{"id":"vidhyamitra:city-day:mathura:-3225-05-21:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3225-05-21","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3225-05-21","date_display":"May 21, 3226 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":-3225,"month":5,"day":21,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":543266.770833,"kali_year":-123,"ahargana":-45198.7292,"sun":{"sidereal_longitude":91.4223,"rashi":4,"rashi_name":"Karka"},"moon":{"sidereal_longitude":242.7006,"rashi":9,"rashi_name":"Dhanu"},"tithi":{"number":13,"name":"Trayodaśī","paksha":"Śukla","full_name":"Śukla Trayodaśī","elongation_degrees":151.2784,"elapsed_within_tithi_degrees":7.2784},"nakshatra":{"number":19,"name":"Mūla","pada":1,"moon_longitude":242.7006,"elapsed_within_degrees":2.7006},"yoga":{"number":26,"name":"Indra","sum_longitude":334.1229},"karana":{"half_tithi_index":25,"name":"Taitila"},"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":-3225,"month":5,"day":21,"hour":6,"minute":30,"calendar":"julian"},"julian_day":543266.770833,"ahargana":-45198.7292,"kali_year":-123,"ayanamsa_lahiri":-49.1315,"grahas":{"sun":{"sidereal_longitude":91.4223,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":7,"name":"Punarvasu","pada":4},"retrograde":false},"moon":{"sidereal_longitude":242.7006,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":1},"retrograde":false,"latitude":-0.6143},"mars":{"sidereal_longitude":87.2532,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":7,"name":"Punarvasu","pada":3},"retrograde":false},"mercury":{"sidereal_longitude":89.5552,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":7,"name":"Punarvasu","pada":3},"retrograde":false},"jupiter":{"sidereal_longitude":189.1716,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":15,"name":"Svātī","pada":1},"retrograde":false},"venus":{"sidereal_longitude":46.9759,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":4,"name":"Rohiṇī","pada":3},"retrograde":false},"saturn":{"sidereal_longitude":282.6287,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":22,"name":"Śravaṇa","pada":1},"retrograde":true},"rahu":{"sidereal_longitude":54.8462,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":5,"name":"Mṛgaśīrṣā","pada":1},"retrograde":false},"ketu":{"sidereal_longitude":234.8462,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","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":-3225,"month":5,"day":21,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":543266.770833,"kali_year":-123,"ahargana":-45198.7292,"sun":{"sidereal_longitude":91.4223,"rashi":4,"rashi_name":"Karka"},"moon":{"sidereal_longitude":242.7006,"rashi":9,"rashi_name":"Dhanu"},"tithi":{"number":13,"name":"Trayodaśī","paksha":"Śukla","full_name":"Śukla Trayodaśī","elongation_degrees":151.2784,"elapsed_within_tithi_degrees":7.2784},"nakshatra":{"number":19,"name":"Mūla","pada":1,"moon_longitude":242.7006,"elapsed_within_degrees":2.7006},"yoga":{"number":26,"name":"Indra","sum_longitude":334.1229},"karana":{"half_tithi_index":25,"name":"Taitila"},"vara":{"number":0,"name":"Śukravāra (Friday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-0.614,"elongation":151.278},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-0.614,"opposition_distance":28.722}},"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":"05:39","sunsetLocal":"18:53","solarNoonLocal":"12:16","dayLengthHours":13.239640345332418,"dayLengthDisplay":"13 Hours 14 Mins 23 Secs","nightLengthDisplay":"10 Hours 45 Mins 37 Secs","moonriseLocal":"16:29","moonsetLocal":"04:12","rahuKala":{"name":"Rāhu