{"id":"vidhyamitra:city-day:mathura:2045-10-13:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/2045-10-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"2045-10-13","date_display":"October 13, 2045 CE","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":"Sub-degree on Moon at any Kali-Yuga date (~2-5° residual max)","tradition_chain":"Āryabhaṭa(499) → Brahmagupta(628) → Bhāskara II(1150) → Mādhava(~1400) → Parameśvara(1430) → Nīlakaṇṭha(1501) → this","input":{"year":2045,"month":10,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2468266.770833,"kali_year":5147,"ahargana":1879801.2708,"sun":{"sidereal_longitude":174.7744,"rashi":6,"rashi_name":"Kanyā"},"moon":{"sidereal_longitude":209.5333,"rashi":7,"rashi_name":"Tulā"},"tithi":{"number":3,"name":"Tṛtīyā","paksha":"Śukla","full_name":"Śukla Tṛtīyā","elongation_degrees":34.7589,"elapsed_within_tithi_degrees":10.7589},"nakshatra":{"number":16,"name":"Viśākhā","pada":3,"moon_longitude":209.5333,"elapsed_within_degrees":9.5333},"yoga":{"number":2,"name":"Prīti","sum_longitude":24.3078},"karana":{"half_tithi_index":5,"name":"Gara"},"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":2045,"month":10,"day":13,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2468266.770833,"ahargana":1879801.2708,"kali_year":5147,"ayanamsa_lahiri":24.4925,"grahas":{"sun":{"sidereal_longitude":175.62361600000008,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":14,"name":"Citrā","pada":1},"retrograde":false},"moon":{"sidereal_longitude":209.80531599999995,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":16,"name":"Viśākhā","pada":3},"retrograde":false,"latitude":-4.4999},"mars":{"sidereal_longitude":126.692816,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","pada":3},"retrograde":false},"mercury":{"sidereal_longitude":196.59911599999998,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":15,"name":"Svātī","pada":3},"retrograde":false},"jupiter":{"sidereal_longitude":308.4343160000001,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":24,"name":"Śatabhiṣā","pada":1},"retrograde":true},"venus":{"sidereal_longitude":221.62101600000005,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":17,"name":"Anurādhā","pada":3},"retrograde":false},"saturn":{"sidereal_longitude":222.99271599999997,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":17,"name":"Anurādhā","pada":3},"retrograde":false},"rahu":{"sidereal_longitude":299.0824,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":2},"retrograde":false},"ketu":{"sidereal_longitude":119.0824,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":9,"name":"Āśleṣā","pada":4},"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":"Sub-degree on Moon at any Kali-Yuga date (~2-5° residual max)","tradition_chain":"Āryabhaṭa(499) → Brahmagupta(628) → Bhāskara II(1150) → Mādhava(~1400) → Parameśvara(1430) → Nīlakaṇṭha(1501) → this","input":{"year":2045,"month":10,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2468266.770833,"kali_year":5147,"ahargana":1879801.2708,"sun":{"sidereal_longitude":174.7744,"rashi":6,"rashi_name":"Kanyā"},"moon":{"sidereal_longitude":209.5333,"rashi":7,"rashi_name":"Tulā"},"tithi":{"number":3,"name":"Tṛtīyā","paksha":"Śukla","full_name":"Śukla Tṛtīyā","elongation_degrees":34.7589,"elapsed_within_tithi_degrees":10.7589},"nakshatra":{"number":16,"name":"Viśākhā","pada":3,"moon_longitude":209.5333,"elapsed_within_degrees":9.5333},"yoga":{"number":2,"name":"Prīti","sum_longitude":24.3078},"karana":{"half_tithi_index":5,"name":"Gara"},"vara":{"number":0,"name":"Śukravāra (Friday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-4.5,"elongation":34.759},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-4.5,"opposition_distance":145.241}},"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":"06:18","sunsetLocal":"17:52","solarNoonLocal":"12:05","dayLengthHours":11.577199064534511,"dayLengthDisplay":"11 Hours 34 Mins 38 Secs","nightLengthDisplay":"12 Hours 25 Mins 22 Secs","moonriseLocal":"09:00","moonsetLocal":"19:43","rahuKala":{"name":"Rāhu