{"id":"vidhyamitra:city-day:mathura:-3164-09-20:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3164-09-20","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3164-09-20","date_display":"September 20, 3165 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":-3164,"month":9,"day":20,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":565669.770833,"kali_year":-62,"ahargana":-22795.7292,"sun":{"sidereal_longitude":210.757,"rashi":8,"rashi_name":"Vṛścika"},"moon":{"sidereal_longitude":233.1301,"rashi":8,"rashi_name":"Vṛścika"},"tithi":{"number":2,"name":"Dvitīyā","paksha":"Śukla","full_name":"Śukla Dvitīyā","elongation_degrees":22.3731,"elapsed_within_tithi_degrees":10.3731},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":2,"moon_longitude":233.1301,"elapsed_within_degrees":6.4635},"yoga":{"number":7,"name":"Sukarma","sum_longitude":83.8871},"karana":{"half_tithi_index":3,"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":-3164,"month":9,"day":20,"hour":6,"minute":30,"calendar":"julian"},"julian_day":565669.770833,"ahargana":-22795.7292,"kali_year":-62,"ayanamsa_lahiri":-48.2747,"grahas":{"sun":{"sidereal_longitude":210.757,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":16,"name":"Viśākhā","pada":4},"retrograde":false},"moon":{"sidereal_longitude":233.1301,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":2},"retrograde":false,"latitude":-4.3401},"mars":{"sidereal_longitude":260.3126,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":3},"retrograde":false},"mercury":{"sidereal_longitude":233.3585,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":3},"retrograde":false},"jupiter":{"sidereal_longitude":253.3533,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":1},"retrograde":false},"venus":{"sidereal_longitude":205.5582,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":16,"name":"Viśākhā","pada":2},"retrograde":false},"saturn":{"sidereal_longitude":302.55,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":3},"retrograde":false},"rahu":{"sidereal_longitude":307.8274,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":24,"name":"Śatabhiṣā","pada":1},"retrograde":false},"ketu":{"sidereal_longitude":127.8274,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","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":-3164,"month":9,"day":20,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":565669.770833,"kali_year":-62,"ahargana":-22795.7292,"sun":{"sidereal_longitude":210.757,"rashi":8,"rashi_name":"Vṛścika"},"moon":{"sidereal_longitude":233.1301,"rashi":8,"rashi_name":"Vṛścika"},"tithi":{"number":2,"name":"Dvitīyā","paksha":"Śukla","full_name":"Śukla Dvitīyā","elongation_degrees":22.3731,"elapsed_within_tithi_degrees":10.3731},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":2,"moon_longitude":233.1301,"elapsed_within_degrees":6.4635},"yoga":{"number":7,"name":"Sukarma","sum_longitude":83.8871},"karana":{"half_tithi_index":3,"name":"Kaulava"},"vara":{"number":3,"name":"Somavāra (Monday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-4.34,"elongation":22.373},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-4.34,"opposition_distance":157.627}},"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":"18:30","solarNoonLocal":"12:12","dayLengthHours":12.60613565151877,"dayLengthDisplay":"12 Hours 36 Mins 22 Secs","nightLengthDisplay":"11 Hours 23 Mins 38 Secs","moonriseLocal":"07:43","moonsetLocal":"19:40","rahuKala":{"name":"Rāhu Kāla","start":"07:28","end":"09:03","startHours":7.472003884654555,"endHours":9.047770841094401,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"10:37","end":"12:12","startHours":10.623537797534247,"endHours":12.199304753974094,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"13:47","end":"15:21","startHours":13.77507171041394,"endHours":15.350838666853786,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"08:50","end":"09:15","startHours":8.837668580235755,"endHours":9.257873101953047,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:25","end":"06:45","startHours":6.421492580361324,"endHours":6.757656197735158,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:47","end":"12:37","startHours":11.779100232256802,"endHours":12.619509275691385,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"04:13","end":"05:03","startHours":4.21541884134554,"endHours":5.055827884780124,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"04:51","end":"05:54","startHours":4.845725623921478