{"id":"vidhyamitra:city-day:mathura:-3129-10-21:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3129-10-21","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3129-10-21","date_display":"October 21, 3130 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":-3129,"month":10,"day":21,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":578483.770833,"kali_year":-27,"ahargana":-9981.7292,"sun":{"sidereal_longitude":241.3416,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":237.1542,"rashi":8,"rashi_name":"Vṛścika"},"tithi":{"number":30,"name":"Amāvasyā","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Amāvasyā","elongation_degrees":355.8127,"elapsed_within_tithi_degrees":7.8127},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":4,"moon_longitude":237.1542,"elapsed_within_degrees":10.4876},"yoga":{"number":9,"name":"Śūla","sum_longitude":118.4958},"karana":{"half_tithi_index":59,"name":"Nāga"},"vara":{"number":0,"name":"Śukravāra (Friday)"}},"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":-3129,"month":10,"day":21,"hour":6,"minute":30,"calendar":"julian"},"julian_day":578483.770833,"ahargana":-9981.7292,"kali_year":-27,"ayanamsa_lahiri":-47.7846,"grahas":{"sun":{"sidereal_longitude":241.3416,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":1},"retrograde":false},"moon":{"sidereal_longitude":237.1542,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":4},"retrograde":false,"latitude":-4.1798},"mars":{"sidereal_longitude":190.1723,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":15,"name":"Svātī","pada":2},"retrograde":false},"mercury":{"sidereal_longitude":228.0386,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":1},"retrograde":false},"jupiter":{"sidereal_longitude":244.7467,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":2},"retrograde":false},"venus":{"sidereal_longitude":227.2656,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":1},"retrograde":false},"saturn":{"sidereal_longitude":16.2415,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":2,"name":"Bharaṇī","pada":1},"retrograde":true},"rahu":{"sidereal_longitude":348.88,"rashi":{"number":12,"name":"Mīna"},"nakshatra":{"number":27,"name":"Revatī","pada":1},"retrograde":false},"ketu":{"sidereal_longitude":168.88,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":13,"name":"Hasta","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":-3129,"month":10,"day":21,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":578483.770833,"kali_year":-27,"ahargana":-9981.7292,"sun":{"sidereal_longitude":241.3416,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":237.1542,"rashi":8,"rashi_name":"Vṛścika"},"tithi":{"number":30,"name":"Amāvasyā","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Amāvasyā","elongation_degrees":355.8127,"elapsed_within_tithi_degrees":7.8127},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":4,"moon_longitude":237.1542,"elapsed_within_degrees":10.4876},"yoga":{"number":9,"name":"Śūla","sum_longitude":118.4958},"karana":{"half_tithi_index":59,"name":"Nāga"},"vara":{"number":0,"name":"Śukravāra (Friday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-4.18,"elongation":4.187},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-4.18,"opposition_distance":175.813}},"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":"06:11","sunsetLocal":"17:56","solarNoonLocal":"12:03","dayLengthHours":11.753430310068957,"dayLengthDisplay":"11 Hours 45 Mins 12 Secs","nightLengthDisplay":"12 Hours 14 Mins 48 Secs","moonriseLocal":"05:52","moonsetLocal":"17:42","rahuKala":{"name":"Rāhu