{"id":"vidhyamitra:city-day:mathura:-3165-04-02:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3165-04-02","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3165-04-02","date_display":"April 2, 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":4,"day":2,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":565132.770833,"kali_year":-63,"ahargana":-23332.7292,"sun":{"sidereal_longitude":44.4745,"rashi":2,"rashi_name":"Vṛṣabha"},"moon":{"sidereal_longitude":358.908,"rashi":12,"rashi_name":"Mīna"},"tithi":{"number":27,"name":"Dvādaśī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Dvādaśī","elongation_degrees":314.4335,"elapsed_within_tithi_degrees":2.4335},"nakshatra":{"number":27,"name":"Revatī","pada":4,"moon_longitude":358.908,"elapsed_within_degrees":12.2413},"yoga":{"number":4,"name":"Saubhāgya","sum_longitude":43.3824},"karana":{"half_tithi_index":52,"name":"Kaulava"},"vara":{"number":5,"name":"Budhavāra (Wednesday)"}},"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":4,"day":2,"hour":6,"minute":30,"calendar":"julian"},"julian_day":565132.770833,"ahargana":-23332.7292,"kali_year":-63,"ayanamsa_lahiri":-48.2952,"grahas":{"sun":{"sidereal_longitude":44.4745,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":4,"name":"Rohiṇī","pada":2},"retrograde":false},"moon":{"sidereal_longitude":358.908,"rashi":{"number":12,"name":"Mīna"},"nakshatra":{"number":27,"name":"Revatī","pada":4},"retrograde":false,"latitude":1.7298},"mars":{"sidereal_longitude":31.7843,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":3,"name":"Kṛttikā","pada":2},"retrograde":false},"mercury":{"sidereal_longitude":22.1567,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":2,"name":"Bharaṇī","pada":3},"retrograde":false},"jupiter":{"sidereal_longitude":214.6874,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":17,"name":"Anurādhā","pada":1},"retrograde":true},"venus":{"sidereal_longitude":49.7687,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":4,"name":"Rohiṇī","pada":3},"retrograde":false},"saturn":{"sidereal_longitude":297.4796,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":2},"retrograde":false},"rahu":{"sidereal_longitude":336.2803,"rashi":{"number":12,"name":"Mīna"},"nakshatra":{"number":26,"name":"Uttara Bhādrapadā","pada":1},"retrograde":false},"ketu":{"sidereal_longitude":156.2803,"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":4,"day":2,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":565132.770833,"kali_year":-63,"ahargana":-23332.7292,"sun":{"sidereal_longitude":44.4745,"rashi":2,"rashi_name":"Vṛṣabha"},"moon":{"sidereal_longitude":358.908,"rashi":12,"rashi_name":"Mīna"},"tithi":{"number":27,"name":"Dvādaśī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Dvādaśī","elongation_degrees":314.4335,"elapsed_within_tithi_degrees":2.4335},"nakshatra":{"number":27,"name":"Revatī","pada":4,"moon_longitude":358.908,"elapsed_within_degrees":12.2413},"yoga":{"number":4,"name":"Saubhāgya","sum_longitude":43.3824},"karana":{"half_tithi_index":52,"name":"Kaulava"},"vara":{"number":5,"name":"Budhavāra (Wednesday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":1.73,"elongation":45.567},"lunar":{"type":"lunar","occurs":false,"moon_latitude":1.73,"opposition_distance":134.433}},"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":"06:23","sunsetLocal":"18:24","solarNoonLocal":"12:23","dayLengthHours":12.01984581210986,"dayLengthDisplay":"12 Hours 01 Mins 11 Secs","nightLengthDisplay":"11 Hours 58 Mins 49 Secs","moonriseLocal":"03:56","moonsetLocal":"14:46","rahuKala":{"name":"Rāhu Kāla","start":"12:23","end":"13:53","startHours":12.388896077310331,"endHours":13.891376803824066,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"07:53","end":"09:23","startHours":7.881453897769134,"endHours":9.383934624282867,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"10:53","end":"12:23","startHours":10.8864153507966,"endHours":12.388896077310331,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:11","end":"09:35","startHours":9.183603860747702,"endHours":9.584265387818032,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:53","end":"07:12","startHours":6.879800080093313,"endHours":7.2003293017495755,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