{"id":"vidhyamitra:city-day:mathura:-3165-05-03:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3165-05-03","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3165-05-03","date_display":"May 3, 3166 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":-3165,"month":5,"day":3,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":565163.770833,"kali_year":-63,"ahargana":-23301.7292,"sun":{"sidereal_longitude":73.8828,"rashi":3,"rashi_name":"Mithuna"},"moon":{"sidereal_longitude":43.7426,"rashi":2,"rashi_name":"Vṛṣabha"},"tithi":{"number":28,"name":"Trayodaśī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Trayodaśī","elongation_degrees":329.8599,"elapsed_within_tithi_degrees":5.8599},"nakshatra":{"number":4,"name":"Rohiṇī","pada":2,"moon_longitude":43.7426,"elapsed_within_degrees":3.7426},"yoga":{"number":9,"name":"Śūla","sum_longitude":117.6254},"karana":{"half_tithi_index":54,"name":"Gara"},"vara":{"number":1,"name":"Śanivāra (Saturday)"}},"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":-3165,"month":5,"day":3,"hour":6,"minute":30,"calendar":"julian"},"julian_day":565163.770833,"ahargana":-23301.7292,"kali_year":-63,"ayanamsa_lahiri":-48.294,"grahas":{"sun":{"sidereal_longitude":73.8828,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":6,"name":"Ārdrā","pada":3},"retrograde":false},"moon":{"sidereal_longitude":43.7426,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":4,"name":"Rohiṇī","pada":2},"retrograde":false,"latitude":4.2035},"mars":{"sidereal_longitude":54.0718,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":5,"name":"Mṛgaśīrṣā","pada":1},"retrograde":false},"mercury":{"sidereal_longitude":67.1314,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":6,"name":"Ārdrā","pada":1},"retrograde":false},"jupiter":{"sidereal_longitude":211.3458,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":16,"name":"Viśākhā","pada":4},"retrograde":true},"venus":{"sidereal_longitude":87.6812,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":7,"name":"Punarvasu","pada":3},"retrograde":false},"saturn":{"sidereal_longitude":296.778,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":2},"retrograde":true},"rahu":{"sidereal_longitude":334.6377,"rashi":{"number":12,"name":"Mīna"},"nakshatra":{"number":26,"name":"Uttara Bhādrapadā","pada":1},"retrograde":false},"ketu":{"sidereal_longitude":154.6377,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":12,"name":"Uttara Phalgunī","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":-3165,"month":5,"day":3,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":565163.770833,"kali_year":-63,"ahargana":-23301.7292,"sun":{"sidereal_longitude":73.8828,"rashi":3,"rashi_name":"Mithuna"},"moon":{"sidereal_longitude":43.7426,"rashi":2,"rashi_name":"Vṛṣabha"},"tithi":{"number":28,"name":"Trayodaśī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Trayodaśī","elongation_degrees":329.8599,"elapsed_within_tithi_degrees":5.8599},"nakshatra":{"number":4,"name":"Rohiṇī","pada":2,"moon_longitude":43.7426,"elapsed_within_degrees":3.7426},"yoga":{"number":9,"name":"Śūla","sum_longitude":117.6254},"karana":{"half_tithi_index":54,"name":"Gara"},"vara":{"number":1,"name":"Śanivāra (Saturday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":4.204,"elongation":30.14},"lunar":{"type":"lunar","occurs":false,"moon_latitude":4.204,"opposition_distance":149.86}},"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":"05:51","sunsetLocal":"18:41","solarNoonLocal":"12:16","dayLengthHours":12.821918633247812,"dayLengthDisplay":"12 Hours 49 Mins 19 Secs","nightLengthDisplay":"11 Hours 10 Mins 41 Secs","moonriseLocal":"04:17","moonsetLocal":"16:14","rahuKala":{"name":"Rāhu