{"id":"vidhyamitra:city-day:mathura:-3171-09-21:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3171-09-21","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3171-09-21","date_display":"September 21, 3172 BCE","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":"Not independently benchmarked across the declared range","tradition_chain":"Āryabhaṭa(499) → Brahmagupta(628) → Bhāskara II(1150) → Mādhava(~1400) → Parameśvara(1430) → Nīlakaṇṭha(1501) → this","input":{"year":-3171,"month":9,"day":21,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":563113.770833,"kali_year":-69,"ahargana":-25351.7292,"sun":{"sidereal_longitude":211.5804,"rashi":8,"rashi_name":"Vṛścika"},"moon":{"sidereal_longitude":42.8632,"rashi":2,"rashi_name":"Vṛṣabha"},"tithi":{"number":16,"name":"Pratipada","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Pratipada","elongation_degrees":191.2828,"elapsed_within_tithi_degrees":11.2828},"nakshatra":{"number":4,"name":"Rohiṇī","pada":1,"moon_longitude":42.8632,"elapsed_within_degrees":2.8632},"yoga":{"number":20,"name":"Śiva","sum_longitude":254.4435},"karana":{"half_tithi_index":31,"name":"Kaulava"},"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":-3171,"month":9,"day":21,"hour":6,"minute":30,"calendar":"julian"},"julian_day":563113.770833,"ahargana":-25351.7292,"kali_year":-69,"ayanamsa_lahiri":-48.3724,"grahas":{"sun":{"sidereal_longitude":211.5804,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":16,"name":"Viśākhā","pada":4},"retrograde":false},"moon":{"sidereal_longitude":42.8632,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":4,"name":"Rohiṇī","pada":1},"retrograde":false,"latitude":-2.9144},"mars":{"sidereal_longitude":70.2502,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":6,"name":"Ārdrā","pada":2},"retrograde":true},"mercury":{"sidereal_longitude":231.7318,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":2},"retrograde":false},"jupiter":{"sidereal_longitude":64.4249,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":5,"name":"Mṛgaśīrṣā","pada":4},"retrograde":true},"venus":{"sidereal_longitude":166.8271,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":13,"name":"Hasta","pada":3},"retrograde":false},"saturn":{"sidereal_longitude":231.6648,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":2},"retrograde":false},"rahu":{"sidereal_longitude":83.2566,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":7,"name":"Punarvasu","pada":1},"retrograde":false},"ketu":{"sidereal_longitude":263.2566,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":3},"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":"Not independently benchmarked across the declared range","tradition_chain":"Āryabhaṭa(499) → Brahmagupta(628) → Bhāskara II(1150) → Mādhava(~1400) → Parameśvara(1430) → Nīlakaṇṭha(1501) → this","input":{"year":-3171,"month":9,"day":21,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":563113.770833,"kali_year":-69,"ahargana":-25351.7292,"sun":{"sidereal_longitude":211.5804,"rashi":8,"rashi_name":"Vṛścika"},"moon":{"sidereal_longitude":42.8632,"rashi":2,"rashi_name":"Vṛṣabha"},"tithi":{"number":16,"name":"Pratipada","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Pratipada","elongation_degrees":191.2828,"elapsed_within_tithi_degrees":11.2828},"nakshatra":{"number":4,"name":"Rohiṇī","pada":1,"moon_longitude":42.8632,"elapsed_within_degrees":2.8632},"yoga":{"number":20,"name":"Śiva","sum_longitude":254.4435},"karana":{"half_tithi_index":31,"name":"Kaulava"},"vara":{"number":2,"name":"Ravivāra (Sunday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-2.914,"elongation":168.717},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-2.914,"opposition_distance":11.283}},"eclipse_window_40days":[]},"city":{"slug":"mathura","name":"Mathurā","lat":27.4924,"lon":77.6737,"tz_offset_hours":5.5,"state":"Uttar