Kāla","start":"10:38","end":"12:05","startHours":10.633896296798596,"endHours":12.08104617986541,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"14:59","end":"16:25","startHours":14.975345945999038,"endHours":16.422495829065852,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"07:44","end":"09:11","startHours":7.739596530664969,"endHours":9.186746413731782,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:00","end":"09:23","startHours":8.993793095989542,"endHours":9.379699731474025,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:46","end":"07:05","startHours":6.77482994195376,"endHours":7.083555250341347,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:42","end":"12:28","startHours":11.695139544380927,"endHours":12.466952815349893,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"04:45","end":"05:31","startHours":4.74882010566022,"endHours":5.520633376629188,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"05:20","end":"06:18","startHours":5.327680058886946,"endHours":6.2924466475981555,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:01","end":"14:47","startHours":14.010579357287831,"endHours":14.7823926282568,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:40","end":"18:04","startHours":17.669645712132667,"endHours":18.069645712132665,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:52","end":"18:21","startHours":17.869645712132666,"endHours":18.35202900648827,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:37","end":"19:22","startHours":17.619645712132666,"endHours":19.369645712132666,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:42","end":"00:28","startHours":23.695139544380925,"endHours":24.466952815349895,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Chala","start":"06:18","end":"07:44","startHours":6.2924466475981555,"endHours":7.739596530664969,"quality":"neutral"},{"name":"Labha","start":"07:44","end":"09:11","startHours":7.739596530664969,"endHours":9.186746413731782,"quality":"auspicious"},{"name":"Amṛta","start":"09:11","end":"10:38","startHours":9.186746413731782,"endHours":10.633896296798596,"quality":"auspicious"},{"name":"Kāla","start":"10:38","end":"12:05","startHours":10.633896296798596,"endHours":12.08104617986541,"quality":"inauspicious"},{"name":"Śubha","start":"12:05","end":"13:32","startHours":12.08104617986541,"endHours":13.528196062932224,"quality":"auspicious"},{"name":"Roga","start":"13:32","end":"14:59","startHours":13.528196062932224,"endHours":14.975345945999038,"quality":"inauspicious"},{"name":"Udveg","start":"14:59","end":"16:25","startHours":14.975345945999038,"endHours":16.422495829065852,"quality":"inauspicious"},{"name":"Chala","start":"16:25","end":"17:52","startHours":16.422495829065852,"endHours":17.869645712132666,"quality":"neutral"}],"nightChoghadiyas":[{"name":"Roga","start":"17:52","end":"19:25","startHours":17.869645712132666,"endHours":19.422495829065852,"quality":"inauspicious"},{"name":"Udveg","start":"19:25","end":"20:59","startHours":19.422495829065852,"endHours":20.975345945999038,"quality":"inauspicious"},{"name":"Chala","start":"20:59","end":"22:32","startHours":20.975345945999038,"endHours":22.528196062932224,"quality":"neutral"},{"name":"Labha","start":"22:32","end":"00:05","startHours":22.528196062932224,"endHours":24.08104617986541,"quality":"auspicious"},{"name":"Amṛta","start":"00:05","end":"01:38","startHours":24.08104617986541,"endHours":25.633896296798596,"quality":"auspicious"},{"name":"Kāla","start":"01:38","end":"03:11","startHours":25.633896296798596,"endHours":27.186746413731782,"quality":"inauspicious"},{"name":"Śubha","start":"03:11","end":"04:44","startHours":27.186746413731782,"endHours":28.73959653066497,"quality":"auspicious"},{"name":"Roga","start":"04:44","end":"06:18","startHours":28.73959653066497,"endHours":30.292446647598155,"quality":"inauspicious"}],"horas":[{"name":"Hora 1","start":"06:18","end":"07:18","startHours":6.2924466475981555,"endHours":7.2924466475981555,"planetary_lord":"Venus"},{"name":"Hora 2","start":"07:18","end":"08:18","startHours":7.2924466475981555,"endHours":8.292446647598155,"planetary_lord":"Sun"},{"name":"Hora 3","start":"08:18","end":"09:18","startHours":8.292446647598155,"endHours":9.292446647598155,"planetary_lord":"Mars"},{"name":"Hora 4","start":"09:18","end":"10:18","startHours":9.292446647598155,"endHours":10.292446647598155,"planetary_lord":"Jupiter"},{"name":"Hora 5","start":"10:18","end":"11:18","startHours":10.292446647598155,"endHours":11.292446647598155,"planetary_lord":"Saturn"},{"name":"Hora 6","start":"11:18","end":"12:18","startHours":11.292446647598155,"endHours":12.292446647598155,"planetary_lord":"Moon"},{"name":"Hora 7","start":"12:18","end":"13:18","startHours":12.292446647598155,"endHours":13.292446647598155,"planetary_lord":"Mercury"},{"name":"Hora 8","start":"13:18","end":"14:18","startHours":13.292446647598155,"endHours":14.292446647598155,"planetary_lord":"Venus"},{"name":"Hora 9","start":"14:18","end":"15:18","startHours":14.292446647598155,"endHours":15.292446647598155,"planetary_lord":"Sun"},{"name":"Hora 10","start":"15:18","end":"16:18","startHours":15.292446647598155,"endHours":16.292446647598155,"planetary_lord":"Mars"},{"name":"Hora 11","start":"16:18","end":"17:18","startHours":16.292446647598155,"endHours":17.292446647598155,"planetary_lord":"Jupiter"},{"name":"Hora 