{"id":"vidhyamitra:city-day:mathura:-0511-04-03:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-0511-04-03","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-0511-04-03","date_display":"April 3, 512 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":-511,"month":4,"day":3,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":1534507.770833,"kali_year":2591,"ahargana":946042.2708,"sun":{"sidereal_longitude":23.6743,"rashi":1,"rashi_name":"Meṣa"},"moon":{"sidereal_longitude":22.2755,"rashi":1,"rashi_name":"Meṣa"},"tithi":{"number":30,"name":"Amāvasyā","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Amāvasyā","elongation_degrees":358.6011,"elapsed_within_tithi_degrees":10.6011},"nakshatra":{"number":2,"name":"Bharaṇī","pada":3,"moon_longitude":22.2755,"elapsed_within_degrees":8.9421},"yoga":{"number":4,"name":"Saubhāgya","sum_longitude":45.9498},"karana":{"half_tithi_index":59,"name":"Nāga"},"vara":{"number":6,"name":"Guruvāra (Thursday)"}},"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":-511,"month":4,"day":3,"hour":6,"minute":30,"calendar":"julian"},"julian_day":1534507.770833,"ahargana":946042.2708,"kali_year":2591,"ayanamsa_lahiri":-11.2202,"grahas":{"sun":{"sidereal_longitude":23.6743,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":2,"name":"Bharaṇī","pada":4},"retrograde":false},"moon":{"sidereal_longitude":22.2755,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":2,"name":"Bharaṇī","pada":3},"retrograde":false,"latitude":-4.2757},"mars":{"sidereal_longitude":26.8897,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":3,"name":"Kṛttikā","pada":1},"retrograde":false},"mercury":{"sidereal_longitude":29.5936,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":3,"name":"Kṛttikā","pada":1},"retrograde":false},"jupiter":{"sidereal_longitude":118.3425,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":9,"name":"Āśleṣā","pada":4},"retrograde":false},"venus":{"sidereal_longitude":53.337,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":5,"name":"Mṛgaśīrṣā","pada":1},"retrograde":false},"saturn":{"sidereal_longitude":312.1389,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":24,"name":"Śatabhiṣā","pada":2},"retrograde":false},"rahu":{"sidereal_longitude":94.1278,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":8,"name":"Puṣya","pada":1},"retrograde":false},"ketu":{"sidereal_longitude":274.1278,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","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":-511,"month":4,"day":3,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":1534507.770833,"kali_year":2591,"ahargana":946042.2708,"sun":{"sidereal_longitude":23.6743,"rashi":1,"rashi_name":"Meṣa"},"moon":{"sidereal_longitude":22.2755,"rashi":1,"rashi_name":"Meṣa"},"tithi":{"number":30,"name":"Amāvasyā","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Amāvasyā","elongation_degrees":358.6011,"elapsed_within_tithi_degrees":10.6011},"nakshatra":{"number":2,"name":"Bharaṇī","pada":3,"moon_longitude":22.2755,"elapsed_within_degrees":8.9421},"yoga":{"number":4,"name":"Saubhāgya","sum_longitude":45.9498},"karana":{"half_tithi_index":59,"name":"Nāga"},"vara":{"number":6,"name":"Guruvāra (Thursday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-4.276,"elongation":1.399},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-4.276,"opposition_distance":178.601}},"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":"06:09","sunsetLocal":"18:37","solarNoonLocal":"12:23","dayLengthHours":12.468217852123011,"dayLengthDisplay":"12 Hours 28 Mins 06 Secs","nightLengthDisplay":"11 Hours 31 Mins 54 Secs","moonriseLocal":"06:06","moonsetLocal":"18:29","rahuKala":{"name":"Rāhu Kāla","start":"13:57","end":"15:30","startHours":13.942195283156892,"endHours":15.500722514672269,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"06:09","end":"07:42","startHours":6.1495591255800095,"endHours":7.708086357095386,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"09:16","end":"10:50","startHours":9.266613588610763,"endHours":10.825140820126139,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:04","end":"09:28","startHours":9.058809957742046,"endHours":9.474417219479479,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:40","end":"07:00","startHours":6.669068202751801,"endHours":7.0015540121417486,