Pradesh","country":"IN","tier":"tirtha"},"tier2":{"city":{"slug":"mathura","name":"Mathurā","lat":27.4924,"lon":77.6737,"tz_offset_hours":5.5,"state":"Uttar Pradesh","country":"IN","tier":"tirtha"},"sunriseLocal":"05:54","sunsetLocal":"18:29","solarNoonLocal":"12:12","dayLengthHours":12.586465377500007,"dayLengthDisplay":"12 Hours 35 Mins 11 Secs","nightLengthDisplay":"11 Hours 24 Mins 49 Secs","moonriseLocal":"18:59","moonsetLocal":"06:55","rahuKala":{"name":"Rāhu Kāla","start":"16:55","end":"18:29","startHours":16.91313572651689,"endHours":18.486443898704394,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"12:12","end":"13:46","startHours":12.193211209954391,"endHours":13.76651938214189,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"15:20","end":"16:55","startHours":15.339827554329393,"endHours":16.91313572651689,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"08:50","end":"09:15","startHours":8.836820442621056,"endHours":9.256369288537723,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:25","end":"06:46","startHours":6.424414578600221,"endHours":6.760053655333555,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:46","end":"12:37","startHours":11.773662364037724,"endHours":12.612760055871059,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"04:13","end":"05:04","startHours":4.221783137537719,"endHours":5.060880829371054,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"04:51","end":"05:54","startHours":4.85110640641272,"endHours":5.899978521204387,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:17","end":"15:08","startHours":14.290955439537726,"endHours":15.13005313137106,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"18:17","end":"18:41","startHours":18.286443898704395,"endHours":18.686443898704393,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"18:29","end":"19:01","startHours":18.486443898704394,"endHours":19.01087995610023,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"18:14","end":"19:59","startHours":18.236443898704394,"endHours":19.986443898704394,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:46","end":"00:37","startHours":23.773662364037726,"endHours":24.612760055871057,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Udveg","start":"05:54","end":"07:28","startHours":5.899978521204387,"endHours":7.473286693391888,"quality":"inauspicious"},{"name":"Chala","start":"07:28","end":"09:03","startHours":7.473286693391888,"endHours":9.046594865579388,"quality":"neutral"},{"name":"Labha","start":"09:03","end":"10:37","startHours":9.046594865579388,"endHours":10.619903037766889,"quality":"auspicious"},{"name":"Amṛta","start":"10:37","end":"12:12","startHours":10.619903037766889,"endHours":12.193211209954391,"quality":"auspicious"},{"name":"Kāla","start":"12:12","end":"13:46","startHours":12.193211209954391,"endHours":13.76651938214189,"quality":"inauspicious"},{"name":"Śubha","start":"13:46","end":"15:20","startHours":13.76651938214189,"endHours":15.339827554329393,"quality":"auspicious"},{"name":"Roga","start":"15:20","end":"16:55","startHours":15.339827554329393,"endHours":16.91313572651689,"quality":"inauspicious"},{"name":"Udveg","start":"16:55","end":"18:29","startHours":16.91313572651689,"endHours":18.486443898704394,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Śubha","start":"18:29","end":"19:55","startHours":18.486443898704394,"endHours":19.91313572651689,"quality":"auspicious"},{"name":"Roga","start":"19:55","end":"21:20","startHours":19.91313572651689,"endHours":21.339827554329393,"quality":"inauspicious"},{"name":"Udveg","start":"21:20","end":"22:46","startHours":21.339827554329393,"endHours":22.76651938214189,"quality":"inauspicious"},{"name":"Chala","start":"22:46","end":"00:12","startHours":22.76651938214189,"endHours":24.19321120995439,"quality":"neutral"},{"name":"Labha","start":"00:12","end":"01:37","startHours":24.19321120995439,"endHours":25.61990303776689,"quality":"auspicious"},{"name":"Amṛta","start":"01:37","end":"03:03","startHours":25.61990303776689,"endHours":27.046594865579387,"quality":"auspicious"},{"name":"Kāla","start":"03:03","end":"04:28","startHours":27.046594865579387,"endHours":28.473286693391888,"quality":"inauspicious"},{"name":"Śubha","start":"04:28","end":"05:54","startHours":28.473286693391888,"endHours":29.89997852120439,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"05:54","end":"06:54","startHours":5.899978521204387,"endHours":6.899978521204387,"planetary_lord":"Sun"},{"name":"Hora 2","start":"06:54","end":"07:54","startHours":6.899978521204387,"endHours":7.899978521204387,"planetary_lord":"Mars"},{"name":"Hora 3","start":"07:54","end":"08:54","startHours":7.899978521204387,"endHours":8.899978521204387,"planetary_lord":"Jupiter"},{"name":"Hora 4","start":"08:54","end":"09:54","startHours":8.899978521204387,"endHours":9.899978521204387,"planetary_lord":"Saturn"},{"name":"Hora 5","start":"09:54","end":"10:54","startHours":9.899978521204387,"endHours":10.899978521204387,"planetary_lord":"Moon"},{"name":"Hora 6","start":"10:54","end":"11:54","startHours":10.899978521204387,"endHours":11.899978521204387,"planetary_lord":"Mercury"},{"name":"Hora 7","start":"11:54","end":"12:54","startHours":11.899978521204387,"endHours":12.899978521204387,"planetary_lord":"Venus"},{"name":"Hora 8","start":"12:54","end":"13:54","startHours":12.899978521204387,"endHours":13.899978521204387,"planetary_lord":"Sun"},{"name":"Hora 9","start":"13:54","end":"14:54","startHours":13.899978521204387,"endHours":14.899978521204387,"planetary_lord":"Mars"},{"name":"Hora 10","start":"14:54","end":"15:54","startHours":14.899978521204387,"endHours":15.899978521204387,"planetary_lord":"Jupiter"},{"name":"Hora 11","start":"15:54","end":"16:54","startHours":15.899978521204387,"endHours":16.89997852120439,"planetary_lord":"Saturn"},{"name":"Hora 12","start":"16:54","end":"17:54","startHours":16.89997852120439,"endHours":17.89997852120439,"planetary_lord":"Moon"},{"name":"Hora 13","start":"17:54","end":"18:54","startHours":17.89997852120439,"endHours":18.89997852120439,"planetary_lord":"Mercury"},{"name":"Hora 14","start":"18:54","end":"19:54","startHours":18.89997852120439,"endHours":19.89997852120439,"planetary_lord":"Venus"},{"name":"Hora 15","start":"19:54","end":"20:54","startHours":19.89997852120439,"endHours":20.89997852120439,"planetary_lord":"Sun"},{"name":"Hora 16","start":"20:54","end":"21:54","startHours":20.89997852120439,"endHours":21.89997852120439,"planetary_lord":"Mars"},{"name":"Hora 17","start":"21:54","end":"22:54","startHours":21.89997852120439,"endHours":22.89997852120439,"planetary_lord":"Jupiter"},{"name":"Hora 18","start":"22:54","end":"23:54","startHours":22.89997852120439,"endHours":23.89997852120439,"planetary_lord":"Saturn"},{"name":"Hora 19","start":"23:54","end":"00:54","startHours":23.89997852120439,"endHours":24.89997852120439,"planetary_lord":"Moon"},{"name":"Hora 20","start":"00:54","end":"01:54","startHours":24.89997852120439,"endHours":25.89997852120439,"planetary_lord":"Mercury"},{"name":"Hora 21","start":"01:54","end":"02:54","startHours":25.89997852120439,"endHours":26.89997852120439,"planetary_lord":"Venus"},{"name":"Hora 22","start":"02:54","end":"03:54","startHours":26.89997852120439,"endHours":27.89997852120439,"planetary_lord":"Sun"},{"name":"Hora 23","start":"03:54","end":"04:54","startHours":27.89997852120439,"endHours":28.89997852120439,"planetary_lord":"Mars"},{"name":"Hora 