{"id":"vidhyamitra:city-day:rishikesh:2050-01-20:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/rishikesh/2050-01-20","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"2050-01-20","date_display":"January 20, 2050 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":2050,"month":1,"day":20,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2469826.770833,"kali_year":5151,"ahargana":1881361.2708,"sun":{"sidereal_longitude":275.4113,"rashi":10,"rashi_name":"Makara"},"moon":{"sidereal_longitude":233.3951,"rashi":8,"rashi_name":"Vṛścika"},"tithi":{"number":27,"name":"Dvādaśī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Dvādaśī","elongation_degrees":317.9838,"elapsed_within_tithi_degrees":5.9838},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":3,"moon_longitude":233.3951,"elapsed_within_degrees":6.7285},"yoga":{"number":12,"name":"Dhruva","sum_longitude":148.8064},"karana":{"half_tithi_index":52,"name":"Kaulava"},"vara":{"number":6,"name":"Guruvāra (Thursday)"}},"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":2050,"month":1,"day":20,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2469826.770833,"ahargana":1881361.2708,"kali_year":5151,"ayanamsa_lahiri":24.5522,"grahas":{"sun":{"sidereal_longitude":275.603212,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":3},"retrograde":false},"moon":{"sidereal_longitude":231.93141200000002,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":2},"retrograde":false,"latitude":1.3121},"mars":{"sidereal_longitude":214.51231200000007,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":17,"name":"Anurādhā","pada":1},"retrograde":false},"mercury":{"sidereal_longitude":251.015712,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":4},"retrograde":false},"jupiter":{"sidereal_longitude":94.03221199999996,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":8,"name":"Puṣya","pada":1},"retrograde":true},"venus":{"sidereal_longitude":279.968112,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":4},"retrograde":false},"saturn":{"sidereal_longitude":274.55501200000003,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":3},"retrograde":false},"rahu":{"sidereal_longitude":216.4261,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":17,"name":"Anurādhā","pada":1},"retrograde":false},"ketu":{"sidereal_longitude":36.4261,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":3,"name":"Kṛttikā","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":"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":2050,"month":1,"day":20,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2469826.770833,"kali_year":5151,"ahargana":1881361.2708,"sun":{"sidereal_longitude":275.4113,"rashi":10,"rashi_name":"Makara"},"moon":{"sidereal_longitude":233.3951,"rashi":8,"rashi_name":"Vṛścika"},"tithi":{"number":27,"name":"Dvādaśī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Dvādaśī","elongation_degrees":317.9838,"elapsed_within_tithi_degrees":5.9838},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":3,"moon_longitude":233.3951,"elapsed_within_degrees":6.7285},"yoga":{"number":12,"name":"Dhruva","sum_longitude":148.8064},"karana":{"half_tithi_index":52,"name":"Kaulava"},"vara":{"number":6,"name":"Guruvāra (Thursday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":1.312,"elongation":42.016},"lunar":{"type":"lunar","occurs":false,"moon_latitude":1.312,"opposition_distance":137.984}},"eclipse_window_40days":[]},"city":{"slug":"rishikesh","name":"Ṛṣikeśa","lat":30.0869,"lon":78.2676,"tz_offset_hours":5.5,"state":"Uttarakhand","country":"IN","tier":"tirtha"},"tier2":{"city":{"slug":"rishikesh","name":"Ṛṣikeśa","lat":30.0869,"lon":78.2676,"tz_offset_hours":5.5,"state":"Uttarakhand","country":"IN","tier":"tirtha"},"sunriseLocal":"07:13","sunsetLocal":"17:43","solarNoonLocal":"12:28","dayLengthHours":10.506157315071373,"dayLengthDisplay":"10 Hours 30 Mins 22 Secs","nightLengthDisplay":"13 Hours 29 Mins 38 Secs","moonriseLocal":"04:26","moonsetLocal":"14:40","rahuKala":{"name":"Rāhu