{"id":"vidhyamitra:city-day:mathura:2103-01-13:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/2103-01-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"2103-01-13","date_display":"January 13, 2103 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":2103,"month":1,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2489176.770833,"kali_year":5204,"ahargana":1900711.2708,"sun":{"sidereal_longitude":266.4638,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":322.7645,"rashi":11,"rashi_name":"Kumbha"},"tithi":{"number":5,"name":"Pañcamī","paksha":"Śukla","full_name":"Śukla Pañcamī","elongation_degrees":56.3007,"elapsed_within_tithi_degrees":8.3007},"nakshatra":{"number":25,"name":"Pūrva Bhādrapadā","pada":1,"moon_longitude":322.7645,"elapsed_within_degrees":2.7645},"yoga":{"number":18,"name":"Varīyān","sum_longitude":229.2283},"karana":{"half_tithi_index":9,"name":"Bālava"},"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":2103,"month":1,"day":13,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2489176.770833,"ahargana":1900711.2708,"kali_year":5204,"ayanamsa_lahiri":25.2923,"grahas":{"sun":{"sidereal_longitude":266.8526999999999,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":1},"retrograde":false},"moon":{"sidereal_longitude":326.4984999999999,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":25,"name":"Pūrva Bhādrapadā","pada":2},"retrograde":false,"latitude":3.525},"mars":{"sidereal_longitude":250.42499999999995,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":4},"retrograde":false},"mercury":{"sidereal_longitude":242.01749999999993,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":1},"retrograde":false},"jupiter":{"sidereal_longitude":253.45139999999992,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":1},"retrograde":false},"venus":{"sidereal_longitude":290.9892,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":22,"name":"Śravaṇa","pada":4},"retrograde":false},"saturn":{"sidereal_longitude":212.9294,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":16,"name":"Viśākhā","pada":4},"retrograde":false},"rahu":{"sidereal_longitude":271.17,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":2},"retrograde":false},"ketu":{"sidereal_longitude":91.17,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":7,"name":"Punarvasu","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":2103,"month":1,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2489176.770833,"kali_year":5204,"ahargana":1900711.2708,"sun":{"sidereal_longitude":266.4638,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":322.7645,"rashi":11,"rashi_name":"Kumbha"},"tithi":{"number":5,"name":"Pañcamī","paksha":"Śukla","full_name":"Śukla Pañcamī","elongation_degrees":56.3007,"elapsed_within_tithi_degrees":8.3007},"nakshatra":{"number":25,"name":"Pūrva Bhādrapadā","pada":1,"moon_longitude":322.7645,"elapsed_within_degrees":2.7645},"yoga":{"number":18,"name":"Varīyān","sum_longitude":229.2283},"karana":{"half_tithi_index":9,"name":"Bālava"},"vara":{"number":1,"name":"Śanivāra (Saturday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":3.525,"elongation":56.301},"lunar":{"type":"lunar","occurs":false,"moon_latitude":3.525,"opposition_distance":123.699}},"eclipse_window_40days":[{"offset_days":-4,"type":"solar","occurs":true,"moon_latitude":-0.501,"elongation":2.631},{"offset_days":10,"type":"lunar","occurs":true,"moon_latitude":-0.361,"opposition_distance":1.481}]},"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":"17:44","solarNoonLocal":"12:28","dayLengthHours":10.550634301119684,"dayLengthDisplay":"10 Hours 33 Mins 02 Secs","nightLengthDisplay":"13 Hours 26 Mins 58 Secs","moonriseLocal":"10:31","moonsetLocal":"22:22","rahuKala":{"name":"Rāhu Kāla","start":"09:50","end":"11:09","startHours":9.828026949576307,"endHours":11.146856237216266,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"13:47","end":"15:06","startHours":13.784514812496187,"endHours":15.103344100136148,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"07:11","end":"08:31","startHours":7.190368374296385,"endHours":8.509197661936346,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:39","end":"10:00","startHours":9.652183044557646,"endHours":10.003870854594968,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:38","end":"07:55","startHours":7.629978136843039,"endHours":7.911328384872897,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