrees":250.3656,"elapsed_within_tithi_degrees":10.3656},"nakshatra":{"number":13,"name":"Hasta","pada":2,"moon_longitude":163.4636,"elapsed_within_degrees":3.4636},"yoga":{"number":6,"name":"Atigaṇḍa","sum_longitude":76.5616},"karana":{"half_tithi_index":41,"name":"Vaṇija"},"vara":{"number":2,"name":"Ravivāra (Sunday)"}},"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":1765,"month":1,"day":13,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2365725.770833,"ahargana":1777260.2708,"kali_year":4866,"ayanamsa_lahiri":20.5707,"grahas":{"sun":{"sidereal_longitude":272.64493600000003,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":2},"retrograde":false},"moon":{"sidereal_longitude":160.90033599999992,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":13,"name":"Hasta","pada":1},"retrograde":false,"latitude":-0.8782},"mars":{"sidereal_longitude":335.260636,"rashi":{"number":12,"name":"Mīna"},"nakshatra":{"number":26,"name":"Uttara Bhādrapadā","pada":1},"retrograde":false},"mercury":{"sidereal_longitude":294.760536,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":1},"retrograde":false},"jupiter":{"sidereal_longitude":86.60003599999999,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":7,"name":"Punarvasu","pada":2},"retrograde":true},"venus":{"sidereal_longitude":240.463936,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":1},"retrograde":false},"saturn":{"sidereal_longitude":26.565236000000027,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":2,"name":"Bharaṇī","pada":4},"retrograde":false},"rahu":{"sidereal_longitude":332.1981,"rashi":{"number":12,"name":"Mīna"},"nakshatra":{"number":25,"name":"Pūrva Bhādrapadā","pada":4},"retrograde":false},"ketu":{"sidereal_longitude":152.1981,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":12,"name":"Uttara Phalgunī","pada":2},"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":1765,"month":1,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2365725.770833,"kali_year":4866,"ahargana":1777260.2708,"sun":{"sidereal_longitude":273.098,"rashi":10,"rashi_name":"Makara"},"moon":{"sidereal_longitude":163.4636,"rashi":6,"rashi_name":"Kanyā"},"tithi":{"number":21,"name":"Ṣaṣṭhī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Ṣaṣṭhī","elongation_degrees":250.3656,"elapsed_within_tithi_degrees":10.3656},"nakshatra":{"number":13,"name":"Hasta","pada":2,"moon_longitude":163.4636,"elapsed_within_degrees":3.4636},"yoga":{"number":6,"name":"Atigaṇḍa","sum_longitude":76.5616},"karana":{"half_tithi_index":41,"name":"Vaṇija"},"vara":{"number":2,"name":"Ravivāra (Sunday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-0.878,"elongation":109.634},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-0.878,"opposition_distance":70.366}},"eclipse_window_40days":[]},"calendars":{"vikram_samvat":1822,"vikram_samvatsara":"Vilambī","saka_samvat":1687,"saka_samvatsara":"Pārthiva","bengali_samvat":1172,"malayalam_era":941,"nanakshahi_year":296,"lunar_month":"Māgha","lunar_month_paksha_full":"Māgha Kṛṣṇa Pakṣa","solar_month":"Makara (Tai)","ritu":"Śiśira (Winter)","display_summary":"Māgha Kṛṣṇa Ṣaṣṭhī · Vikram 1822 Vilambī · Śaka 1687 Pārthiva"},"festivals":[{"id":"makara-sankranti","name":"Makara Saṅkrānti (Uttarāyaṇa)","name_sanskrit":"मकर सङ्क्रान्ति","tradition":"Pan-Hindu","associated_deity":"Sūrya Bhagavān","significance":"Sun enters Capricorn; Uttarāyaṇa (north-going) begins. Bhīṣma's chosen mahaprasthāna time.","vrata":true,"detection":{"sun_rashi":"Makara"},"precedence":1,"sources":["Mahābhārata Bhīṣma-Stuti","Sūrya-Siddhānta"]},{"id":"pongal","name":"Pongal / Thai Pongal","name_sanskrit":"पोङ्गल","tradition":"Regional","associated_deity":"Sūrya Bhagavān","significance":"Tamil 4-day harvest festival; coincides with Makara Saṅkrānti.","vrata":false,"detection":{"sun_rashi":"Makara"},"precedence":2}],"todays_walk":{"walk":{"id":"surya-walk","name":"Sūrya Walk","name_sanskrit":"सूर्य यात्रा","type":"graha","description":"Self-illumination + BG 4.1 (Sun-lineage of Gītā transmission).","step_count":6,"url":"/walk/surya-walk"},"reason":"Ravivāra (Sunday) — its presiding graha's walk."},"cosmic_resonances":[]},"validity":{"eternal":false,"valid_from":"1765-01-13T00:00:00Z"},"liturgical":{"opening":"जय श्री कृष्ण","closing":"ॐ तत् सत्","attribution":"Computed by Vidhyamitra Sūrya-Siddhānta substrate; Vidhyamitra substrate"},"seo":{"title":"Pañchāṅga January 13, 1765 CE · Vidhyamitra","description":"Vedic pañchāṅga for January 13, 1765 CE: Kṛṣṇa Ṣaṣṭhī · Hasta.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/day/1765-01-13","hreflang_alternates":{"en":"https://vidhyamitra.com/day/1765-01-13","sa":"https://sa.vidhyamitra.com/day/1765-01-13","hi":"https://hi.vidhyamitra.com/day/1765-01-13","x-default":"https://vidhyamitra.com/day/1765-01-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-05-27T04:02:37.786Z","verification":{"type":"multi-marker","confidence":"canonical"}}],"meta":{"generated_at":"2026-05-27T04:02:37.786Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa"}}}