Kāla","start":"10:35","end":"12:03","startHours":10.58875086846297,"endHours":12.057929657221589,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"15:00","end":"16:28","startHours":14.996287234738828,"endHours":16.46546602349745,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"07:39","end":"09:07","startHours":7.65039329094573,"endHours":9.11957207970435,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"08:55","end":"09:19","startHours":8.923681574536534,"endHours":9.315462584872165,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:40","end":"06:59","startHours":6.67094076510665,"endHours":6.984365573375156,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:40","end":"12:27","startHours":11.666148646885956,"endHours":12.449710667557222,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"04:37","end":"05:24","startHours":4.614090460844583,"endHours":5.397652481515847,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"05:12","end":"06:11","startHours":5.20176197634803,"endHours":6.18121450218711,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:01","end":"14:48","startHours":14.016834708899747,"endHours":14.80039672957101,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:44","end":"18:08","startHours":17.734644812256068,"endHours":18.134644812256067,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:56","end":"18:25","startHours":17.934644812256067,"endHours":18.424371075175607,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:41","end":"19:26","startHours":17.684644812256067,"endHours":19.434644812256067,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:40","end":"00:27","startHours":23.666148646885958,"endHours":24.44971066755722,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Chala","start":"06:11","end":"07:39","startHours":6.18121450218711,"endHours":7.65039329094573,"quality":"neutral"},{"name":"Labha","start":"07:39","end":"09:07","startHours":7.65039329094573,"endHours":9.11957207970435,"quality":"auspicious"},{"name":"Amṛta","start":"09:07","end":"10:35","startHours":9.11957207970435,"endHours":10.58875086846297,"quality":"auspicious"},{"name":"Kāla","start":"10:35","end":"12:03","startHours":10.58875086846297,"endHours":12.057929657221589,"quality":"inauspicious"},{"name":"Śubha","start":"12:03","end":"13:32","startHours":12.057929657221589,"endHours":13.527108445980208,"quality":"auspicious"},{"name":"Roga","start":"13:32","end":"15:00","startHours":13.527108445980208,"endHours":14.996287234738828,"quality":"inauspicious"},{"name":"Udveg","start":"15:00","end":"16:28","startHours":14.996287234738828,"endHours":16.46546602349745,"quality":"inauspicious"},{"name":"Chala","start":"16:28","end":"17:56","startHours":16.46546602349745,"endHours":17.934644812256067,"quality":"neutral"}],"nightChoghadiyas":[{"name":"Roga","start":"17:56","end":"19:28","startHours":17.934644812256067,"endHours":19.46546602349745,"quality":"inauspicious"},{"name":"Udveg","start":"19:28","end":"21:00","startHours":19.46546602349745,"endHours":20.99628723473883,"quality":"inauspicious"},{"name":"Chala","start":"21:00","end":"22:32","startHours":20.99628723473883,"endHours":22.527108445980208,"quality":"neutral"},{"name":"Labha","start":"22:32","end":"00:03","startHours":22.527108445980208,"endHours":24.05792965722159,"quality":"auspicious"},{"name":"Amṛta","start":"00:03","end":"01:35","startHours":24.05792965722159,"endHours":25.58875086846297,"quality":"auspicious"},{"name":"Kāla","start":"01:35","end":"03:07","startHours":25.58875086846297,"endHours":27.119572079704348,"quality":"inauspicious"},{"name":"Śubha","start":"03:07","end":"04:39","startHours":27.119572079704348,"endHours":28.65039329094573,"quality":"auspicious"},{"name":"Roga","start":"04:39","end":"06:11","startHours":28.65039329094573,"endHours":30.18121450218711,"quality":"inauspicious"}],"horas":[{"name":"Hora 1","start":"06:11","end":"07:11","startHours":6.18121450218711,"endHours":7.18121450218711,"planetary_lord":"Venus"},{"name":"Hora 2","start":"07:11","end":"08:11","startHours":7.18121450218711,"endHours":8.18121450218711,"planetary_lord":"Sun"},{"name":"Hora 3","start":"08:11","end":"09:11","startHours":8.18121450218711,"endHours":9.18121450218711,"planetary_lord":"Mars"},{"name":"Hora 4","start":"09:11","end":"10:11","startHours":9.18121450218711,"endHours":10.18121450218711,"planetary_lord":"Jupiter"},{"name":"Hora 5","start":"10:11","end":"11:11","startHours":10.18121450218711,"endHours":11.18121450218711,"planetary_lord":"Saturn"},{"name":"Hora 6","start":"11:11","end":"12:11","startHours":11.18121450218711,"endHours":12.18121450218711,"planetary_lord":"Moon"},{"name":"Hora 7","start":"12:11","end":"13:11","startHours":12.18121450218711,"endHours":13.18121450218711,"planetary_lord":"Mercury"},{"name":"Hora 