{"id":"vidhyamitra:city-day:mathura:-3165-05-18:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3165-05-18","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3165-05-18","date_display":"May 18, 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":18,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":565178.770833,"kali_year":-63,"ahargana":-23286.7292,"sun":{"sidereal_longitude":88.0824,"rashi":3,"rashi_name":"Mithuna"},"moon":{"sidereal_longitude":250.8586,"rashi":9,"rashi_name":"Dhanu"},"tithi":{"number":14,"name":"Caturdaśī","paksha":"Śukla","full_name":"Śukla Caturdaśī","elongation_degrees":162.7762,"elapsed_within_tithi_degrees":6.7762},"nakshatra":{"number":19,"name":"Mūla","pada":4,"moon_longitude":250.8586,"elapsed_within_degrees":10.8586},"yoga":{"number":26,"name":"Indra","sum_longitude":338.9409},"karana":{"half_tithi_index":27,"name":"Vaṇija"},"vara":{"number":2,"name":"Ravivāra (Sunday)"}},"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":18,"hour":6,"minute":30,"calendar":"julian"},"julian_day":565178.770833,"ahargana":-23286.7292,"kali_year":-63,"ayanamsa_lahiri":-48.2934,"grahas":{"sun":{"sidereal_longitude":88.0824,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":7,"name":"Punarvasu","pada":3},"retrograde":false},"moon":{"sidereal_longitude":250.8586,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":4},"retrograde":false,"latitude":-4.4662},"mars":{"sidereal_longitude":64.5135,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":5,"name":"Mṛgaśīrṣā","pada":4},"retrograde":false},"mercury":{"sidereal_longitude":95.2197,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":8,"name":"Puṣya","pada":1},"retrograde":false},"jupiter":{"sidereal_longitude":210.6642,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":16,"name":"Viśākhā","pada":4},"retrograde":true},"venus":{"sidereal_longitude":105.9721,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":8,"name":"Puṣya","pada":4},"retrograde":false},"saturn":{"sidereal_longitude":295.9078,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":1},"retrograde":true},"rahu":{"sidereal_longitude":333.843,"rashi":{"number":12,"name":"Mīna"},"nakshatra":{"number":26,"name":"Uttara Bhādrapadā","pada":1},"retrograde":false},"ketu":{"sidereal_longitude":153.843,"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":18,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":565178.770833,"kali_year":-63,"ahargana":-23286.7292,"sun":{"sidereal_longitude":88.0824,"rashi":3,"rashi_name":"Mithuna"},"moon":{"sidereal_longitude":250.8586,"rashi":9,"rashi_name":"Dhanu"},"tithi":{"number":14,"name":"Caturdaśī","paksha":"Śukla","full_name":"Śukla Caturdaśī","elongation_degrees":162.7762,"elapsed_within_tithi_degrees":6.7762},"nakshatra":{"number":19,"name":"Mūla","pada":4,"moon_longitude":250.8586,"elapsed_within_degrees":10.8586},"yoga":{"number":26,"name":"Indra","sum_longitude":338.9409},"karana":{"half_tithi_index":27,"name":"Vaṇija"},"vara":{"number":2,"name":"Ravivāra (Sunday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-4.466,"elongation":162.776},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-4.466,"opposition_distance":17.224}},"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":"05:40","sunsetLocal":"18:51","solarNoonLocal":"12:16","dayLengthHours":13.18053401404746,"dayLengthDisplay":"13 Hours 10 Mins 50 Secs","nightLengthDisplay":"10 Hours 49 Mins 10 Secs","moonriseLocal":"17:22","moonsetLocal":"04:51","rahuKala":{"name":"Rāhu