,"endHours":5.896236928214709,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:18","end":"15:08","startHours":14.300327362560555,"endHours":15.14073640599514,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"18:18","end":"18:42","startHours":18.30237257973348,"endHours":18.702372579733478,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"18:30","end":"19:02","startHours":18.50237257973348,"endHours":19.027628231880094,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"18:15","end":"20:00","startHours":18.25237257973348,"endHours":20.00237257973348,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:47","end":"00:37","startHours":23.779100232256802,"endHours":24.619509275691385,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Amṛta","start":"05:54","end":"07:28","startHours":5.896236928214709,"endHours":7.472003884654555,"quality":"auspicious"},{"name":"Kāla","start":"07:28","end":"09:03","startHours":7.472003884654555,"endHours":9.047770841094401,"quality":"inauspicious"},{"name":"Śubha","start":"09:03","end":"10:37","startHours":9.047770841094401,"endHours":10.623537797534247,"quality":"auspicious"},{"name":"Roga","start":"10:37","end":"12:12","startHours":10.623537797534247,"endHours":12.199304753974094,"quality":"inauspicious"},{"name":"Udveg","start":"12:12","end":"13:47","startHours":12.199304753974094,"endHours":13.77507171041394,"quality":"inauspicious"},{"name":"Chala","start":"13:47","end":"15:21","startHours":13.77507171041394,"endHours":15.350838666853786,"quality":"neutral"},{"name":"Labha","start":"15:21","end":"16:56","startHours":15.350838666853786,"endHours":16.926605623293632,"quality":"auspicious"},{"name":"Amṛta","start":"16:56","end":"18:30","startHours":16.926605623293632,"endHours":18.50237257973348,"quality":"auspicious"}],"nightChoghadiyas":[{"name":"Chala","start":"18:30","end":"19:56","startHours":18.50237257973348,"endHours":19.926605623293632,"quality":"neutral"},{"name":"Labha","start":"19:56","end":"21:21","startHours":19.926605623293632,"endHours":21.350838666853786,"quality":"auspicious"},{"name":"Amṛta","start":"21:21","end":"22:47","startHours":21.350838666853786,"endHours":22.77507171041394,"quality":"auspicious"},{"name":"Kāla","start":"22:47","end":"00:12","startHours":22.77507171041394,"endHours":24.199304753974094,"quality":"inauspicious"},{"name":"Śubha","start":"00:12","end":"01:37","startHours":24.199304753974094,"endHours":25.623537797534247,"quality":"auspicious"},{"name":"Roga","start":"01:37","end":"03:03","startHours":25.623537797534247,"endHours":27.0477708410944,"quality":"inauspicious"},{"name":"Udveg","start":"03:03","end":"04:28","startHours":27.0477708410944,"endHours":28.472003884654555,"quality":"inauspicious"},{"name":"Chala","start":"04:28","end":"05:54","startHours":28.472003884654555,"endHours":29.89623692821471,"quality":"neutral"}],"horas":[{"name":"Hora 1","start":"05:54","end":"06:54","startHours":5.896236928214709,"endHours":6.896236928214709,"planetary_lord":"Moon"},{"name":"Hora 2","start":"06:54","end":"07:54","startHours":6.896236928214709,"endHours":7.896236928214709,"planetary_lord":"Mercury"},{"name":"Hora 3","start":"07:54","end":"08:54","startHours":7.896236928214709,"endHours":8.896236928214709,"planetary_lord":"Venus"},{"name":"Hora 4","start":"08:54","end":"09:54","startHours":8.896236928214709,"endHours":9.896236928214709,"planetary_lord":"Sun"},{"name":"Hora 5","start":"09:54","end":"10:54","startHours":9.896236928214709,"endHours":10.896236928214709,"planetary_lord":"Mars"},{"name":"Hora 6","start":"10:54","end":"11:54","startHours":10.896236928214709,"endHours":11.896236928214709,"planetary_lord":"Jupiter"},{"name":"Hora 7","start":"11:54","end":"12:54","startHours":11.896236928214709,"endHours":12.896236928214709,"planetary_lord":"Saturn"},{"name":"Hora 8","start":"12:54","end":"13:54","startHours":12.896236928214709,"endHours":13.896236928214709,"planetary_lord":"Moon"},{"name":"Hora 9","start":"13:54","end":"14:54","startHours":13.896236928214709,"endHours":14.896236928214709,"planetary_lord":"Mercury"},{"name":"Hora 10","start":"14:54","end":"15:54","startHours":14.896236928214709,"endHours":15.896236928214709,"planetary_lord":"Venus"},{"name":"Hora 11","start":"15:54","end":"16:54","startHours":15.896236928214709,"endHours":16.89623692821471,"planetary_lord":"Sun"},{"name":"Hora 12","start":"16:54","end":"17:54","startHours":16.89623692821471,"endHours":17.89623692821471,"planetary_lord":"Mars"},{"name":"Hora 