:59","end":"12:47","startHours":11.988234550240005,"endHours":12.789557604380661,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"04:47","end":"05:35","startHours":4.7763270629740875,"endHours":5.577650117114745,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"05:23","end":"06:23","startHours":5.37731935357958,"endHours":6.378973171255402,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:24","end":"15:12","startHours":14.392203712661978,"endHours":15.193526766802636,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"18:12","end":"18:36","startHours":18.198818983365264,"endHours":18.598818983365263,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"18:24","end":"18:54","startHours":18.398818983365263,"endHours":18.899645892203175,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"18:09","end":"19:54","startHours":18.148818983365263,"endHours":19.898818983365263,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:59","end":"00:47","startHours":23.988234550240005,"endHours":24.789557604380665,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Labha","start":"06:23","end":"07:53","startHours":6.378973171255402,"endHours":7.881453897769134,"quality":"auspicious"},{"name":"Amṛta","start":"07:53","end":"09:23","startHours":7.881453897769134,"endHours":9.383934624282867,"quality":"auspicious"},{"name":"Kāla","start":"09:23","end":"10:53","startHours":9.383934624282867,"endHours":10.8864153507966,"quality":"inauspicious"},{"name":"Śubha","start":"10:53","end":"12:23","startHours":10.8864153507966,"endHours":12.388896077310331,"quality":"auspicious"},{"name":"Roga","start":"12:23","end":"13:53","startHours":12.388896077310331,"endHours":13.891376803824066,"quality":"inauspicious"},{"name":"Udveg","start":"13:53","end":"15:24","startHours":13.891376803824066,"endHours":15.393857530337797,"quality":"inauspicious"},{"name":"Chala","start":"15:24","end":"16:54","startHours":15.393857530337797,"endHours":16.89633825685153,"quality":"neutral"},{"name":"Labha","start":"16:54","end":"18:24","startHours":16.89633825685153,"endHours":18.398818983365263,"quality":"auspicious"}],"nightChoghadiyas":[{"name":"Udveg","start":"18:24","end":"19:54","startHours":18.398818983365263,"endHours":19.896338256851532,"quality":"inauspicious"},{"name":"Chala","start":"19:54","end":"21:24","startHours":19.896338256851532,"endHours":21.393857530337797,"quality":"neutral"},{"name":"Labha","start":"21:24","end":"22:53","startHours":21.393857530337797,"endHours":22.891376803824066,"quality":"auspicious"},{"name":"Amṛta","start":"22:53","end":"00:23","startHours":22.891376803824066,"endHours":24.388896077310335,"quality":"auspicious"},{"name":"Kāla","start":"00:23","end":"01:53","startHours":24.388896077310335,"endHours":25.8864153507966,"quality":"inauspicious"},{"name":"Śubha","start":"01:53","end":"03:23","startHours":25.8864153507966,"endHours":27.38393462428287,"quality":"auspicious"},{"name":"Roga","start":"03:23","end":"04:53","startHours":27.38393462428287,"endHours":28.881453897769134,"quality":"inauspicious"},{"name":"Udveg","start":"04:53","end":"06:23","startHours":28.881453897769134,"endHours":30.378973171255403,"quality":"inauspicious"}],"horas":[{"name":"Hora 1","start":"06:23","end":"07:23","startHours":6.378973171255402,"endHours":7.378973171255402,"planetary_lord":"Mercury"},{"name":"Hora 2","start":"07:23","end":"08:23","startHours":7.378973171255402,"endHours":8.378973171255403,"planetary_lord":"Venus"},{"name":"Hora 3","start":"08:23","end":"09:23","startHours":8.378973171255403,"endHours":9.378973171255403,"planetary_lord":"Sun"},{"name":"Hora 4","start":"09:23","end":"10:23","startHours":9.378973171255403,"endHours":10.378973171255403,"planetary_lord":"Mars"},{"name":"Hora 5","start":"10:23","end":"11:23","startHours":10.378973171255403,"endHours":11.378973171255403,"planetary_lord":"Jupiter"},{"name":"Hora 6","start":"11:23","end":"12:23","startHours":11.378973171255403,"endHours":12.378973171255403,"planetary_lord":"Saturn"},{"name":"Hora 7","start":"12:23","end":"13:23","startHours":12.378973171255403,"endHours":13.378973171255403,"planetary_lord":"Moon"},{"name":"Hora 8","start":"13:23","end":"14:23","startHours":13.378973171255403,"endHours":14.378973171255403,"planetary_lord":"Mercury"},{"name":"Hora 