{"id":"vidhyamitra:city-day:mathura:-3146-09-13:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3146-09-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3146-09-13","date_display":"September 13, 3147 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":-3146,"month":9,"day":13,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":572236.770833,"kali_year":-44,"ahargana":-16228.7292,"sun":{"sidereal_longitude":203.0042,"rashi":7,"rashi_name":"Tulā"},"moon":{"sidereal_longitude":9.758,"rashi":1,"rashi_name":"Meṣa"},"tithi":{"number":14,"name":"Caturdaśī","paksha":"Śukla","full_name":"Śukla Caturdaśī","elongation_degrees":166.7538,"elapsed_within_tithi_degrees":10.7538},"nakshatra":{"number":1,"name":"Aśvinī","pada":3,"moon_longitude":9.758,"elapsed_within_degrees":9.758},"yoga":{"number":16,"name":"Siddhi","sum_longitude":212.7622},"karana":{"half_tithi_index":27,"name":"Vaṇija"},"vara":{"number":4,"name":"Maṅgalavāra (Tuesday)"}},"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":-3146,"month":9,"day":13,"hour":6,"minute":30,"calendar":"julian"},"julian_day":572236.770833,"ahargana":-16228.7292,"kali_year":-44,"ayanamsa_lahiri":-48.0235,"grahas":{"sun":{"sidereal_longitude":203.0042,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":16,"name":"Viśākhā","pada":1},"retrograde":false},"moon":{"sidereal_longitude":9.758,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":1,"name":"Aśvinī","pada":3},"retrograde":false,"latitude":3.4398},"mars":{"sidereal_longitude":159.33,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":12,"name":"Uttara Phalgunī","pada":4},"retrograde":false},"mercury":{"sidereal_longitude":201.0325,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":16,"name":"Viśākhā","pada":1},"retrograde":false},"jupiter":{"sidereal_longitude":107.1039,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":9,"name":"Āśleṣā","pada":1},"retrograde":false},"venus":{"sidereal_longitude":234.5449,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":3},"retrograde":false},"saturn":{"sidereal_longitude":187.3904,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":15,"name":"Svātī","pada":1},"retrograde":false},"rahu":{"sidereal_longitude":319.8762,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":24,"name":"Śatabhiṣā","pada":4},"retrograde":false},"ketu":{"sidereal_longitude":139.8762,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":11,"name":"Pūrva 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":"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":-3146,"month":9,"day":13,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":572236.770833,"kali_year":-44,"ahargana":-16228.7292,"sun":{"sidereal_longitude":203.0042,"rashi":7,"rashi_name":"Tulā"},"moon":{"sidereal_longitude":9.758,"rashi":1,"rashi_name":"Meṣa"},"tithi":{"number":14,"name":"Caturdaśī","paksha":"Śukla","full_name":"Śukla Caturdaśī","elongation_degrees":166.7538,"elapsed_within_tithi_degrees":10.7538},"nakshatra":{"number":1,"name":"Aśvinī","pada":3,"moon_longitude":9.758,"elapsed_within_degrees":9.758},"yoga":{"number":16,"name":"Siddhi","sum_longitude":212.7622},"karana":{"half_tithi_index":27,"name":"Vaṇija"},"vara":{"number":4,"name":"Maṅgalavāra (Tuesday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":3.44,"elongation":166.754},"lunar":{"type":"lunar","occurs":false,"moon_latitude":3.44,"opposition_distance":13.246}},"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":"05:50","sunsetLocal":"18:39","solarNoonLocal":"12:15","dayLengthHours":12.806906337586788,"dayLengthDisplay":"12 Hours 48 Mins 25 Secs","nightLengthDisplay":"11 Hours 11 Mins 35 Secs","moonriseLocal":"17:49","moonsetLocal":"04:54","rahuKala":{"name":"Rāhu Kāla","start":"15:27","end":"17:03","startHours":15.444248735565596,"endHours":17.045112027763945,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"09:02","end":"10:38","startHours":9.040795566772202,"endHours":10.641658858970551,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"12:15","end":"13:51","startHours":12.242522151168899,"endHours":13.843385443367247,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"08:50","end":"09:15","startHours":8.827347127812422,"endHours":9.254244005731982,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:22","end":"06:43","startHours":6.372690079774954,"endHours":6.7142075821106015,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