"12:07","end":"12:49","startHours":12.113997714818904,"endHours":12.81737333489355,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:47","end":"06:29","startHours":5.783617134147094,"endHours":6.48699275422174,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"06:19","end":"07:11","startHours":6.311148849203079,"endHours":7.190368374296385,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:13","end":"14:56","startHours":14.224124575042842,"endHours":14.927500195117487,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:32","end":"17:56","startHours":17.54100267541607,"endHours":17.94100267541607,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:44","end":"18:11","startHours":17.74100267541607,"endHours":18.180612437962722,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:29","end":"19:14","startHours":17.49100267541607,"endHours":19.24100267541607,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"00:07","end":"00:49","startHours":24.113997714818904,"endHours":24.81737333489355,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Kāla","start":"07:11","end":"08:31","startHours":7.190368374296385,"endHours":8.509197661936346,"quality":"inauspicious"},{"name":"Śubha","start":"08:31","end":"09:50","startHours":8.509197661936346,"endHours":9.828026949576307,"quality":"auspicious"},{"name":"Roga","start":"09:50","end":"11:09","startHours":9.828026949576307,"endHours":11.146856237216266,"quality":"inauspicious"},{"name":"Udveg","start":"11:09","end":"12:28","startHours":11.146856237216266,"endHours":12.465685524856227,"quality":"inauspicious"},{"name":"Chala","start":"12:28","end":"13:47","startHours":12.465685524856227,"endHours":13.784514812496187,"quality":"neutral"},{"name":"Labha","start":"13:47","end":"15:06","startHours":13.784514812496187,"endHours":15.103344100136148,"quality":"auspicious"},{"name":"Amṛta","start":"15:06","end":"16:25","startHours":15.103344100136148,"endHours":16.42217338777611,"quality":"auspicious"},{"name":"Kāla","start":"16:25","end":"17:44","startHours":16.42217338777611,"endHours":17.74100267541607,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Labha","start":"17:44","end":"19:25","startHours":17.74100267541607,"endHours":19.42217338777611,"quality":"auspicious"},{"name":"Amṛta","start":"19:25","end":"21:06","startHours":19.42217338777611,"endHours":21.103344100136148,"quality":"auspicious"},{"name":"Kāla","start":"21:06","end":"22:47","startHours":21.103344100136148,"endHours":22.784514812496187,"quality":"inauspicious"},{"name":"Śubha","start":"22:47","end":"00:28","startHours":22.784514812496187,"endHours":24.465685524856227,"quality":"auspicious"},{"name":"Roga","start":"00:28","end":"02:09","startHours":24.465685524856227,"endHours":26.14685623721627,"quality":"inauspicious"},{"name":"Udveg","start":"02:09","end":"03:50","startHours":26.14685623721627,"endHours":27.828026949576305,"quality":"inauspicious"},{"name":"Chala","start":"03:50","end":"05:31","startHours":27.828026949576305,"endHours":29.509197661936348,"quality":"neutral"},{"name":"Labha","start":"05:31","end":"07:11","startHours":29.509197661936348,"endHours":31.190368374296384,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"07:11","end":"08:11","startHours":7.190368374296385,"endHours":8.190368374296385,"planetary_lord":"Saturn"},{"name":"Hora 2","start":"08:11","end":"09:11","startHours":8.190368374296385,"endHours":9.190368374296385,"planetary_lord":"Moon"},{"name":"Hora 3","start":"09:11","end":"10:11","startHours":9.190368374296385,"endHours":10.190368374296385,"planetary_lord":"Mercury"},{"name":"Hora 4","start":"10:11","end":"11:11","startHours":10.190368374296385,"endHours":11.190368374296385,"planetary_lord":"Venus"},{"name":"Hora 5","start":"11:11","end":"12:11","startHours":11.190368374296385,"endHours":12.190368374296385,"planetary_lord":"Sun"},{"name":"Hora 6","start":"12:11","end":"13:11","startHours":12.190368374296385,"endHours":13.190368374296385,"planetary_lord":"Mars"},{"name":"Hora 7","start":"13:11","end":"14:11","startHours":13.190368374296385,"endHours":14.190368374296385,"planetary_lord":"Jupiter"},{"name":"Hora 8","start":"14:11","end":"15:11","startHours":14.190368374296385,"endHours":15.190368374296385,"planetary_lord":"Saturn"},{"name":"Hora 9","start":"15:11","end":"16:11","startHours":15.190368374296385,"endHours":16.190368374296384,"planetary_lord":"Moon"},{"name":"Hora 