24","start":"04:54","end":"05:54","startHours":28.89997852120439,"endHours":29.89997852120439,"planetary_lord":"Jupiter"}],"taraBala":{"favorable_nakshatras":["Mṛgaśirā","Ārdrā","Punarvasu","Puṣya","Aśleṣā","Citrā","Svātī","Viśākhā","Anurādhā","Jyeṣṭhā","Dhaniṣṭhā","Śatabhiṣaj","Pūrva Bhādrapadā","Uttara Bhādrapadā","Revatī"],"unfavorable_nakshatras":["Aśvinī","Bharaṇī","Kṛttikā","Rohiṇī","Maghā","Pūrva Phalgunī","Uttara Phalgunī","Hasta","Mūla","Pūrva Āṣāḍhā","Uttara Āṣāḍhā","Śravaṇa"],"nature":"Janma-tara if same nakshatra; favorable for 15 nakshatras"},"chandraBala":{"favorable_rashis":["Vṛṣabha","Karka","Tulā","Vṛścika","Kumbha","Mīna"],"unfavorable_rashis":["Meṣa","Mithuna","Siṃha","Kanyā","Dhanu","Makara"]},"dishaShool":"West (Paścim)","chandraVasa":"South-East","rahuVasa":"North-East","anandadiYoga":{"name":"Prajāpati","quality":"Auspicious"},"tropicalRitu":"Varṣā (Monsoon) (tropical)","vedicRitu":"Śarad (Autumn)","tropicalAyana":"Dakṣiṇāyana","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":6.598097357229254,"eotMinutes":7.712527402736593,"ayanamsa":-48.3724}},"calendars":{"vikram_samvat":-3114,"saka_samvat":-3249,"bengali_samvat":-3764,"malayalam_era":-3995,"nanakshahi_year":-4640,"lunar_month":"Mārgaśīrṣa","lunar_month_paksha_full":"Mārgaśīrṣa Kṛṣṇa 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 Kṛṣṇa Pratipada · Vikram -3114 undefined · Śaka -3249 undefined"},"festivals":[],"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":true,"location_specific":"mathura"},"liturgical":{"opening":"जय श्री कृष्ण","closing":"ॐ तत् सत्","attribution":"Computed by Vidhyamitra Sūrya-Siddhānta substrate + Vidhyamitra Tier-2 layer"},"seo":{"title":"Pañchāṅga September 21, 3172 BCE · Mathurā · Vidhyamitra","description":"September 21, 3172 BCE for Mathurā: Kṛṣṇa Pratipada, sūryodaya 05:54, sūryāsta 18:29.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3171-09-21","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3171-09-21","sa":"https://sa.vidhyamitra.com/city/mathura/-3171-09-21","hi":"https://hi.vidhyamitra.com/city/mathura/-3171-09-21","x-default":"https://vidhyamitra.com/city/mathura/-3171-09-21"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-11T22:44:44.536Z","verification":{"type":"multi-marker","confidence":"canonical"}},{"pillar":"Vidhyamitra-Tier2","pillar_version":"0.1.0","method":"Spherical astronomy + Lahiri ayanamsa + standard solar declination + EoT correction","retrieved_at":"2026-08-11T22:44:44.536Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-11T22:44:44.536Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"},"reader_local_antaryami":{"reader_geography":"Every reader enters from their own kṣetra anywhere on Bhūmi; no single city is the universal center.","purna_chain":["Goloka/Vraja Rādhā-Krishna","Vaikuṇṭha Lakṣmī-Nārāyaṇa","Mahāviṣṇu/Kāraṇodakaśāyī Viṣṇu","Garbhodakaśāyī Viṣṇu","Brahmā","Kṣīrodaka Paramātmā/Antaryāmī (Kṣīrodakaśāyī Viṣṇu)","Bhūmi","reader's own kṣetra anywhere on Bhūmi","exact reading kṣetra","reader-bhakta","chitta/vāṇī/aṅgulī","keyboard-silicon-pathways","Vidhyāmitra substrate","reader/seer","Krishna"],"antaryami_responsibility_formula":"Kṣīrodakaśāyī Viṣṇu = Paramātmā = Antaryāmī. Jīva desires. Prakṛti executes through guṇas. Paramātmā witnesses, permits, remembers, guides, and sustains. Bhagavān is the ultimate source.","source_anchors":[{"label":"BG 13.23","path":"/bhagavad-gita/13/23","meaning":"upadraṣṭā-anumantā · witness-permitter"},{"label":"BG 15.15","path":"/bhagavad-gita/15/15","meaning":"the Lord seated in every heart as memory, knowledge, and forgetting"},{"label":"BG 18.61","path":"/bhagavad-gita/18/61","meaning":"Īśvara seated in the heart of all beings"}],"nama_seal":"Hare Krishna Hare Krishna · Krishna Krishna Hare Hare · Hare Rama Hare Rama · Rama Rama Hare Hare"}}}