:49","end":"12:40","startHours":11.815625273249339,"endHours":12.66941902908846,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"04:08","end":"04:59","startHours":4.131481470697266,"endHours":4.985275226536386,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"04:46","end":"05:50","startHours":4.771826787576606,"endHours":5.839068982375505,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:23","end":"15:14","startHours":14.377006540766697,"endHours":15.230800296605816,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"18:27","end":"18:51","startHours":18.445975319962294,"endHours":18.845975319962292,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"18:39","end":"19:11","startHours":18.645975319962293,"endHours":19.179596417361743,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"18:24","end":"20:09","startHours":18.395975319962293,"endHours":20.145975319962293,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:49","end":"00:40","startHours":23.81562527324934,"endHours":24.66941902908846,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Roga","start":"05:50","end":"07:26","startHours":5.839068982375505,"endHours":7.439932274573853,"quality":"inauspicious"},{"name":"Udveg","start":"07:26","end":"09:02","startHours":7.439932274573853,"endHours":9.040795566772202,"quality":"inauspicious"},{"name":"Chala","start":"09:02","end":"10:38","startHours":9.040795566772202,"endHours":10.641658858970551,"quality":"neutral"},{"name":"Labha","start":"10:38","end":"12:15","startHours":10.641658858970551,"endHours":12.242522151168899,"quality":"auspicious"},{"name":"Amṛta","start":"12:15","end":"13:51","startHours":12.242522151168899,"endHours":13.843385443367247,"quality":"auspicious"},{"name":"Kāla","start":"13:51","end":"15:27","startHours":13.843385443367247,"endHours":15.444248735565596,"quality":"inauspicious"},{"name":"Śubha","start":"15:27","end":"17:03","startHours":15.444248735565596,"endHours":17.045112027763945,"quality":"auspicious"},{"name":"Roga","start":"17:03","end":"18:39","startHours":17.045112027763945,"endHours":18.645975319962293,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Kāla","start":"18:39","end":"20:03","startHours":18.645975319962293,"endHours":20.045112027763945,"quality":"inauspicious"},{"name":"Śubha","start":"20:03","end":"21:27","startHours":20.045112027763945,"endHours":21.444248735565594,"quality":"auspicious"},{"name":"Roga","start":"21:27","end":"22:51","startHours":21.444248735565594,"endHours":22.843385443367247,"quality":"inauspicious"},{"name":"Udveg","start":"22:51","end":"00:15","startHours":22.843385443367247,"endHours":24.2425221511689,"quality":"inauspicious"},{"name":"Chala","start":"00:15","end":"01:38","startHours":24.2425221511689,"endHours":25.64165885897055,"quality":"neutral"},{"name":"Labha","start":"01:38","end":"03:02","startHours":25.64165885897055,"endHours":27.040795566772204,"quality":"auspicious"},{"name":"Amṛta","start":"03:02","end":"04:26","startHours":27.040795566772204,"endHours":28.439932274573852,"quality":"auspicious"},{"name":"Kāla","start":"04:26","end":"05:50","startHours":28.439932274573852,"endHours":29.839068982375505,"quality":"inauspicious"}],"horas":[{"name":"Hora 1","start":"05:50","end":"06:50","startHours":5.839068982375505,"endHours":6.839068982375505,"planetary_lord":"Mars"},{"name":"Hora 2","start":"06:50","end":"07:50","startHours":6.839068982375505,"endHours":7.839068982375505,"planetary_lord":"Jupiter"},{"name":"Hora 3","start":"07:50","end":"08:50","startHours":7.839068982375505,"endHours":8.839068982375505,"planetary_lord":"Saturn"},{"name":"Hora 4","start":"08:50","end":"09:50","startHours":8.839068982375505,"endHours":9.839068982375505,"planetary_lord":"Moon"},{"name":"Hora 5","start":"09:50","end":"10:50","startHours":9.839068982375505,"endHours":10.839068982375505,"planetary_lord":"Mercury"},{"name":"Hora 6","start":"10:50","end":"11:50","startHours":10.839068982375505,"endHours":11.839068982375505,"planetary_lord":"Venus"},{"name":"Hora 7","start":"11:50","end":"12:50","startHours":11.839068982375505,"endHours":12.839068982375505,"planetary_lord":"Sun"},{"name":"Hora 8","start":"12:50","end":"13:50","startHours":12.839068982375505,"endHours":13.839068982375505,"planetary_lord":"Mars"},{"name":"Hora 9","start":"13:50","end":"14:50","startHours":13.839068982375505,"endHours":14.839068982375505,"planetary_lord":"Jupiter"},{"name":"Hora 