{"id":"vidhyamitra:city-day:mathura:1663-01-13:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/1663-01-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"1663-01-13","date_display":"January 13, 1663 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":1663,"month":1,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2328470.770833,"kali_year":4764,"ahargana":1740005.2708,"sun":{"sidereal_longitude":274.5277,"rashi":10,"rashi_name":"Makara"},"moon":{"sidereal_longitude":317.5347,"rashi":11,"rashi_name":"Kumbha"},"tithi":{"number":4,"name":"Caturthī","paksha":"Śukla","full_name":"Śukla Caturthī","elongation_degrees":43.007,"elapsed_within_tithi_degrees":7.007},"nakshatra":{"number":24,"name":"Śatabhiṣā","pada":4,"moon_longitude":317.5347,"elapsed_within_degrees":10.868},"yoga":{"number":18,"name":"Varīyān","sum_longitude":232.0624},"karana":{"half_tithi_index":7,"name":"Viṣṭi"},"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":1663,"month":1,"day":13,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2328470.770833,"ahargana":1740005.2708,"kali_year":4764,"ayanamsa_lahiri":19.1459,"grahas":{"sun":{"sidereal_longitude":273.82775100000003,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":3},"retrograde":false},"moon":{"sidereal_longitude":316.01645099999996,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":24,"name":"Śatabhiṣā","pada":3},"retrograde":false,"latitude":0.6732},"mars":{"sidereal_longitude":276.183451,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":3},"retrograde":false},"mercury":{"sidereal_longitude":260.536151,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":3},"retrograde":false},"jupiter":{"sidereal_longitude":232.25465099999997,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":2},"retrograde":false},"venus":{"sidereal_longitude":271.461851,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":2},"retrograde":false},"saturn":{"sidereal_longitude":238.33685100000002,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":4},"retrograde":false},"rahu":{"sidereal_longitude":146.1473,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":11,"name":"Pūrva Phalgunī","pada":4},"retrograde":false},"ketu":{"sidereal_longitude":326.1473,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":25,"name":"Pūrva Bhādrapadā","pada":2},"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":1663,"month":1,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2328470.770833,"kali_year":4764,"ahargana":1740005.2708,"sun":{"sidereal_longitude":274.5277,"rashi":10,"rashi_name":"Makara"},"moon":{"sidereal_longitude":317.5347,"rashi":11,"rashi_name":"Kumbha"},"tithi":{"number":4,"name":"Caturthī","paksha":"Śukla","full_name":"Śukla Caturthī","elongation_degrees":43.007,"elapsed_within_tithi_degrees":7.007},"nakshatra":{"number":24,"name":"Śatabhiṣā","pada":4,"moon_longitude":317.5347,"elapsed_within_degrees":10.868},"yoga":{"number":18,"name":"Varīyān","sum_longitude":232.0624},"karana":{"half_tithi_index":7,"name":"Viṣṭi"},"vara":{"number":1,"name":"Śanivāra (Saturday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":0.673,"elongation":43.007},"lunar":{"type":"lunar","occurs":false,"moon_latitude":0.673,"opposition_distance":136.993}},"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":"07:11","sunsetLocal":"17:45","solarNoonLocal":"12:28","dayLengthHours":10.561606925141618,"dayLengthDisplay":"10 Hours 33 Mins 42 Secs","nightLengthDisplay":"13 Hours 26 Mins 18 Secs","moonriseLocal":"09:34","moonsetLocal":"20:59","rahuKala":{"name":"Rāhu Kāla","start":"09:50","end":"11:09","startHours":9.825283793570822,"endHours":11.145484659213526,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"13:47","end":"15:06","startHours":13.78588639049893,"endHours":15.106087256141631,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"07:11","end":"08:30","startHours":7.184882062285419,"endHours":8.505082927928122,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:39","end":"10:00","startHours":9.64925701148513,"endHours":10.001310575656516,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:37","end":"07:54","startHours":7.624949017499652,"endHours":7.906591868836762,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"12:07","end":"12:49","startHours":12.11363196068484,"endHours":12.817739089027613,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:47","end":"06:29","startHours":5.776667805599869,"endHours":6.480774933942644,