Kāla","start":"09:04","end":"10:40","startHours":9.063697200379362,"endHours":10.666437029535338,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"13:52","end":"15:28","startHours":13.871916687847289,"endHours":15.474656517003268,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"05:51","end":"07:28","startHours":5.8582175420674085,"endHours":7.460957371223385,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"08:51","end":"09:17","startHours":8.849998556491897,"endHours":9.277395844266826,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:24","end":"06:44","startHours":6.392464151786068,"endHours":6.73438198200601,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:51","end":"12:42","startHours":11.841779570916387,"endHours":12.69657414646624,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"04:09","end":"05:00","startHours":4.1486283909677,"endHours":5.0034229665175545,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"04:47","end":"05:51","startHours":4.789724322630091,"endHours":5.8582175420674085,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:24","end":"15:16","startHours":14.40616329756595,"endHours":15.260957873115805,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"18:29","end":"18:53","startHours":18.48013617531522,"endHours":18.88013617531522,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"18:41","end":"19:13","startHours":18.68013617531522,"endHours":19.214382785033877,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"18:26","end":"20:11","startHours":18.43013617531522,"endHours":20.18013617531522,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:51","end":"00:42","startHours":23.841779570916387,"endHours":24.69657414646624,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Kāla","start":"05:51","end":"07:28","startHours":5.8582175420674085,"endHours":7.460957371223385,"quality":"inauspicious"},{"name":"Śubha","start":"07:28","end":"09:04","startHours":7.460957371223385,"endHours":9.063697200379362,"quality":"auspicious"},{"name":"Roga","start":"09:04","end":"10:40","startHours":9.063697200379362,"endHours":10.666437029535338,"quality":"inauspicious"},{"name":"Udveg","start":"10:40","end":"12:16","startHours":10.666437029535338,"endHours":12.269176858691313,"quality":"inauspicious"},{"name":"Chala","start":"12:16","end":"13:52","startHours":12.269176858691313,"endHours":13.871916687847289,"quality":"neutral"},{"name":"Labha","start":"13:52","end":"15:28","startHours":13.871916687847289,"endHours":15.474656517003268,"quality":"auspicious"},{"name":"Amṛta","start":"15:28","end":"17:05","startHours":15.474656517003268,"endHours":17.077396346159244,"quality":"auspicious"},{"name":"Kāla","start":"17:05","end":"18:41","startHours":17.077396346159244,"endHours":18.68013617531522,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Labha","start":"18:41","end":"20:05","startHours":18.68013617531522,"endHours":20.077396346159244,"quality":"auspicious"},{"name":"Amṛta","start":"20:05","end":"21:28","startHours":20.077396346159244,"endHours":21.474656517003268,"quality":"auspicious"},{"name":"Kāla","start":"21:28","end":"22:52","startHours":21.474656517003268,"endHours":22.87191668784729,"quality":"inauspicious"},{"name":"Śubha","start":"22:52","end":"00:16","startHours":22.87191668784729,"endHours":24.269176858691313,"quality":"auspicious"},{"name":"Roga","start":"00:16","end":"01:40","startHours":24.269176858691313,"endHours":25.666437029535338,"quality":"inauspicious"},{"name":"Udveg","start":"01:40","end":"03:04","startHours":25.666437029535338,"endHours":27.06369720037936,"quality":"inauspicious"},{"name":"Chala","start":"03:04","end":"04:28","startHours":27.06369720037936,"endHours":28.460957371223383,"quality":"neutral"},{"name":"Labha","start":"04:28","end":"05:51","startHours":28.460957371223383,"endHours":29.858217542067408,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"05:51","end":"06:51","startHours":5.8582175420674085,"endHours":6.8582175420674085,"planetary_lord":"Saturn"},{"name":"Hora 2","start":"06:51","end":"07:51","startHours":6.8582175420674085,"endHours":7.8582175420674085,"planetary_lord":"Moon"},{"name":"Hora 3","start":"07:51","end":"08:51","startHours":7.8582175420674085,"endHours":8.858217542067408,"planetary_lord":"Mercury"},{"name":"Hora 4","start":"08:51","end":"09:51","startHours":8.858217542067408,"endHours":9.858217542067408,"planetary_lord":"Venus"},{"name":"Hora 5","start":"09:51","end":"10:51","startHours":9.858217542067408,"endHours":10.858217542067408,"planetary_lord":"Sun"},{"name":"Hora 6","start":"10:51","end":"11:51","startHours":10.858217542067408,"endHours":11.858217542067408,"planetary_lord":"Mars"},{"name":"Hora 7","start":"11:51","end":"12:51","startHours":11.858217542067408,"endHours":12.858217542067408,"planetary_lord":"Jupiter"},{"name":"Hora 