10","start":"14:50","end":"15:50","startHours":14.839068982375505,"endHours":15.839068982375505,"planetary_lord":"Saturn"},{"name":"Hora 11","start":"15:50","end":"16:50","startHours":15.839068982375505,"endHours":16.839068982375505,"planetary_lord":"Moon"},{"name":"Hora 12","start":"16:50","end":"17:50","startHours":16.839068982375505,"endHours":17.839068982375505,"planetary_lord":"Mercury"},{"name":"Hora 13","start":"17:50","end":"18:50","startHours":17.839068982375505,"endHours":18.839068982375505,"planetary_lord":"Venus"},{"name":"Hora 14","start":"18:50","end":"19:50","startHours":18.839068982375505,"endHours":19.839068982375505,"planetary_lord":"Sun"},{"name":"Hora 15","start":"19:50","end":"20:50","startHours":19.839068982375505,"endHours":20.839068982375505,"planetary_lord":"Mars"},{"name":"Hora 16","start":"20:50","end":"21:50","startHours":20.839068982375505,"endHours":21.839068982375505,"planetary_lord":"Jupiter"},{"name":"Hora 17","start":"21:50","end":"22:50","startHours":21.839068982375505,"endHours":22.839068982375505,"planetary_lord":"Saturn"},{"name":"Hora 18","start":"22:50","end":"23:50","startHours":22.839068982375505,"endHours":23.839068982375505,"planetary_lord":"Moon"},{"name":"Hora 19","start":"23:50","end":"00:50","startHours":23.839068982375505,"endHours":24.839068982375505,"planetary_lord":"Mercury"},{"name":"Hora 20","start":"00:50","end":"01:50","startHours":24.839068982375505,"endHours":25.839068982375505,"planetary_lord":"Venus"},{"name":"Hora 21","start":"01:50","end":"02:50","startHours":25.839068982375505,"endHours":26.839068982375505,"planetary_lord":"Sun"},{"name":"Hora 22","start":"02:50","end":"03:50","startHours":26.839068982375505,"endHours":27.839068982375505,"planetary_lord":"Mars"},{"name":"Hora 23","start":"03:50","end":"04:50","startHours":27.839068982375505,"endHours":28.839068982375505,"planetary_lord":"Jupiter"},{"name":"Hora 24","start":"04:50","end":"05:50","startHours":28.839068982375505,"endHours":29.839068982375505,"planetary_lord":"Saturn"}],"taraBala":{"favorable_nakshatras":["Bharaṇī","Kṛttikā","Rohiṇī","Mṛgaśirā","Ārdrā","Pūrva Phalgunī","Uttara Phalgunī","Hasta","Citrā","Svātī","Pūrva Āṣāḍhā","Uttara Āṣāḍhā","Śravaṇa","Dhaniṣṭhā","Śatabhiṣaj"],"unfavorable_nakshatras":["Aśvinī","Punarvasu","Puṣya","Aśleṣā","Maghā","Viśākhā","Anurādhā","Jyeṣṭhā","Mūla","Pūrva Bhādrapadā","Uttara Bhādrapadā","Revatī"],"nature":"Janma-tara if same nakshatra; favorable for 15 nakshatras"},"chandraBala":{"favorable_rashis":["Meṣa","Mithuna","Kanyā","Tulā","Makara","Kumbha"],"unfavorable_rashis":["Vṛṣabha","Karka","Siṃha","Vṛścika","Dhanu","Mīna"]},"dishaShool":"North (Uttara)","chandraVasa":"East","rahuVasa":"North","anandadiYoga":{"name":"Vajra","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":9.683785075163124,"eotMinutes":4.753870929866006,"ayanamsa":-48.0235}},"calendars":{"vikram_samvat":-3089,"saka_samvat":-3224,"bengali_samvat":-3739,"malayalam_era":-3970,"nanakshahi_year":-4615,"lunar_month":"Kārtika","lunar_month_paksha_full":"Kārtika Śukla Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Kārtika","lunar_month_amanta":"Kārtika","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Tulā (Aippasi)","ritu":"Śarad (Autumn)","display_summary":"Kārtika Śukla Caturdaśī · Vikram -3089 undefined · Śaka -3224 undefined"},"festivals":[],"todays_walk":{"walk":{"id":"mangala-walk","name":"Maṅgala Walk","name_sanskrit":"मङ्गल यात्रा","type":"graha","description":"Right action + BG 2.31-38 (kṣatriya-dharma).","step_count":7,"url":"/walk/mangala-walk"},"reason":"Maṅgalavāra (Tuesday) — 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 13, 3147 BCE · Mathurā · Vidhyamitra","description":"September 13, 3147 BCE for Mathurā: Śukla Caturdaśī, sūryodaya 05:50, sūryāsta 18:39.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3146-09-13","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3146-09-13","sa":"https://sa.vidhyamitra.com/city/mathura/-3146-09-13","hi":"https://hi.vidhyamitra.com/city/mathura/-3146-09-13","x-default":"https://vidhyamitra.com/city/mathura/-3146-09-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-12T17:19:51.275Z","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":"2026-08-12T17:19:51.275Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-12T17:19:51.275Z","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"}}}