13","start":"17:54","end":"18:54","startHours":17.89623692821471,"endHours":18.89623692821471,"planetary_lord":"Jupiter"},{"name":"Hora 14","start":"18:54","end":"19:54","startHours":18.89623692821471,"endHours":19.89623692821471,"planetary_lord":"Saturn"},{"name":"Hora 15","start":"19:54","end":"20:54","startHours":19.89623692821471,"endHours":20.89623692821471,"planetary_lord":"Moon"},{"name":"Hora 16","start":"20:54","end":"21:54","startHours":20.89623692821471,"endHours":21.89623692821471,"planetary_lord":"Mercury"},{"name":"Hora 17","start":"21:54","end":"22:54","startHours":21.89623692821471,"endHours":22.89623692821471,"planetary_lord":"Venus"},{"name":"Hora 18","start":"22:54","end":"23:54","startHours":22.89623692821471,"endHours":23.89623692821471,"planetary_lord":"Sun"},{"name":"Hora 19","start":"23:54","end":"00:54","startHours":23.89623692821471,"endHours":24.89623692821471,"planetary_lord":"Mars"},{"name":"Hora 20","start":"00:54","end":"01:54","startHours":24.89623692821471,"endHours":25.89623692821471,"planetary_lord":"Jupiter"},{"name":"Hora 21","start":"01:54","end":"02:54","startHours":25.89623692821471,"endHours":26.89623692821471,"planetary_lord":"Saturn"},{"name":"Hora 22","start":"02:54","end":"03:54","startHours":26.89623692821471,"endHours":27.89623692821471,"planetary_lord":"Moon"},{"name":"Hora 23","start":"03:54","end":"04:54","startHours":27.89623692821471,"endHours":28.89623692821471,"planetary_lord":"Mercury"},{"name":"Hora 24","start":"04:54","end":"05:54","startHours":28.89623692821471,"endHours":29.89623692821471,"planetary_lord":"Venus"}],"taraBala":{"favorable_nakshatras":["Aśvinī","Bharaṇī","Kṛttikā","Rohiṇī","Mṛgaśirā","Maghā","Pūrva Phalgunī","Uttara Phalgunī","Hasta","Citrā","Mūla","Pūrva Āṣāḍhā","Uttara Āṣāḍhā","Śravaṇa","Dhaniṣṭhā"],"unfavorable_nakshatras":["Ārdrā","Punarvasu","Puṣya","Aśleṣā","Svātī","Viśākhā","Anurādhā","Jyeṣṭhā","Śatabhiṣaj","Pūrva Bhādrapadā","Uttara Bhādrapadā","Revatī"],"nature":"Janma-tara if same nakshatra; favorable for 15 nakshatras"},"chandraBala":{"favorable_rashis":["Meṣa","Vṛṣabha","Siṃha","Kanyā","Vṛścika","Makara"],"unfavorable_rashis":["Mithuna","Karka","Tulā","Dhanu","Kumbha","Mīna"]},"dishaShool":"East (Pūrva)","chandraVasa":"North-East","rahuVasa":"North-East","anandadiYoga":{"name":"Mausala","quality":"Inauspicious"},"tropicalRitu":"Varṣā (Monsoon) (tropical)","vedicRitu":"Śarad (Autumn)","tropicalAyana":"Dakṣiṇāyana","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":6.875806726535102,"eotMinutes":7.346914761554353,"ayanamsa":-48.2747}},"calendars":{"vikram_samvat":-3107,"saka_samvat":-3242,"bengali_samvat":-3757,"malayalam_era":-3988,"nanakshahi_year":-4633,"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 -3107 undefined · Śaka -3242 undefined"},"festivals":[],"todays_walk":{"walk":{"id":"chandra-walk","name":"Candra Walk","name_sanskrit":"चन्द्र यात्रा","type":"graha","description":"Manas-control + BG 6.5-7, 6.34-35.","step_count":5,"url":"/walk/chandra-walk","steps":[{"label":"BG 6.5","url":"/bhagavad-gita/6/5","purpose":"Lift the self by the Self; begin the walk with inner responsibility."},{"label":"BG 6.6","url":"/bhagavad-gita/6/6","purpose":"See the mind as friend when mastered and enemy when unmastered."},{"label":"BG 6.7","url":"/bhagavad-gita/6/7","purpose":"Stabilize the conquered mind in heat/cold, honor/dishonor, pleasure/pain."},{"label":"BG 6.34","url":"/bhagavad-gita/6/34","purpose":"Name the restless mind honestly before trying to discipline it."},{"label":"BG 6.35","url":"/bhagavad-gita/6/35","purpose":"Complete with abhyāsa and vairāgya: practice and detachment."}]},"reason":"Somavāra (Monday) — 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 20, 3165 BCE · Mathurā · Vidhyamitra","description":"September 20, 3165 BCE for Mathurā: Śukla Dvitīyā, sūryodaya 05:54, sūryāsta 18:30.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3164-09-20","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3164-09-20","sa":"https://sa.vidhyamitra.com/city/mathura/-3164-09-20","hi":"https://hi.vidhyamitra.com/city/mathura/-3164-09-20","x-default":"https://vidhyamitra.com/city/mathura/-3164-09-20"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-13T04:02:50.971Z","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":"2026-08-13T04:02:50.971Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-13T04:02:50.971Z","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"}}}