10","start":"16:11","end":"17:11","startHours":16.190368374296384,"endHours":17.190368374296384,"planetary_lord":"Mercury"},{"name":"Hora 11","start":"17:11","end":"18:11","startHours":17.190368374296384,"endHours":18.190368374296384,"planetary_lord":"Venus"},{"name":"Hora 12","start":"18:11","end":"19:11","startHours":18.190368374296384,"endHours":19.190368374296384,"planetary_lord":"Sun"},{"name":"Hora 13","start":"19:11","end":"20:11","startHours":19.190368374296384,"endHours":20.190368374296384,"planetary_lord":"Mars"},{"name":"Hora 14","start":"20:11","end":"21:11","startHours":20.190368374296384,"endHours":21.190368374296384,"planetary_lord":"Jupiter"},{"name":"Hora 15","start":"21:11","end":"22:11","startHours":21.190368374296384,"endHours":22.190368374296384,"planetary_lord":"Saturn"},{"name":"Hora 16","start":"22:11","end":"23:11","startHours":22.190368374296384,"endHours":23.190368374296384,"planetary_lord":"Moon"},{"name":"Hora 17","start":"23:11","end":"00:11","startHours":23.190368374296384,"endHours":24.190368374296384,"planetary_lord":"Mercury"},{"name":"Hora 18","start":"00:11","end":"01:11","startHours":24.190368374296384,"endHours":25.190368374296384,"planetary_lord":"Venus"},{"name":"Hora 19","start":"01:11","end":"02:11","startHours":25.190368374296384,"endHours":26.190368374296384,"planetary_lord":"Sun"},{"name":"Hora 20","start":"02:11","end":"03:11","startHours":26.190368374296384,"endHours":27.190368374296384,"planetary_lord":"Mars"},{"name":"Hora 21","start":"03:11","end":"04:11","startHours":27.190368374296384,"endHours":28.190368374296384,"planetary_lord":"Jupiter"},{"name":"Hora 22","start":"04:11","end":"05:11","startHours":28.190368374296384,"endHours":29.190368374296384,"planetary_lord":"Saturn"},{"name":"Hora 23","start":"05:11","end":"06:11","startHours":29.190368374296384,"endHours":30.190368374296384,"planetary_lord":"Moon"},{"name":"Hora 24","start":"06:11","end":"07:11","startHours":30.190368374296384,"endHours":31.190368374296384,"planetary_lord":"Mercury"}],"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","Vṛścika","Dhanu","Kumbha"],"unfavorable_rashis":["Vṛṣabha","Mithuna","Kanyā","Tulā","Makara","Mīna"]},"dishaShool":"East (Pūrva)","chandraVasa":"South","rahuVasa":"East","anandadiYoga":{"name":"Amṛta","quality":"Auspicious"},"drikRitu":"Hemanta (Pre-winter) (Drik)","vedicRitu":"Hemanta (Pre-winter)","drikAyana":"Uttarāyaṇa","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization (Drikpanchang-parity)","declination":-21.616535802043593,"eotMinutes":-8.635931491373626,"ayanamsa":25.2923}},"calendars":{"vikram_samvat":2160,"vikram_samvatsara":"Dhātṛ","saka_samvat":2025,"saka_samvatsara":"Rudhirodgāri","bengali_samvat":1510,"malayalam_era":1279,"nanakshahi_year":634,"lunar_month":"Pauṣa","lunar_month_paksha_full":"Pauṣa Śukla Pakṣa","solar_month":"Dhanus (Mārgaḻi)","ritu":"Hemanta (Pre-winter)","display_summary":"Pauṣa Śukla Pañcamī · Vikram 2160 Dhātṛ · Śaka 2025 Rudhirodgāri"},"festivals":[{"id":"lohri","name":"Lohri","name_sanskrit":"लोहड़ी","tradition":"Regional","significance":"Punjab harvest festival; eve of Makara Saṅkrānti. (Approximated as 13/14 January annually; correct via Sun in Dhanu/Makara cusp.)","vrata":false,"detection":{"sun_rashi":"Dhanu"},"precedence":4},{"id":"dhanu-sankranti","name":"Dhanu Saṅkrānti","name_sanskrit":"धनु सङ्क्रान्ति","tradition":"Pan-Hindu","significance":"Sun enters Sagittarius; Dhanu-māsa (Khara-māsa).","vrata":false,"detection":{"sun_rashi":"Dhanu"},"precedence":5}],"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, 2103 CE · Mathurā · Vidhyamitra","description":"January 13, 2103 CE for Mathurā: Śukla Pañcamī, sūryodaya 07:11, sūryāsta 17:44.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/2103-01-13","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/2103-01-13","sa":"https://sa.vidhyamitra.com/city/mathura/2103-01-13","hi":"https://hi.vidhyamitra.com/city/mathura/2103-01-13","x-default":"https://vidhyamitra.com/city/mathura/2103-01-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-05-14T17:36:39.273Z","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":"2026-05-14T17:36:39.273Z","verification":{"type":"community-validated","markers":["matches Drikpanchang ±1 minute on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-05-14T17:36:39.273Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"}}}