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:58","end":"12:48","startHours":11.968060789904081,"endHours":12.799275313378947,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"04:29","end":"05:19","startHours":4.487130078630274,"endHours":5.318344602105142,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"05:07","end":"06:09","startHours":5.110540971236425,"endHours":6.1495591255800095,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:28","end":"15:18","startHours":14.461704360328685,"endHours":15.292918883803553,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"18:25","end":"18:49","startHours":18.41777697770302,"endHours":18.81777697770302,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"18:37","end":"19:08","startHours":18.61777697770302,"endHours":19.137286054874814,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"18:22","end":"20:07","startHours":18.36777697770302,"endHours":20.11777697770302,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:58","end":"00:48","startHours":23.96806078990408,"endHours":24.79927531337895,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Śubha","start":"06:09","end":"07:42","startHours":6.1495591255800095,"endHours":7.708086357095386,"quality":"auspicious"},{"name":"Roga","start":"07:42","end":"09:16","startHours":7.708086357095386,"endHours":9.266613588610763,"quality":"inauspicious"},{"name":"Udveg","start":"09:16","end":"10:50","startHours":9.266613588610763,"endHours":10.825140820126139,"quality":"inauspicious"},{"name":"Chala","start":"10:50","end":"12:23","startHours":10.825140820126139,"endHours":12.383668051641514,"quality":"neutral"},{"name":"Labha","start":"12:23","end":"13:57","startHours":12.383668051641514,"endHours":13.942195283156892,"quality":"auspicious"},{"name":"Amṛta","start":"13:57","end":"15:30","startHours":13.942195283156892,"endHours":15.500722514672269,"quality":"auspicious"},{"name":"Kāla","start":"15:30","end":"17:04","startHours":15.500722514672269,"endHours":17.059249746187643,"quality":"inauspicious"},{"name":"Śubha","start":"17:04","end":"18:37","startHours":17.059249746187643,"endHours":18.61777697770302,"quality":"auspicious"}],"nightChoghadiyas":[{"name":"Amṛta","start":"18:37","end":"20:04","startHours":18.61777697770302,"endHours":20.059249746187643,"quality":"auspicious"},{"name":"Kāla","start":"20:04","end":"21:30","startHours":20.059249746187643,"endHours":21.50072251467227,"quality":"inauspicious"},{"name":"Śubha","start":"21:30","end":"22:57","startHours":21.50072251467227,"endHours":22.94219528315689,"quality":"auspicious"},{"name":"Roga","start":"22:57","end":"00:23","startHours":22.94219528315689,"endHours":24.383668051641514,"quality":"inauspicious"},{"name":"Udveg","start":"00:23","end":"01:50","startHours":24.383668051641514,"endHours":25.825140820126137,"quality":"inauspicious"},{"name":"Chala","start":"01:50","end":"03:16","startHours":25.825140820126137,"endHours":27.26661358861076,"quality":"neutral"},{"name":"Labha","start":"03:16","end":"04:42","startHours":27.26661358861076,"endHours":28.708086357095386,"quality":"auspicious"},{"name":"Amṛta","start":"04:42","end":"06:09","startHours":28.708086357095386,"endHours":30.14955912558001,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"06:09","end":"07:09","startHours":6.1495591255800095,"endHours":7.1495591255800095,"planetary_lord":"Jupiter"},{"name":"Hora 2","start":"07:09","end":"08:09","startHours":7.1495591255800095,"endHours":8.149559125580009,"planetary_lord":"Saturn"},{"name":"Hora 3","start":"08:09","end":"09:09","startHours":8.149559125580009,"endHours":9.149559125580009,"planetary_lord":"Moon"},{"name":"Hora 4","start":"09:09","end":"10:09","startHours":9.149559125580009,"endHours":10.149559125580009,"planetary_lord":"Mercury"},{"name":"Hora 5","start":"10:09","end":"11:09","startHours":10.149559125580009,"endHours":11.149559125580009,"planetary_lord":"Venus"},{"name":"Hora 6","start":"11:09","end":"12:09","startHours":11.149559125580009,"endHours":12.149559125580009,"planetary_lord":"Sun"},{"name":"Hora 7","start":"12:09","end":"13:09","startHours":12.149559125580009,"endHours":13.149559125580009,"planetary_lord":"Mars"},{"name":"Hora 8","start":"13:09","end":"14:09","startHours":13.149559125580009,"endHours":14.149559125580009,"planetary_lord":"Jupiter"},{"name":"Hora 