Kāla","start":"10:36","end":"12:16","startHours":10.607807993792147,"endHours":12.262763036958699,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"15:34","end":"17:14","startHours":15.572673123291803,"endHours":17.227628166458356,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"07:18","end":"08:57","startHours":7.297897907459041,"endHours":8.952852950625594,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"08:44","end":"09:10","startHours":8.732192278203387,"endHours":9.1735136230478,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:12","end":"06:33","startHours":6.194594545348006,"endHours":6.547651621223538,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:49","end":"12:42","startHours":11.821441692114284,"endHours":12.704084381803114,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"03:53","end":"04:46","startHours":3.877657484914833,"endHours":4.760300174603661,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"04:32","end":"05:39","startHours":4.539639502181454,"endHours":5.642942864292489,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:28","end":"15:21","startHours":14.469369761180769,"endHours":15.352012450869596,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"18:41","end":"19:05","startHours":18.68258320962491,"endHours":19.082583209624907,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"18:53","end":"19:26","startHours":18.882583209624908,"endHours":19.434234890680425,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"18:38","end":"20:23","startHours":18.632583209624908,"endHours":20.382583209624908,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:49","end":"00:42","startHours":23.821441692114284,"endHours":24.704084381803114,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Chala","start":"05:39","end":"07:18","startHours":5.642942864292489,"endHours":7.297897907459041,"quality":"neutral"},{"name":"Labha","start":"07:18","end":"08:57","startHours":7.297897907459041,"endHours":8.952852950625594,"quality":"auspicious"},{"name":"Amṛta","start":"08:57","end":"10:36","startHours":8.952852950625594,"endHours":10.607807993792147,"quality":"auspicious"},{"name":"Kāla","start":"10:36","end":"12:16","startHours":10.607807993792147,"endHours":12.262763036958699,"quality":"inauspicious"},{"name":"Śubha","start":"12:16","end":"13:55","startHours":12.262763036958699,"endHours":13.917718080125251,"quality":"auspicious"},{"name":"Roga","start":"13:55","end":"15:34","startHours":13.917718080125251,"endHours":15.572673123291803,"quality":"inauspicious"},{"name":"Udveg","start":"15:34","end":"17:14","startHours":15.572673123291803,"endHours":17.227628166458356,"quality":"inauspicious"},{"name":"Chala","start":"17:14","end":"18:53","startHours":17.227628166458356,"endHours":18.882583209624908,"quality":"neutral"}],"nightChoghadiyas":[{"name":"Roga","start":"18:53","end":"20:14","startHours":18.882583209624908,"endHours":20.227628166458356,"quality":"inauspicious"},{"name":"Udveg","start":"20:14","end":"21:34","startHours":20.227628166458356,"endHours":21.572673123291803,"quality":"inauspicious"},{"name":"Chala","start":"21:34","end":"22:55","startHours":21.572673123291803,"endHours":22.91771808012525,"quality":"neutral"},{"name":"Labha","start":"22:55","end":"00:16","startHours":22.91771808012525,"endHours":24.2627630369587,"quality":"auspicious"},{"name":"Amṛta","start":"00:16","end":"01:36","startHours":24.2627630369587,"endHours":25.607807993792147,"quality":"auspicious"},{"name":"Kāla","start":"01:36","end":"02:57","startHours":25.607807993792147,"endHours":26.952852950625594,"quality":"inauspicious"},{"name":"Śubha","start":"02:57","end":"04:18","startHours":26.952852950625594,"endHours":28.297897907459042,"quality":"auspicious"},{"name":"Roga","start":"04:18","end":"05:39","startHours":28.297897907459042,"endHours":29.64294286429249,"quality":"inauspicious"}],"horas":[{"name":"Hora 1","start":"05:39","end":"06:39","startHours":5.642942864292489,"endHours":6.642942864292489,"planetary_lord":"Venus"},{"name":"Hora 2","start":"06:39","end":"07:39","startHours":6.642942864292489,"endHours":7.642942864292489,"planetary_lord":"Sun"},{"name":"Hora 3","start":"07:39","end":"08:39","startHours":7.642942864292489,"endHours":8.64294286429249,"planetary_lord":"Mars"},{"name":"Hora 4","start":"08:39","end":"09:39","startHours":8.64294286429249,"endHours":9.64294286429249,"planetary_lord":"Jupiter"},{"name":"Hora 5","start":"09:39","end":"10:39","startHours":9.64294286429249,"endHours":10.64294286429249,"planetary_lord":"Saturn"},{"name":"Hora 6","start":"10:39","end":"11:39","startHours":10.64294286429249,"endHours":11.64294286429249,"planetary_lord":"Moon"},{"name":"Hora 7","start":"11:39","end":"12:39","startHours":11.64294286429249,"endHours":12.64294286429249,"planetary_lord":"Mercury"},{"name":"Hora 