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"06:18","end":"07:11","startHours":6.30474815185695,"endHours":7.184882062285419,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:14","end":"14:56","startHours":14.225953345713165,"endHours":14.93006047405594,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:33","end":"17:57","startHours":17.546488987427036,"endHours":17.946488987427035,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:45","end":"18:11","startHours":17.746488987427036,"endHours":18.18655594264127,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:30","end":"19:15","startHours":17.496488987427036,"endHours":19.246488987427036,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"00:07","end":"00:49","startHours":24.113631960684838,"endHours":24.817739089027615,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Kāla","start":"07:11","end":"08:30","startHours":7.184882062285419,"endHours":8.505082927928122,"quality":"inauspicious"},{"name":"Śubha","start":"08:30","end":"09:50","startHours":8.505082927928122,"endHours":9.825283793570822,"quality":"auspicious"},{"name":"Roga","start":"09:50","end":"11:09","startHours":9.825283793570822,"endHours":11.145484659213526,"quality":"inauspicious"},{"name":"Udveg","start":"11:09","end":"12:28","startHours":11.145484659213526,"endHours":12.465685524856227,"quality":"inauspicious"},{"name":"Chala","start":"12:28","end":"13:47","startHours":12.465685524856227,"endHours":13.78588639049893,"quality":"neutral"},{"name":"Labha","start":"13:47","end":"15:06","startHours":13.78588639049893,"endHours":15.106087256141631,"quality":"auspicious"},{"name":"Amṛta","start":"15:06","end":"16:26","startHours":15.106087256141631,"endHours":16.426288121784335,"quality":"auspicious"},{"name":"Kāla","start":"16:26","end":"17:45","startHours":16.426288121784335,"endHours":17.746488987427036,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Labha","start":"17:45","end":"19:26","startHours":17.746488987427036,"endHours":19.42628812178433,"quality":"auspicious"},{"name":"Amṛta","start":"19:26","end":"21:06","startHours":19.42628812178433,"endHours":21.10608725614163,"quality":"auspicious"},{"name":"Kāla","start":"21:06","end":"22:47","startHours":21.10608725614163,"endHours":22.78588639049893,"quality":"inauspicious"},{"name":"Śubha","start":"22:47","end":"00:28","startHours":22.78588639049893,"endHours":24.465685524856227,"quality":"auspicious"},{"name":"Roga","start":"00:28","end":"02:09","startHours":24.465685524856227,"endHours":26.145484659213523,"quality":"inauspicious"},{"name":"Udveg","start":"02:09","end":"03:50","startHours":26.145484659213523,"endHours":27.825283793570822,"quality":"inauspicious"},{"name":"Chala","start":"03:50","end":"05:30","startHours":27.825283793570822,"endHours":29.50508292792812,"quality":"neutral"},{"name":"Labha","start":"05:30","end":"07:11","startHours":29.50508292792812,"endHours":31.184882062285418,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"07:11","end":"08:11","startHours":7.184882062285419,"endHours":8.184882062285418,"planetary_lord":"Saturn"},{"name":"Hora 2","start":"08:11","end":"09:11","startHours":8.184882062285418,"endHours":9.184882062285418,"planetary_lord":"Moon"},{"name":"Hora 3","start":"09:11","end":"10:11","startHours":9.184882062285418,"endHours":10.184882062285418,"planetary_lord":"Mercury"},{"name":"Hora 4","start":"10:11","end":"11:11","startHours":10.184882062285418,"endHours":11.184882062285418,"planetary_lord":"Venus"},{"name":"Hora 5","start":"11:11","end":"12:11","startHours":11.184882062285418,"endHours":12.184882062285418,"planetary_lord":"Sun"},{"name":"Hora 6","start":"12:11","end":"13:11","startHours":12.184882062285418,"endHours":13.184882062285418,"planetary_lord":"Mars"},{"name":"Hora 7","start":"13:11","end":"14:11","startHours":13.184882062285418,"endHours":14.184882062285418,"planetary_lord":"Jupiter"},{"name":"Hora 8","start":"14:11","end":"15:11","startHours":14.184882062285418,"endHours":15.184882062285418,"planetary_lord":"Saturn"},{"name":"Hora 9","start":"15:11","end":"16:11","startHours":15.184882062285418,"endHours":16.184882062285418,"planetary_lord":"Moon"},{"name":"Hora 10","start":"16:11","end":"17:11","startHours":16.184882062285418,"endHours":17.184882062285418,"planetary_lord":"Mercury"},{"name":"Hora 11","start":"17:11","end":"18:11","startHours":17.184882062285418,"endHours":18.184882062285418,"planetary_lord":"Venus"},{"name":"Hora 