Kāla","start":"17:12","end":"18:51","startHours":17.202967218759973,"endHours":18.850533970515905,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"12:16","end":"13:54","startHours":12.260266963492175,"endHours":13.907833715248106,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"15:33","end":"17:12","startHours":15.55540046700404,"endHours":17.202967218759973,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"08:45","end":"09:11","startHours":8.745457893079518,"endHours":9.184809026881101,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:13","end":"06:34","startHours":6.219188873720422,"endHours":6.570669780761688,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:49","end":"12:42","startHours":11.820915829690593,"endHours":12.699618097293756,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"03:55","end":"04:47","startHours":3.912595421262117,"endHours":4.7912976888652805,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"04:34","end":"05:40","startHours":4.57162212196449,"endHours":5.669999956468445,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:27","end":"15:20","startHours":14.457022632500085,"endHours":15.335724900103248,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"18:39","end":"19:03","startHours":18.650533970515905,"endHours":19.050533970515904,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"18:51","end":"19:24","startHours":18.850533970515905,"endHours":19.399722887767883,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"18:36","end":"20:21","startHours":18.600533970515905,"endHours":20.350533970515905,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:49","end":"00:42","startHours":23.82091582969059,"endHours":24.699618097293758,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Udveg","start":"05:40","end":"07:19","startHours":5.669999956468445,"endHours":7.317566708224377,"quality":"inauspicious"},{"name":"Chala","start":"07:19","end":"08:58","startHours":7.317566708224377,"endHours":8.96513345998031,"quality":"neutral"},{"name":"Labha","start":"08:58","end":"10:37","startHours":8.96513345998031,"endHours":10.612700211736243,"quality":"auspicious"},{"name":"Amṛta","start":"10:37","end":"12:16","startHours":10.612700211736243,"endHours":12.260266963492175,"quality":"auspicious"},{"name":"Kāla","start":"12:16","end":"13:54","startHours":12.260266963492175,"endHours":13.907833715248106,"quality":"inauspicious"},{"name":"Śubha","start":"13:54","end":"15:33","startHours":13.907833715248106,"endHours":15.55540046700404,"quality":"auspicious"},{"name":"Roga","start":"15:33","end":"17:12","startHours":15.55540046700404,"endHours":17.202967218759973,"quality":"inauspicious"},{"name":"Udveg","start":"17:12","end":"18:51","startHours":17.202967218759973,"endHours":18.850533970515905,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Śubha","start":"18:51","end":"20:12","startHours":18.850533970515905,"endHours":20.202967218759973,"quality":"auspicious"},{"name":"Roga","start":"20:12","end":"21:33","startHours":20.202967218759973,"endHours":21.55540046700404,"quality":"inauspicious"},{"name":"Udveg","start":"21:33","end":"22:54","startHours":21.55540046700404,"endHours":22.907833715248106,"quality":"inauspicious"},{"name":"Chala","start":"22:54","end":"00:16","startHours":22.907833715248106,"endHours":24.260266963492175,"quality":"neutral"},{"name":"Labha","start":"00:16","end":"01:37","startHours":24.260266963492175,"endHours":25.612700211736243,"quality":"auspicious"},{"name":"Amṛta","start":"01:37","end":"02:58","startHours":25.612700211736243,"endHours":26.965133459980308,"quality":"auspicious"},{"name":"Kāla","start":"02:58","end":"04:19","startHours":26.965133459980308,"endHours":28.317566708224376,"quality":"inauspicious"},{"name":"Śubha","start":"04:19","end":"05:40","startHours":28.317566708224376,"endHours":29.669999956468445,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"05:40","end":"06:40","startHours":5.669999956468445,"endHours":6.669999956468445,"planetary_lord":"Sun"},{"name":"Hora 2","start":"06:40","end":"07:40","startHours":6.669999956468445,"endHours":7.669999956468445,"planetary_lord":"Mars"},{"name":"Hora 3","start":"07:40","end":"08:40","startHours":7.669999956468445,"endHours":8.669999956468445,"planetary_lord":"Jupiter"},{"name":"Hora 4","start":"08:40","end":"09:40","startHours":8.669999956468445,"endHours":9.669999956468445,"planetary_lord":"Saturn"},{"name":"Hora 5","start":"09:40","end":"10:40","startHours":9.669999956468445,"endHours":10.669999956468445,"planetary_lord":"Moon"},{"name":"Hora 6","start":"10:40","end":"11:40","startHours":10.669999956468445,"endHours":11.669999956468445,"planetary_lord":"Mercury"},{"name":"Hora 