{"id":"vidhyamitra:city-day:vrindavan:2021-01-13:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/vrindavan/2021-01-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"2021-01-13","date_display":"January 13, 2021 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":2021,"month":1,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2459227.770833,"kali_year":5122,"ahargana":1870762.2708,"sun":{"sidereal_longitude":268.7426,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":268.3942,"rashi":9,"rashi_name":"Dhanu"},"tithi":{"number":30,"name":"Amāvasyā","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Amāvasyā","elongation_degrees":359.6516,"elapsed_within_tithi_degrees":11.6516},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":1,"moon_longitude":268.3942,"elapsed_within_degrees":1.7275},"yoga":{"number":14,"name":"Harṣaṇa","sum_longitude":177.1368},"karana":{"half_tithi_index":59,"name":"Nāga"},"vara":{"number":5,"name":"Budhavāra (Wednesday)"}},"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":2021,"month":1,"day":13,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2459227.770833,"ahargana":1870762.2708,"kali_year":5122,"ayanamsa_lahiri":24.1468,"grahas":{"sun":{"sidereal_longitude":268.920472,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":1},"retrograde":false},"moon":{"sidereal_longitude":266.7197719999999,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":1},"retrograde":false,"latitude":-2.2742},"mars":{"sidereal_longitude":8.461171999999976,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":1,"name":"Aśvinī","pada":3},"retrograde":false},"mercury":{"sidereal_longitude":283.01497199999994,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":22,"name":"Śravaṇa","pada":1},"retrograde":false},"jupiter":{"sidereal_longitude":281.424972,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":22,"name":"Śravaṇa","pada":1},"retrograde":false},"venus":{"sidereal_longitude":251.08257200000003,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":4},"retrograde":false},"saturn":{"sidereal_longitude":278.879772,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":4},"retrograde":false},"rahu":{"sidereal_longitude":58.0122,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":5,"name":"Mṛgaśīrṣā","pada":2},"retrograde":false},"ketu":{"sidereal_longitude":238.0122,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","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":2021,"month":1,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2459227.770833,"kali_year":5122,"ahargana":1870762.2708,"sun":{"sidereal_longitude":268.7426,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":268.3942,"rashi":9,"rashi_name":"Dhanu"},"tithi":{"number":30,"name":"Amāvasyā","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Amāvasyā","elongation_degrees":359.6516,"elapsed_within_tithi_degrees":11.6516},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":1,"moon_longitude":268.3942,"elapsed_within_degrees":1.7275},"yoga":{"number":14,"name":"Harṣaṇa","sum_longitude":177.1368},"karana":{"half_tithi_index":59,"name":"Nāga"},"vara":{"number":5,"name":"Budhavāra (Wednesday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-2.274,"elongation":0.348},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-2.274,"opposition_distance":179.652}},"eclipse_window_40days":[{"offset_days":-14,"type":"lunar","occurs":true,"moon_latitude":1.091,"opposition_distance":1.549}]},"city":{"slug":"vrindavan","name":"Vṛndāvana","lat":27.565,"lon":77.6593,"tz_offset_hours":5.5,"state":"Uttar Pradesh","country":"IN","tier":"tirtha"},"tier2":{"city":{"slug":"vrindavan","name":"Vṛndāvana","lat":27.565,"lon":77.6593,"tz_offset_hours":5.5,"state":"Uttar Pradesh","country":"IN","tier":"tirtha"},"sunriseLocal":"07:11","sunsetLocal":"17:45","solarNoonLocal":"12:28","dayLengthHours":10.558031549488046,"dayLengthDisplay":"10 Hours 33 Mins 29 Secs","nightLengthDisplay":"13 Hours 26 Mins 31 Secs","moonriseLocal":"07:05","moonsetLocal":"17:34","rahuKala":{"name":"Rāhu Kāla","start":"12:28","end":"13:47","startHours":12.466645524856226,"endHours":13.786399468542232,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"08:30","end":"09:50","startHours":8.507383693798209,"endHours":9.827137637484215,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"11:09","end":"12:28","startHours":11.146891581170221,"endHours":12.466645524856226,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:39","end":"10:00","startHours":9.651170444992747,"endHours":10.003104829975683,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:38","end":"07:55","startHours":7.627547731340872,"endHours":7.90909523932722,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"12:07","end":"12:49","startHours":12.114711139873293,"endHours":12.818579909839162,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:47","end":"06:29","startHours":5.779892210180464,"endHours":6.483760980146334,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"06:18","end":"07:11","startHours":6.307793787654867,"endHours":7.187629750112204,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:14","end":"14:56","startHours":14.226317449770901,"endHours":14.930186219736772,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:33","end":"17:57","startHours":17.54566129960025,"endHours":17.94566129960025,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:45","end":"18:11","startHours":17.74566129960025,"endHours":18.185579280828918,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:30","end":"19:15","startHours":17.49566129960025,"endHours":19.24566129960025,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"00:07","end":"00:49","startHours":24.11471113987329,"endHours":24.818579909839162,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Labha","start":"07:11","end":"08:30","startHours":7.187629750112204,"endHours":8.507383693798209,"quality":"auspicious"},{"name":"Amṛta","start":"08:30","end":"09:50","startHours":8.507383693798209,"endHours":9.827137637484215,"quality":"auspicious"},{"name":"Kāla","start":"09:50","end":"11:09","startHours":9.827137637484215,"endHours":11.146891581170221,"quality":"inauspicious"},{"name":"Śubha","start":"11:09","end":"12:28","startHours":11.146891581170221,"endHours":12.466645524856226,"quality":"auspicious"},{"name":"Roga","start":"12:28","end":"13:47","startHours":12.466645524856226,"endHours":13.786399468542232,"quality":"inauspicious"},{"name":"Udveg","start":"13:47","end":"15:06","startHours":13.786399468542232,"endHours":15.106153412228238,"quality":"inauspicious"},{"name":"Chala","start":"15:06","end":"16:26","startHours":15.106153412228238,"endHours":16.425907355914244,"quality":"neutral"},{"name":"Labha","start":"16:26","end":"17:45","startHours":16.425907355914244,"endHours":17.74566129960025,"quality":"auspicious"}],"nightChoghadiyas":[{"name":"Udveg","start":"17:45","end":"19:26","startHours":17.74566129960025,"endHours":19.425907355914244,"quality":"inauspicious"},{"name":"Chala","start":"19:26","end":"21:06","startHours":19.425907355914244,"endHours":21.106153412228238,"quality":"neutral"},{"name":"Labha","start":"21:06","end":"22:47","startHours":21.106153412228238,"endHours":22.786399468542236,"quality":"auspicious"},{"name":"Amṛta","start":"22:47","end":"00:28","startHours":22.786399468542236,"endHours":24.466645524856226,"quality":"auspicious"},{"name":"Kāla","start":"00:28","end":"02:09","startHours":24.466645524856226,"endHours":26.146891581170223,"quality":"inauspicious"},{"name":"Śubha","start":"02:09","end":"03:50","startHours":26.146891581170223,"endHours":27.827137637484217,"quality":"auspicious"},{"name":"Roga","start":"03:50","end":"05:30","startHours":27.827137637484217,"endHours":29.50738369379821,"quality":"inauspicious"},{"name":"Udveg","start":"05:30","end":"07:11","startHours":29.50738369379821,"endHours":31.187629750112205,"quality":"inauspicious"}],"horas":[{"name":"Hora 1","start":"07:11","end":"08:11","startHours":7.187629750112204,"endHours":8.187629750112205,"planetary_lord":"Mercury"},{"name":"Hora 2","start":"08:11","end":"09:11","startHours":8.187629750112205,"endHours":9.187629750112205,"planetary_lord":"Venus"},{"name":"Hora 3","start":"09:11","end":"10:11","startHours":9.187629750112205,"endHours":10.187629750112205,"planetary_lord":"Sun"},{"name":"Hora 4","start":"10:11","end":"11:11","startHours":10.187629750112205,"endHours":11.187629750112205,"planetary_lord":"Mars"},{"name":"Hora 5","start":"11:11","end":"12:11","startHours":11.187629750112205,"endHours":12.187629750112205,"planetary_lord":"Jupiter"},{"name":"Hora 6","start":"12:11","end":"13:11","startHours":12.187629750112205,"endHours":13.187629750112205,"planetary_lord":"Saturn"},{"name":"Hora 7","start":"13:11","end":"14:11","startHours":13.187629750112205,"endHours":14.187629750112205,"planetary_lord":"Moon"},{"name":"Hora 8","start":"14:11","end":"15:11","startHours":14.187629750112205,"endHours":15.187629750112205,"planetary_lord":"Mercury"},{"name":"Hora 9","start":"15:11","end":"16:11","startHours":15.187629750112205,"endHours":16.187629750112205,"planetary_lord":"Venus"},{"name":"Hora 