12","start":"18:11","end":"19:11","startHours":18.184882062285418,"endHours":19.184882062285418,"planetary_lord":"Sun"},{"name":"Hora 13","start":"19:11","end":"20:11","startHours":19.184882062285418,"endHours":20.184882062285418,"planetary_lord":"Mars"},{"name":"Hora 14","start":"20:11","end":"21:11","startHours":20.184882062285418,"endHours":21.184882062285418,"planetary_lord":"Jupiter"},{"name":"Hora 15","start":"21:11","end":"22:11","startHours":21.184882062285418,"endHours":22.184882062285418,"planetary_lord":"Saturn"},{"name":"Hora 16","start":"22:11","end":"23:11","startHours":22.184882062285418,"endHours":23.184882062285418,"planetary_lord":"Moon"},{"name":"Hora 17","start":"23:11","end":"00:11","startHours":23.184882062285418,"endHours":24.184882062285418,"planetary_lord":"Mercury"},{"name":"Hora 18","start":"00:11","end":"01:11","startHours":24.184882062285418,"endHours":25.184882062285418,"planetary_lord":"Venus"},{"name":"Hora 19","start":"01:11","end":"02:11","startHours":25.184882062285418,"endHours":26.184882062285418,"planetary_lord":"Sun"},{"name":"Hora 20","start":"02:11","end":"03:11","startHours":26.184882062285418,"endHours":27.184882062285418,"planetary_lord":"Mars"},{"name":"Hora 21","start":"03:11","end":"04:11","startHours":27.184882062285418,"endHours":28.184882062285418,"planetary_lord":"Jupiter"},{"name":"Hora 22","start":"04:11","end":"05:11","startHours":28.184882062285418,"endHours":29.184882062285418,"planetary_lord":"Saturn"},{"name":"Hora 23","start":"05:11","end":"06:11","startHours":29.184882062285418,"endHours":30.184882062285418,"planetary_lord":"Moon"},{"name":"Hora 24","start":"06:11","end":"07:11","startHours":30.184882062285418,"endHours":31.184882062285418,"planetary_lord":"Mercury"}],"taraBala":{"favorable_nakshatras":["Aśvinī","Bharaṇī","Punarvasu","Puṣya","Aśleṣā","Maghā","Pūrva Phalgunī","Viśākhā","Anurādhā","Jyeṣṭhā","Mūla","Pūrva Āṣāḍhā","Pūrva Bhādrapadā","Uttara Bhādrapadā","Revatī"],"unfavorable_nakshatras":["Kṛttikā","Rohiṇī","Mṛgaśirā","Ārdrā","Uttara Phalgunī","Hasta","Citrā","Svātī","Uttara Āṣāḍhā","Śravaṇa","Dhaniṣṭhā","Śatabhiṣaj"],"nature":"Janma-tara if same nakshatra; favorable for 15 nakshatras"},"chandraBala":{"favorable_rashis":["Meṣa","Karka","Siṃha","Vṛścika","Dhanu","Kumbha"],"unfavorable_rashis":["Vṛṣabha","Mithuna","Kanyā","Tulā","Makara","Mīna"]},"dishaShool":"East (Pūrva)","chandraVasa":"South","rahuVasa":"East","anandadiYoga":{"name":"Śubha","quality":"Auspicious"},"tropicalRitu":"Hemanta (Pre-winter)","vedicRitu":"Hemanta (Pre-winter)","tropicalAyana":"Uttarāyaṇa","vedicAyana":"Uttarāyaṇa","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":-21.480594948230717,"eotMinutes":-8.635931491373626,"ayanamsa":19.1459}},"calendars":{"vikram_samvat":1720,"vikram_samvatsara":"Nala","saka_samvat":1585,"saka_samvatsara":"Śobhana","bengali_samvat":1070,"malayalam_era":839,"nanakshahi_year":194,"lunar_month":"Māgha","lunar_month_paksha_full":"Māgha Śukla Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Māgha","lunar_month_amanta":"Māgha","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Makara (Tai)","ritu":"Śiśira (Winter)","display_summary":"Māgha Śukla Caturthī · Vikram 1720 Nala · Śaka 1585 Śobhana"},"festivals":[{"id":"vinayaka-chaturthi","name":"Vināyaka Caturthī (monthly)","name_sanskrit":"विनायक चतुर्थी","tradition":"Pan-Hindu","associated_deity":"Gaṇeśa","significance":"Monthly Śukla-pakṣa Caturthī; auspicious for new ventures.","vrata":true,"detection":{"tithi_number":4,"tithi_paksha":"Śukla"},"precedence":6}],"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":"Śanivāra (Saturday) — its presiding graha's walk."},"cosmic_resonances":[]},"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 January 13, 1663 CE · Mathurā · Vidhyamitra","description":"January 13, 1663 CE for Mathurā: Śukla Caturthī, sūryodaya 07:11, sūryāsta 17:45.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/1663-01-13","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/1663-01-13","sa":"https://sa.vidhyamitra.com/city/mathura/1663-01-13","hi":"https://hi.vidhyamitra.com/city/mathura/1663-01-13","x-default":"https://vidhyamitra.com/city/mathura/1663-01-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-06-05T11:03:45.974Z","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":"2026-06-05T11:03:45.974Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-06-05T11:03:45.974Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"}}}