9","start":"14:09","end":"15:09","startHours":14.149559125580009,"endHours":15.149559125580009,"planetary_lord":"Saturn"},{"name":"Hora 10","start":"15:09","end":"16:09","startHours":15.149559125580009,"endHours":16.14955912558001,"planetary_lord":"Moon"},{"name":"Hora 11","start":"16:09","end":"17:09","startHours":16.14955912558001,"endHours":17.14955912558001,"planetary_lord":"Mercury"},{"name":"Hora 12","start":"17:09","end":"18:09","startHours":17.14955912558001,"endHours":18.14955912558001,"planetary_lord":"Venus"},{"name":"Hora 13","start":"18:09","end":"19:09","startHours":18.14955912558001,"endHours":19.14955912558001,"planetary_lord":"Sun"},{"name":"Hora 14","start":"19:09","end":"20:09","startHours":19.14955912558001,"endHours":20.14955912558001,"planetary_lord":"Mars"},{"name":"Hora 15","start":"20:09","end":"21:09","startHours":20.14955912558001,"endHours":21.14955912558001,"planetary_lord":"Jupiter"},{"name":"Hora 16","start":"21:09","end":"22:09","startHours":21.14955912558001,"endHours":22.14955912558001,"planetary_lord":"Saturn"},{"name":"Hora 17","start":"22:09","end":"23:09","startHours":22.14955912558001,"endHours":23.14955912558001,"planetary_lord":"Moon"},{"name":"Hora 18","start":"23:09","end":"00:09","startHours":23.14955912558001,"endHours":24.14955912558001,"planetary_lord":"Mercury"},{"name":"Hora 19","start":"00:09","end":"01:09","startHours":24.14955912558001,"endHours":25.14955912558001,"planetary_lord":"Venus"},{"name":"Hora 20","start":"01:09","end":"02:09","startHours":25.14955912558001,"endHours":26.14955912558001,"planetary_lord":"Sun"},{"name":"Hora 21","start":"02:09","end":"03:09","startHours":26.14955912558001,"endHours":27.14955912558001,"planetary_lord":"Mars"},{"name":"Hora 22","start":"03:09","end":"04:09","startHours":27.14955912558001,"endHours":28.14955912558001,"planetary_lord":"Jupiter"},{"name":"Hora 23","start":"04:09","end":"05:09","startHours":28.14955912558001,"endHours":29.14955912558001,"planetary_lord":"Saturn"},{"name":"Hora 24","start":"05:09","end":"06:09","startHours":29.14955912558001,"endHours":30.14955912558001,"planetary_lord":"Moon"}],"taraBala":{"favorable_nakshatras":["Kṛttikā","Rohiṇī","Mṛgaśirā","Ārdrā","Punarvasu","Uttara Phalgunī","Hasta","Citrā","Svātī","Viśākhā","Uttara Āṣāḍhā","Śravaṇa","Dhaniṣṭhā","Śatabhiṣaj","Pūrva Bhādrapadā"],"unfavorable_nakshatras":["Aśvinī","Bharaṇī","Puṣya","Aśleṣā","Maghā","Pūrva Phalgunī","Anurādhā","Jyeṣṭhā","Mūla","Pūrva Āṣāḍhā","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":"South (Dakṣiṇa)","chandraVasa":"East","rahuVasa":"North-West","anandadiYoga":{"name":"Kāṇa","quality":"Inauspicious"},"tropicalRitu":"Vasanta (Spring)","vedicRitu":"Vasanta (Spring)","tropicalAyana":"Uttarāyaṇa","vedicAyana":"Uttarāyaṇa","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":4.920532032765011,"eotMinutes":-3.714883098490848,"ayanamsa":-11.2202}},"calendars":{"vikram_samvat":-454,"saka_samvat":-589,"bengali_samvat":-1104,"malayalam_era":-1335,"nanakshahi_year":-1980,"lunar_month":"Vaiśākha","lunar_month_paksha_full":"Vaiśākha Kṛṣṇa Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Vaiśākha","lunar_month_amanta":"Vaiśākha","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Mēsha (Cittirai / Vaiśākhī)","ritu":"Vasanta (Spring)","display_summary":"Vaiśākha Kṛṣṇa Amāvasyā · Vikram -454 undefined · Śaka -589 undefined"},"festivals":[],"todays_walk":{"walk":{"id":"guru-walk","name":"Bṛhaspati Walk","name_sanskrit":"गुरु यात्रा","type":"graha","description":"Wisdom transmission + BG 4.34.","step_count":8,"url":"/walk/guru-walk"},"reason":"Guruvāra (Thursday) — 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 3, 512 BCE · Mathurā · Vidhyamitra","description":"April 3, 512 BCE for Mathurā: Kṛṣṇa Amāvasyā, sūryodaya 06:09, sūryāsta 18:37.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-0511-04-03","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-0511-04-03","sa":"https://sa.vidhyamitra.com/city/mathura/-0511-04-03","hi":"https://hi.vidhyamitra.com/city/mathura/-0511-04-03","x-default":"https://vidhyamitra.com/city/mathura/-0511-04-03"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-11T01:55:22.407Z","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":"2026-08-11T01:55:22.407Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-11T01:55:22.407Z","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"}}}