10","start":"16:11","end":"17:11","startHours":16.187629750112205,"endHours":17.187629750112205,"planetary_lord":"Sun"},{"name":"Hora 11","start":"17:11","end":"18:11","startHours":17.187629750112205,"endHours":18.187629750112205,"planetary_lord":"Mars"},{"name":"Hora 12","start":"18:11","end":"19:11","startHours":18.187629750112205,"endHours":19.187629750112205,"planetary_lord":"Jupiter"},{"name":"Hora 13","start":"19:11","end":"20:11","startHours":19.187629750112205,"endHours":20.187629750112205,"planetary_lord":"Saturn"},{"name":"Hora 14","start":"20:11","end":"21:11","startHours":20.187629750112205,"endHours":21.187629750112205,"planetary_lord":"Moon"},{"name":"Hora 15","start":"21:11","end":"22:11","startHours":21.187629750112205,"endHours":22.187629750112205,"planetary_lord":"Mercury"},{"name":"Hora 16","start":"22:11","end":"23:11","startHours":22.187629750112205,"endHours":23.187629750112205,"planetary_lord":"Venus"},{"name":"Hora 17","start":"23:11","end":"00:11","startHours":23.187629750112205,"endHours":24.187629750112205,"planetary_lord":"Sun"},{"name":"Hora 18","start":"00:11","end":"01:11","startHours":24.187629750112205,"endHours":25.187629750112205,"planetary_lord":"Mars"},{"name":"Hora 19","start":"01:11","end":"02:11","startHours":25.187629750112205,"endHours":26.187629750112205,"planetary_lord":"Jupiter"},{"name":"Hora 20","start":"02:11","end":"03:11","startHours":26.187629750112205,"endHours":27.187629750112205,"planetary_lord":"Saturn"},{"name":"Hora 21","start":"03:11","end":"04:11","startHours":27.187629750112205,"endHours":28.187629750112205,"planetary_lord":"Moon"},{"name":"Hora 22","start":"04:11","end":"05:11","startHours":28.187629750112205,"endHours":29.187629750112205,"planetary_lord":"Mercury"},{"name":"Hora 23","start":"05:11","end":"06:11","startHours":29.187629750112205,"endHours":30.187629750112205,"planetary_lord":"Venus"},{"name":"Hora 24","start":"06:11","end":"07:11","startHours":30.187629750112205,"endHours":31.187629750112205,"planetary_lord":"Sun"}],"taraBala":{"favorable_nakshatras":["Rohiṇī","Mṛgaśirā","Ārdrā","Punarvasu","Puṣya","Hasta","Citrā","Svātī","Viśākhā","Anurādhā","Śravaṇa","Dhaniṣṭhā","Śatabhiṣaj","Pūrva Bhādrapadā","Uttara Bhādrapadā"],"unfavorable_nakshatras":["Aśvinī","Bharaṇī","Kṛttikā","Aśleṣā","Maghā","Pūrva Phalgunī","Uttara Phalgunī","Jyeṣṭhā","Mūla","Pūrva Āṣāḍhā","Uttara Āṣāḍhā","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":"North (Uttara)","chandraVasa":"East","rahuVasa":"South-West","anandadiYoga":{"name":"Saumya","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":-21.464947326685422,"eotMinutes":-8.635931491373626,"ayanamsa":24.1468}},"calendars":{"vikram_samvat":2078,"vikram_samvatsara":"Ānanda","saka_samvat":1943,"saka_samvatsara":"Plava","bengali_samvat":1428,"malayalam_era":1197,"nanakshahi_year":552,"lunar_month":"Pauṣa","lunar_month_paksha_full":"Pauṣa Kṛṣṇa Pakṣa","solar_month":"Dhanus (Mārgaḻi)","ritu":"Hemanta (Pre-winter)","display_summary":"Pauṣa Kṛṣṇa Amāvasyā · Vikram 2078 Ānanda · Śaka 1943 Plava"},"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":"budha-walk","name":"Budha Walk","name_sanskrit":"बुध यात्रा","type":"graha","description":"Discrimination + BG 2.41 (vyavasāyātmikā buddhi).","step_count":6,"url":"/walk/budha-walk"},"reason":"Budhavāra (Wednesday) — its presiding graha's walk."},"cosmic_resonances":[{"historical_date":"-3137-10-20","event":"Karṇa-Vadha (Mahābhārata Day 17)","chart_id":"karna","shared_marker":"same Kṛṣṇa Amāvasyā","url":"/day/-3137-10-20","relevance":0.5}]},"validity":{"eternal":false,"location_specific":"vrindavan"},"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, 2021 CE · Vṛndāvana · Vidhyamitra","description":"January 13, 2021 CE for Vṛndāvana: Kṛṣṇa Amāvasyā, sūryodaya 07:11, sūryāsta 17:45.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/vrindavan/2021-01-13","hreflang_alternates":{"en":"https://vidhyamitra.com/city/vrindavan/2021-01-13","sa":"https://sa.vidhyamitra.com/city/vrindavan/2021-01-13","hi":"https://hi.vidhyamitra.com/city/vrindavan/2021-01-13","x-default":"https://vidhyamitra.com/city/vrindavan/2021-01-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-05-15T07:35:42.888Z","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":"2026-05-15T07:35:42.888Z","verification":{"type":"community-validated","markers":["matches Drikpanchang ±1 minute on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-05-15T07:35:42.888Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"}}}