{"id":"vidhyamitra:day:1642-01-13:en","page_class":"VM-1-day","url":"https://vidhyamitra.com/day/1642-01-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"1642-01-13","date_display":"January 13, 1642 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":1642,"month":1,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2320800.770833,"kali_year":4743,"ahargana":1732335.2708,"sun":{"sidereal_longitude":274.9729,"rashi":10,"rashi_name":"Makara"},"moon":{"sidereal_longitude":59.9707,"rashi":2,"rashi_name":"Vṛṣabha"},"tithi":{"number":13,"name":"Trayodaśī","paksha":"Śukla","full_name":"Śukla Trayodaśī","elongation_degrees":144.9978,"elapsed_within_tithi_degrees":0.9978},"nakshatra":{"number":5,"name":"Mṛgaśīrṣā","pada":2,"moon_longitude":59.9707,"elapsed_within_degrees":6.6374},"yoga":{"number":26,"name":"Indra","sum_longitude":334.9436},"karana":{"half_tithi_index":24,"name":"Kaulava"},"vara":{"number":3,"name":"Somavāra (Monday)"}},"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":1642,"month":1,"day":13,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2320800.770833,"ahargana":1732335.2708,"kali_year":4743,"ayanamsa_lahiri":18.8525,"grahas":{"sun":{"sidereal_longitude":274.221101,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":3},"retrograde":false},"moon":{"sidereal_longitude":60.85340100000002,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":5,"name":"Mr̥gaśirā","pada":3},"retrograde":false,"latitude":-3.3125},"mars":{"sidereal_longitude":236.934301,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":4},"retrograde":false},"mercury":{"sidereal_longitude":255.44450099999995,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":1},"retrograde":false},"jupiter":{"sidereal_longitude":303.037201,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":3},"retrograde":false},"venus":{"sidereal_longitude":252.25340099999994,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":4},"retrograde":false},"saturn":{"sidereal_longitude":324.88890100000003,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":25,"name":"Pūrva Bhādrapadā","pada":2},"retrograde":false},"rahu":{"sidereal_longitude":192.5408,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":15,"name":"Svātī","pada":2},"retrograde":false},"ketu":{"sidereal_longitude":12.5408,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":1,"name":"Aśvinī","pada":4},"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":1642,"month":1,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2320800.770833,"kali_year":4743,"ahargana":1732335.2708,"sun":{"sidereal_longitude":274.9729,"rashi":10,"rashi_name":"Makara"},"moon":{"sidereal_longitude":59.9707,"rashi":2,"rashi_name":"Vṛṣabha"},"tithi":{"number":13,"name":"Trayodaśī","paksha":"Śukla","full_name":"Śukla Trayodaśī","elongation_degrees":144.9978,"elapsed_within_tithi_degrees":0.9978},"nakshatra":{"number":5,"name":"Mṛgaśīrṣā","pada":2,"moon_longitude":59.9707,"elapsed_within_degrees":6.6374},"yoga":{"number":26,"name":"Indra","sum_longitude":334.9436},"karana":{"half_tithi_index":24,"name":"Kaulava"},"vara":{"number":3,"name":"Somavāra (Monday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-3.312,"elongation":144.998},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-3.312,"opposition_distance":35.002}},"eclipse_window_40days":[]},"calendars":{"vikram_samvat":1699,"vikram_samvatsara":"Manmatha","saka_samvat":1564,"saka_samvatsara":"Citrabhānu","bengali_samvat":1049,"malayalam_era":818,"nanakshahi_year":173,"lunar_month":"Pauṣa","lunar_month_paksha_full":"Pauṣa Śukla Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Pauṣa","lunar_month_amanta":"Pauṣa","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Makara (Tai)","ritu":"Hemanta (Pre-winter)","display_summary":"Pauṣa Śukla Trayodaśī · Vikram 1699 Manmatha · Śaka 1564 Citrabhānu"},"festivals":[{"id":"pradosha-vrata","name":"Pradoṣa Vrata","name_sanskrit":"प्रदोष व्रत","tradition":"Shaiva","associated_deity":"Śiva","significance":"Twilight worship of Śiva on Trayodaśī.","vrata":true,"detection":{"any_of":[{"tithi_number":13},{"tithi_number":28}]},"precedence":7}],"todays_walk":{"walk":{"id":"chandra-walk","name":"Candra Walk","name_sanskrit":"चन्द्र यात्रा","type":"graha","description":"Manas-control + BG 6.5-7.","step_count":5,"url":"/walk/chandra-walk"},"reason":"Somavāra (Monday) — its presiding graha's walk."},"cosmic_resonances":[]},"validity":{"eternal":false,"valid_from":"1642-01-13T00:00:00Z"},"liturgical":{"opening":"जय श्री कृष्ण","closing":"ॐ तत् सत्","attribution":"Computed by Vidhyamitra Sūrya-Siddhānta substrate; Vidhyamitra substrate"},"seo":{"title":"Pañchāṅga January 13, 1642 CE · Vidhyamitra","description":"Vedic pañchāṅga for January 13, 1642 CE: Śukla Trayodaśī · Mṛgaśīrṣā.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/day/1642-01-13","hreflang_alternates":{"en":"https://vidhyamitra.com/day/1642-01-13","sa":"https://sa.vidhyamitra.com/day/1642-01-13","hi":"https://hi.vidhyamitra.com/day/1642-01-13","x-default":"https://vidhyamitra.com/day/1642-01-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-06-09T16:46:20.992Z","verification":{"type":"multi-marker","confidence":"canonical"}}],"meta":{"generated_at":"2026-06-09T16:46:20.992Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa"}}}