8","start":"12:51","end":"13:51","startHours":12.858217542067408,"endHours":13.858217542067408,"planetary_lord":"Saturn"},{"name":"Hora 9","start":"13:51","end":"14:51","startHours":13.858217542067408,"endHours":14.858217542067408,"planetary_lord":"Moon"},{"name":"Hora 10","start":"14:51","end":"15:51","startHours":14.858217542067408,"endHours":15.858217542067408,"planetary_lord":"Mercury"},{"name":"Hora 11","start":"15:51","end":"16:51","startHours":15.858217542067408,"endHours":16.858217542067408,"planetary_lord":"Venus"},{"name":"Hora 12","start":"16:51","end":"17:51","startHours":16.858217542067408,"endHours":17.858217542067408,"planetary_lord":"Sun"},{"name":"Hora 13","start":"17:51","end":"18:51","startHours":17.858217542067408,"endHours":18.858217542067408,"planetary_lord":"Mars"},{"name":"Hora 14","start":"18:51","end":"19:51","startHours":18.858217542067408,"endHours":19.858217542067408,"planetary_lord":"Jupiter"},{"name":"Hora 15","start":"19:51","end":"20:51","startHours":19.858217542067408,"endHours":20.858217542067408,"planetary_lord":"Saturn"},{"name":"Hora 16","start":"20:51","end":"21:51","startHours":20.858217542067408,"endHours":21.858217542067408,"planetary_lord":"Moon"},{"name":"Hora 17","start":"21:51","end":"22:51","startHours":21.858217542067408,"endHours":22.858217542067408,"planetary_lord":"Mercury"},{"name":"Hora 18","start":"22:51","end":"23:51","startHours":22.858217542067408,"endHours":23.858217542067408,"planetary_lord":"Venus"},{"name":"Hora 19","start":"23:51","end":"00:51","startHours":23.858217542067408,"endHours":24.858217542067408,"planetary_lord":"Sun"},{"name":"Hora 20","start":"00:51","end":"01:51","startHours":24.858217542067408,"endHours":25.858217542067408,"planetary_lord":"Mars"},{"name":"Hora 21","start":"01:51","end":"02:51","startHours":25.858217542067408,"endHours":26.858217542067408,"planetary_lord":"Jupiter"},{"name":"Hora 22","start":"02:51","end":"03:51","startHours":26.858217542067408,"endHours":27.858217542067408,"planetary_lord":"Saturn"},{"name":"Hora 23","start":"03:51","end":"04:51","startHours":27.858217542067408,"endHours":28.858217542067408,"planetary_lord":"Moon"},{"name":"Hora 24","start":"04:51","end":"05:51","startHours":28.858217542067408,"endHours":29.858217542067408,"planetary_lord":"Mercury"}],"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":"East (Pūrva)","chandraVasa":"South-East","rahuVasa":"East","anandadiYoga":{"name":"Dhātṛ","quality":"Auspicious"},"tropicalRitu":"Vasanta (Spring) (tropical)","vedicRitu":"Grīṣma (Summer)","tropicalAyana":"Uttarāyaṇa","vedicAyana":"Uttarāyaṇa","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":9.891584642042151,"eotMinutes":3.154588478521171,"ayanamsa":-48.294}},"calendars":{"vikram_samvat":-3108,"saka_samvat":-3243,"bengali_samvat":-3758,"malayalam_era":-3989,"nanakshahi_year":-4634,"lunar_month":"Āṣāḍha","lunar_month_paksha_full":"Āṣāḍha Kṛṣṇa Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Āṣāḍha","lunar_month_amanta":"Āṣāḍha","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Mithuna (Āni)","ritu":"Grīṣma (Summer)","display_summary":"Āṣāḍha Kṛṣṇa Trayodaśī · Vikram -3108 undefined · Śaka -3243 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":"shani-walk","name":"Śani Walk","name_sanskrit":"शनि यात्रा","type":"graha","description":"Tapas + endurance + BG 17.14-19.","step_count":7,"url":"/walk/shani-walk"},"reason":"Dedicated festival walk for Pradoṣa Vrata is not live yet; Śanivāra (Saturday) — 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 3, 3166 BCE · Mathurā · Vidhyamitra","description":"May 3, 3166 BCE for Mathurā: Kṛṣṇa Trayodaśī, sūryodaya 05:51, sūryāsta 18:41.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3165-05-03","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3165-05-03","sa":"https://sa.vidhyamitra.com/city/mathura/-3165-05-03","hi":"https://hi.vidhyamitra.com/city/mathura/-3165-05-03","x-default":"https://vidhyamitra.com/city/mathura/-3165-05-03"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-10T14:16:11.058Z","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":"2026-08-10T14:16:11.058Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-10T14:16:11.058Z","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"}}}