8","start":"12:39","end":"13:39","startHours":12.64294286429249,"endHours":13.64294286429249,"planetary_lord":"Venus"},{"name":"Hora 9","start":"13:39","end":"14:39","startHours":13.64294286429249,"endHours":14.64294286429249,"planetary_lord":"Sun"},{"name":"Hora 10","start":"14:39","end":"15:39","startHours":14.64294286429249,"endHours":15.64294286429249,"planetary_lord":"Mars"},{"name":"Hora 11","start":"15:39","end":"16:39","startHours":15.64294286429249,"endHours":16.64294286429249,"planetary_lord":"Jupiter"},{"name":"Hora 12","start":"16:39","end":"17:39","startHours":16.64294286429249,"endHours":17.64294286429249,"planetary_lord":"Saturn"},{"name":"Hora 13","start":"17:39","end":"18:39","startHours":17.64294286429249,"endHours":18.64294286429249,"planetary_lord":"Moon"},{"name":"Hora 14","start":"18:39","end":"19:39","startHours":18.64294286429249,"endHours":19.64294286429249,"planetary_lord":"Mercury"},{"name":"Hora 15","start":"19:39","end":"20:39","startHours":19.64294286429249,"endHours":20.64294286429249,"planetary_lord":"Venus"},{"name":"Hora 16","start":"20:39","end":"21:39","startHours":20.64294286429249,"endHours":21.64294286429249,"planetary_lord":"Sun"},{"name":"Hora 17","start":"21:39","end":"22:39","startHours":21.64294286429249,"endHours":22.64294286429249,"planetary_lord":"Mars"},{"name":"Hora 18","start":"22:39","end":"23:39","startHours":22.64294286429249,"endHours":23.64294286429249,"planetary_lord":"Jupiter"},{"name":"Hora 19","start":"23:39","end":"00:39","startHours":23.64294286429249,"endHours":24.64294286429249,"planetary_lord":"Saturn"},{"name":"Hora 20","start":"00:39","end":"01:39","startHours":24.64294286429249,"endHours":25.64294286429249,"planetary_lord":"Moon"},{"name":"Hora 21","start":"01:39","end":"02:39","startHours":25.64294286429249,"endHours":26.64294286429249,"planetary_lord":"Mercury"},{"name":"Hora 22","start":"02:39","end":"03:39","startHours":26.64294286429249,"endHours":27.64294286429249,"planetary_lord":"Venus"},{"name":"Hora 23","start":"03:39","end":"04:39","startHours":27.64294286429249,"endHours":28.64294286429249,"planetary_lord":"Sun"},{"name":"Hora 24","start":"04:39","end":"05:39","startHours":28.64294286429249,"endHours":29.64294286429249,"planetary_lord":"Mars"}],"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":["Vṛṣabha","Mithuna","Kanyā","Tulā","Dhanu","Kumbha"],"unfavorable_rashis":["Meṣa","Karka","Siṃha","Vṛścika","Makara","Mīna"]},"dishaShool":"West (Paścim)","chandraVasa":"East","rahuVasa":"South-East","anandadiYoga":{"name":"Chatra","quality":"Auspicious"},"tropicalRitu":"Vasanta (Spring) (tropical)","vedicRitu":"Grīṣma (Summer)","tropicalAyana":"Uttarāyaṇa","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":15.523386732454098,"eotMinutes":3.539417782478063,"ayanamsa":-49.1315}},"calendars":{"vikram_samvat":-3168,"saka_samvat":-3303,"bengali_samvat":-3818,"malayalam_era":-4049,"nanakshahi_year":-4694,"lunar_month":"Śrāvaṇa","lunar_month_paksha_full":"Śrāvaṇa Śukla Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Śrāvaṇa","lunar_month_amanta":"Śrāvaṇa","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Karkaṭa (Āḍi)","ritu":"Varṣā (Monsoon)","display_summary":"Śrāvaṇa Śukla Trayodaśī · Vikram -3168 undefined · Śaka -3303 undefined"},"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":"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":"Dedicated festival walk for Pradoṣa Vrata is not live yet; 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 May 21, 3226 BCE · Mathurā · Vidhyamitra","description":"May 21, 3226 BCE for Mathurā: Śukla Trayodaśī, sūryodaya 05:39, sūryāsta 18:53.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3225-05-21","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3225-05-21","sa":"https://sa.vidhyamitra.com/city/mathura/-3225-05-21","hi":"https://hi.vidhyamitra.com/city/mathura/-3225-05-21","x-default":"https://vidhyamitra.com/city/mathura/-3225-05-21"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-10T14:02:44.883Z","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":"2026-08-10T14:02:44.883Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-10T14:02:44.883Z","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"}}}