12","start":"17:18","end":"18:18","startHours":17.292446647598155,"endHours":18.292446647598155,"planetary_lord":"Saturn"},{"name":"Hora 13","start":"18:18","end":"19:18","startHours":18.292446647598155,"endHours":19.292446647598155,"planetary_lord":"Moon"},{"name":"Hora 14","start":"19:18","end":"20:18","startHours":19.292446647598155,"endHours":20.292446647598155,"planetary_lord":"Mercury"},{"name":"Hora 15","start":"20:18","end":"21:18","startHours":20.292446647598155,"endHours":21.292446647598155,"planetary_lord":"Venus"},{"name":"Hora 16","start":"21:18","end":"22:18","startHours":21.292446647598155,"endHours":22.292446647598155,"planetary_lord":"Sun"},{"name":"Hora 17","start":"22:18","end":"23:18","startHours":22.292446647598155,"endHours":23.292446647598155,"planetary_lord":"Mars"},{"name":"Hora 18","start":"23:18","end":"00:18","startHours":23.292446647598155,"endHours":24.292446647598155,"planetary_lord":"Jupiter"},{"name":"Hora 19","start":"00:18","end":"01:18","startHours":24.292446647598155,"endHours":25.292446647598155,"planetary_lord":"Saturn"},{"name":"Hora 20","start":"01:18","end":"02:18","startHours":25.292446647598155,"endHours":26.292446647598155,"planetary_lord":"Moon"},{"name":"Hora 21","start":"02:18","end":"03:18","startHours":26.292446647598155,"endHours":27.292446647598155,"planetary_lord":"Mercury"},{"name":"Hora 22","start":"03:18","end":"04:18","startHours":27.292446647598155,"endHours":28.292446647598155,"planetary_lord":"Venus"},{"name":"Hora 23","start":"04:18","end":"05:18","startHours":28.292446647598155,"endHours":29.292446647598155,"planetary_lord":"Sun"},{"name":"Hora 24","start":"05:18","end":"06:18","startHours":29.292446647598155,"endHours":30.292446647598155,"planetary_lord":"Mars"}],"taraBala":{"favorable_nakshatras":["Aśvinī","Bharaṇī","Kṛttikā","Puṣya","Aśleṣā","Maghā","Pūrva Phalgunī","Uttara Phalgunī","Anurādhā","Jyeṣṭhā","Mūla","Pūrva Āṣāḍhā","Uttara Āṣāḍhā","Uttara Bhādrapadā","Revatī"],"unfavorable_nakshatras":["Rohiṇī","Mṛgaśirā","Ārdrā","Punarvasu","Hasta","Citrā","Svātī","Viśākhā","Śravaṇa","Dhaniṣṭhā","Śatabhiṣaj","Pūrva Bhādrapadā"],"nature":"Janma-tara if same nakshatra; favorable for 15 nakshatras"},"chandraBala":{"favorable_rashis":["Meṣa","Karka","Siṃha","Tulā","Dhanu","Mīna"],"unfavorable_rashis":["Vṛṣabha","Mithuna","Kanyā","Vṛścika","Makara","Kumbha"]},"dishaShool":"West (Paścim)","chandraVasa":"North","rahuVasa":"South-East","anandadiYoga":{"name":"Śrīvatsa","quality":"Auspicious"},"drikRitu":"Śarad (Autumn) (Drik)","vedicRitu":"Varṣā (Monsoon)","drikAyana":"Dakṣiṇāyana","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization (Drikpanchang-parity)","declination":-7.862120595425583,"eotMinutes":14.442429208075392,"ayanamsa":24.4925}},"calendars":{"vikram_samvat":2102,"vikram_samvatsara":"Bahudhānya","saka_samvat":1967,"saka_samvatsara":"Krodhana","bengali_samvat":1452,"malayalam_era":1221,"nanakshahi_year":576,"lunar_month":"Āśvina","lunar_month_paksha_full":"Āśvina Śukla Pakṣa","solar_month":"Kanyā (Puraṭṭāsi)","ritu":"Śarad (Autumn)","display_summary":"Āśvina Śukla Tṛtīyā · Vikram 2102 Bahudhānya · Śaka 1967 Krodhana"},"festivals":[{"id":"kanya-sankranti","name":"Kanyā Saṅkrānti (Mahālaya begins)","name_sanskrit":"कन्या सङ्क्रान्ति","tradition":"Pan-Hindu","significance":"Sun enters Virgo; Mahālaya / Pitṛ-Pakṣa solar marker.","vrata":false,"detection":{"sun_rashi":"Kanyā"},"precedence":4}],"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":"Śukravāra (Friday) — its presiding graha's walk."},"cosmic_resonances":[{"historical_date":"-0562-04-11","event":"Bhagavān Buddha's birth at Lumbinī","chart_id":"buddha","shared_marker":"same Viśākhā","url":"/day/-0562-04-11","relevance":0.5}]},"validity":{"eternal":false,"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 October 13, 2045 CE · Mathurā · Vidhyamitra","description":"October 13, 2045 CE for Mathurā: Śukla Tṛtīyā, sūryodaya 06:18, sūryāsta 17:52.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/2045-10-13","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/2045-10-13","sa":"https://sa.vidhyamitra.com/city/mathura/2045-10-13","hi":"https://hi.vidhyamitra.com/city/mathura/2045-10-13","x-default":"https://vidhyamitra.com/city/mathura/2045-10-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-05-14T15:54:39.768Z","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":"2026-05-14T15:54:39.768Z","verification":{"type":"community-validated","markers":["matches Drikpanchang ±1 minute on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-05-14T15:54:39.768Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"}}}