8","start":"13:11","end":"14:11","startHours":13.18121450218711,"endHours":14.18121450218711,"planetary_lord":"Venus"},{"name":"Hora 9","start":"14:11","end":"15:11","startHours":14.18121450218711,"endHours":15.18121450218711,"planetary_lord":"Sun"},{"name":"Hora 10","start":"15:11","end":"16:11","startHours":15.18121450218711,"endHours":16.18121450218711,"planetary_lord":"Mars"},{"name":"Hora 11","start":"16:11","end":"17:11","startHours":16.18121450218711,"endHours":17.18121450218711,"planetary_lord":"Jupiter"},{"name":"Hora 12","start":"17:11","end":"18:11","startHours":17.18121450218711,"endHours":18.18121450218711,"planetary_lord":"Saturn"},{"name":"Hora 13","start":"18:11","end":"19:11","startHours":18.18121450218711,"endHours":19.18121450218711,"planetary_lord":"Moon"},{"name":"Hora 14","start":"19:11","end":"20:11","startHours":19.18121450218711,"endHours":20.18121450218711,"planetary_lord":"Mercury"},{"name":"Hora 15","start":"20:11","end":"21:11","startHours":20.18121450218711,"endHours":21.18121450218711,"planetary_lord":"Venus"},{"name":"Hora 16","start":"21:11","end":"22:11","startHours":21.18121450218711,"endHours":22.18121450218711,"planetary_lord":"Sun"},{"name":"Hora 17","start":"22:11","end":"23:11","startHours":22.18121450218711,"endHours":23.18121450218711,"planetary_lord":"Mars"},{"name":"Hora 18","start":"23:11","end":"00:11","startHours":23.18121450218711,"endHours":24.18121450218711,"planetary_lord":"Jupiter"},{"name":"Hora 19","start":"00:11","end":"01:11","startHours":24.18121450218711,"endHours":25.18121450218711,"planetary_lord":"Saturn"},{"name":"Hora 20","start":"01:11","end":"02:11","startHours":25.18121450218711,"endHours":26.18121450218711,"planetary_lord":"Moon"},{"name":"Hora 21","start":"02:11","end":"03:11","startHours":26.18121450218711,"endHours":27.18121450218711,"planetary_lord":"Mercury"},{"name":"Hora 22","start":"03:11","end":"04:11","startHours":27.18121450218711,"endHours":28.18121450218711,"planetary_lord":"Venus"},{"name":"Hora 23","start":"04:11","end":"05:11","startHours":28.18121450218711,"endHours":29.18121450218711,"planetary_lord":"Sun"},{"name":"Hora 24","start":"05:11","end":"06:11","startHours":29.18121450218711,"endHours":30.18121450218711,"planetary_lord":"Mars"}],"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":"West (Paścim)","chandraVasa":"North-East","rahuVasa":"South-East","anandadiYoga":{"name":"Mudgara","quality":"Inauspicious"},"tropicalRitu":"Śarad (Autumn) (tropical)","vedicRitu":"Hemanta (Pre-winter)","tropicalAyana":"Dakṣiṇāyana","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":-5.3496555158098715,"eotMinutes":15.829420566704727,"ayanamsa":-47.7846}},"calendars":{"vikram_samvat":-3072,"saka_samvat":-3207,"bengali_samvat":-3722,"malayalam_era":-3953,"nanakshahi_year":-4598,"lunar_month":"Pauṣa","lunar_month_paksha_full":"Pauṣa Kṛṣṇa 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":"Dhanus (Mārgaḻi)","ritu":"Hemanta (Pre-winter)","display_summary":"Pauṣa Kṛṣṇa Amāvasyā · Vikram -3072 undefined · Śaka -3207 undefined"},"festivals":[],"todays_walk":{"walk":{"id":"shukra-walk","name":"Śukra Walk","name_sanskrit":"शुक्र यात्रा","type":"graha","description":"Beauty + creativity in dharma + BG 10.36.","step_count":5,"url":"/walk/shukra-walk"},"reason":"Śukravāra (Friday) — 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 October 21, 3130 BCE · Mathurā · Vidhyamitra","description":"October 21, 3130 BCE for Mathurā: Kṛṣṇa Amāvasyā, sūryodaya 06:11, sūryāsta 17:56.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3129-10-21","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3129-10-21","sa":"https://sa.vidhyamitra.com/city/mathura/-3129-10-21","hi":"https://hi.vidhyamitra.com/city/mathura/-3129-10-21","x-default":"https://vidhyamitra.com/city/mathura/-3129-10-21"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-13T16:46:54.307Z","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":"2026-08-13T16:46:54.307Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-13T16:46:54.307Z","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"}}}