7","start":"11:40","end":"12:40","startHours":11.669999956468445,"endHours":12.669999956468445,"planetary_lord":"Venus"},{"name":"Hora 8","start":"12:40","end":"13:40","startHours":12.669999956468445,"endHours":13.669999956468445,"planetary_lord":"Sun"},{"name":"Hora 9","start":"13:40","end":"14:40","startHours":13.669999956468445,"endHours":14.669999956468445,"planetary_lord":"Mars"},{"name":"Hora 10","start":"14:40","end":"15:40","startHours":14.669999956468445,"endHours":15.669999956468445,"planetary_lord":"Jupiter"},{"name":"Hora 11","start":"15:40","end":"16:40","startHours":15.669999956468445,"endHours":16.669999956468445,"planetary_lord":"Saturn"},{"name":"Hora 12","start":"16:40","end":"17:40","startHours":16.669999956468445,"endHours":17.669999956468445,"planetary_lord":"Moon"},{"name":"Hora 13","start":"17:40","end":"18:40","startHours":17.669999956468445,"endHours":18.669999956468445,"planetary_lord":"Mercury"},{"name":"Hora 14","start":"18:40","end":"19:40","startHours":18.669999956468445,"endHours":19.669999956468445,"planetary_lord":"Venus"},{"name":"Hora 15","start":"19:40","end":"20:40","startHours":19.669999956468445,"endHours":20.669999956468445,"planetary_lord":"Sun"},{"name":"Hora 16","start":"20:40","end":"21:40","startHours":20.669999956468445,"endHours":21.669999956468445,"planetary_lord":"Mars"},{"name":"Hora 17","start":"21:40","end":"22:40","startHours":21.669999956468445,"endHours":22.669999956468445,"planetary_lord":"Jupiter"},{"name":"Hora 18","start":"22:40","end":"23:40","startHours":22.669999956468445,"endHours":23.669999956468445,"planetary_lord":"Saturn"},{"name":"Hora 19","start":"23:40","end":"00:40","startHours":23.669999956468445,"endHours":24.669999956468445,"planetary_lord":"Moon"},{"name":"Hora 20","start":"00:40","end":"01:40","startHours":24.669999956468445,"endHours":25.669999956468445,"planetary_lord":"Mercury"},{"name":"Hora 21","start":"01:40","end":"02:40","startHours":25.669999956468445,"endHours":26.669999956468445,"planetary_lord":"Venus"},{"name":"Hora 22","start":"02:40","end":"03:40","startHours":26.669999956468445,"endHours":27.669999956468445,"planetary_lord":"Sun"},{"name":"Hora 23","start":"03:40","end":"04:40","startHours":27.669999956468445,"endHours":28.669999956468445,"planetary_lord":"Mars"},{"name":"Hora 24","start":"04:40","end":"05:40","startHours":28.669999956468445,"endHours":29.669999956468445,"planetary_lord":"Jupiter"}],"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":"North-East","anandadiYoga":{"name":"Siddhi","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":14.745958585120107,"eotMinutes":3.6891821904695723,"ayanamsa":-48.2934}},"calendars":{"vikram_samvat":-3108,"saka_samvat":-3243,"bengali_samvat":-3758,"malayalam_era":-3989,"nanakshahi_year":-4634,"lunar_month":"Āṣāḍha","lunar_month_paksha_full":"Āṣāḍha Śukla 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 Śukla Caturdaśī · Vikram -3108 undefined · Śaka -3243 undefined"},"festivals":[],"todays_walk":{"walk":{"id":"surya-walk","name":"Sūrya Walk","name_sanskrit":"सूर्य यात्रा","type":"graha","description":"Self-illumination + BG 4.1 (Sun-lineage of Gītā transmission).","step_count":6,"url":"/walk/surya-walk"},"reason":"Ravivāra (Sunday) — 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 18, 3166 BCE · Mathurā · Vidhyamitra","description":"May 18, 3166 BCE for Mathurā: Śukla Caturdaśī, sūryodaya 05:40, sūryāsta 18:51.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3165-05-18","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3165-05-18","sa":"https://sa.vidhyamitra.com/city/mathura/-3165-05-18","hi":"https://hi.vidhyamitra.com/city/mathura/-3165-05-18","x-default":"https://vidhyamitra.com/city/mathura/-3165-05-18"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-10T14:07:31.333Z","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":"2026-08-10T14:07:31.333Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-10T14:07:31.333Z","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"}}}