9","start":"14:23","end":"15:23","startHours":14.378973171255403,"endHours":15.378973171255403,"planetary_lord":"Venus"},{"name":"Hora 10","start":"15:23","end":"16:23","startHours":15.378973171255403,"endHours":16.378973171255403,"planetary_lord":"Sun"},{"name":"Hora 11","start":"16:23","end":"17:23","startHours":16.378973171255403,"endHours":17.378973171255403,"planetary_lord":"Mars"},{"name":"Hora 12","start":"17:23","end":"18:23","startHours":17.378973171255403,"endHours":18.378973171255403,"planetary_lord":"Jupiter"},{"name":"Hora 13","start":"18:23","end":"19:23","startHours":18.378973171255403,"endHours":19.378973171255403,"planetary_lord":"Saturn"},{"name":"Hora 14","start":"19:23","end":"20:23","startHours":19.378973171255403,"endHours":20.378973171255403,"planetary_lord":"Moon"},{"name":"Hora 15","start":"20:23","end":"21:23","startHours":20.378973171255403,"endHours":21.378973171255403,"planetary_lord":"Mercury"},{"name":"Hora 16","start":"21:23","end":"22:23","startHours":21.378973171255403,"endHours":22.378973171255403,"planetary_lord":"Venus"},{"name":"Hora 17","start":"22:23","end":"23:23","startHours":22.378973171255403,"endHours":23.378973171255403,"planetary_lord":"Sun"},{"name":"Hora 18","start":"23:23","end":"00:23","startHours":23.378973171255403,"endHours":24.378973171255403,"planetary_lord":"Mars"},{"name":"Hora 19","start":"00:23","end":"01:23","startHours":24.378973171255403,"endHours":25.378973171255403,"planetary_lord":"Jupiter"},{"name":"Hora 20","start":"01:23","end":"02:23","startHours":25.378973171255403,"endHours":26.378973171255403,"planetary_lord":"Saturn"},{"name":"Hora 21","start":"02:23","end":"03:23","startHours":26.378973171255403,"endHours":27.378973171255403,"planetary_lord":"Moon"},{"name":"Hora 22","start":"03:23","end":"04:23","startHours":27.378973171255403,"endHours":28.378973171255403,"planetary_lord":"Mercury"},{"name":"Hora 23","start":"04:23","end":"05:23","startHours":28.378973171255403,"endHours":29.378973171255403,"planetary_lord":"Venus"},{"name":"Hora 24","start":"05:23","end":"06:23","startHours":29.378973171255403,"endHours":30.378973171255403,"planetary_lord":"Sun"}],"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":["Vṛṣabha","Siṃha","Kanyā","Dhanu","Makara","Mīna"],"unfavorable_rashis":["Meṣa","Mithuna","Karka","Tulā","Vṛścika","Kumbha"]},"dishaShool":"North (Uttara)","chandraVasa":"South-West","rahuVasa":"South-West","anandadiYoga":{"name":"Chatra","quality":"Auspicious"},"tropicalRitu":"undefined (tropical)","vedicRitu":"Vasanta (Spring)","tropicalAyana":"Uttarāyaṇa","vedicAyana":"Uttarāyaṇa","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":-1.5186682630034514,"eotMinutes":-4.028564638619968,"ayanamsa":-48.2952}},"calendars":{"vikram_samvat":-3108,"saka_samvat":-3243,"bengali_samvat":-3758,"malayalam_era":-3989,"nanakshahi_year":-4634,"lunar_month":"Jyeṣṭha","lunar_month_paksha_full":"Jyeṣṭha Kṛṣṇa Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Jyeṣṭha","lunar_month_amanta":"Jyeṣṭha","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Vṛṣabha (Vaikāsi)","ritu":"Grīṣma (Summer)","display_summary":"Jyeṣṭha Kṛṣṇa Dvādaśī · Vikram -3108 undefined · Śaka -3243 undefined"},"festivals":[],"todays_walk":{"walk":{"id":"budha-walk","name":"Budha Walk","name_sanskrit":"बुध यात्रा","type":"graha","description":"Discrimination + BG 2.41 (vyavasāyātmikā buddhi).","step_count":6,"url":"/walk/budha-walk"},"reason":"Budhavāra (Wednesday) — 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 April 2, 3166 BCE · Mathurā · Vidhyamitra","description":"April 2, 3166 BCE for Mathurā: Kṛṣṇa Dvādaśī, sūryodaya 06:23, sūryāsta 18:24.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3165-04-02","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3165-04-02","sa":"https://sa.vidhyamitra.com/city/mathura/-3165-04-02","hi":"https://hi.vidhyamitra.com/city/mathura/-3165-04-02","x-default":"https://vidhyamitra.com/city/mathura/-3165-04-02"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-13T00:40:09.783Z","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":"2026-08-13T00:40:09.783Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-13T00:40:09.783Z","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"}}}