Kāla","start":"13:47","end":"15:05","startHours":13.778168053337744,"endHours":15.091437717721664,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"07:13","end":"08:32","startHours":7.211819731418135,"endHours":8.525089395802057,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"09:50","end":"11:09","startHours":9.83835906018598,"endHours":11.1516287245699,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:40","end":"10:01","startHours":9.663256438268123,"endHours":10.013461682103834,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:39","end":"07:56","startHours":7.649576286212776,"endHours":7.929740481281346,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"12:07","end":"12:49","startHours":12.114693145118109,"endHours":12.815103632789535,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:49","end":"06:31","startHours":5.810998756075286,"endHours":6.51140924374671,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"06:20","end":"07:13","startHours":6.336306621828854,"endHours":7.211819731418135,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:13","end":"14:55","startHours":14.215924608132383,"endHours":14.916335095803808,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:31","end":"17:55","startHours":17.51797704648951,"endHours":17.917977046489508,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:43","end":"18:09","startHours":17.71797704648951,"endHours":18.155733601284147,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:28","end":"19:13","startHours":17.46797704648951,"endHours":19.21797704648951,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"00:07","end":"00:49","startHours":24.114693145118107,"endHours":24.815103632789533,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Śubha","start":"07:13","end":"08:32","startHours":7.211819731418135,"endHours":8.525089395802057,"quality":"auspicious"},{"name":"Roga","start":"08:32","end":"09:50","startHours":8.525089395802057,"endHours":9.83835906018598,"quality":"inauspicious"},{"name":"Udveg","start":"09:50","end":"11:09","startHours":9.83835906018598,"endHours":11.1516287245699,"quality":"inauspicious"},{"name":"Chala","start":"11:09","end":"12:28","startHours":11.1516287245699,"endHours":12.464898388953822,"quality":"neutral"},{"name":"Labha","start":"12:28","end":"13:47","startHours":12.464898388953822,"endHours":13.778168053337744,"quality":"auspicious"},{"name":"Amṛta","start":"13:47","end":"15:05","startHours":13.778168053337744,"endHours":15.091437717721664,"quality":"auspicious"},{"name":"Kāla","start":"15:05","end":"16:24","startHours":15.091437717721664,"endHours":16.404707382105585,"quality":"inauspicious"},{"name":"Śubha","start":"16:24","end":"17:43","startHours":16.404707382105585,"endHours":17.71797704648951,"quality":"auspicious"}],"nightChoghadiyas":[{"name":"Amṛta","start":"17:43","end":"19:24","startHours":17.71797704648951,"endHours":19.404707382105588,"quality":"auspicious"},{"name":"Kāla","start":"19:24","end":"21:05","startHours":19.404707382105588,"endHours":21.091437717721664,"quality":"inauspicious"},{"name":"Śubha","start":"21:05","end":"22:47","startHours":21.091437717721664,"endHours":22.778168053337744,"quality":"auspicious"},{"name":"Roga","start":"22:47","end":"00:28","startHours":22.778168053337744,"endHours":24.46489838895382,"quality":"inauspicious"},{"name":"Udveg","start":"00:28","end":"02:09","startHours":24.46489838895382,"endHours":26.1516287245699,"quality":"inauspicious"},{"name":"Chala","start":"02:09","end":"03:50","startHours":26.1516287245699,"endHours":27.83835906018598,"quality":"neutral"},{"name":"Labha","start":"03:50","end":"05:32","startHours":27.83835906018598,"endHours":29.525089395802055,"quality":"auspicious"},{"name":"Amṛta","start":"05:32","end":"07:13","startHours":29.525089395802055,"endHours":31.211819731418135,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"07:13","end":"08:13","startHours":7.211819731418135,"endHours":8.211819731418135,"planetary_lord":"Jupiter"},{"name":"Hora 2","start":"08:13","end":"09:13","startHours":8.211819731418135,"endHours":9.211819731418135,"planetary_lord":"Saturn"},{"name":"Hora 3","start":"09:13","end":"10:13","startHours":9.211819731418135,"endHours":10.211819731418135,"planetary_lord":"Moon"},{"name":"Hora 4","start":"10:13","end":"11:13","startHours":10.211819731418135,"endHours":11.211819731418135,"planetary_lord":"Mercury"},{"name":"Hora 5","start":"11:13","end":"12:13","startHours":11.211819731418135,"endHours":12.211819731418135,"planetary_lord":"Venus"},{"name":"Hora 6","start":"12:13","end":"13:13","startHours":12.211819731418135,"endHours":13.211819731418135,"planetary_lord":"Sun"},{"name":"Hora 7","start":"13:13","end":"14:13","startHours":13.211819731418135,"endHours":14.211819731418135,"planetary_lord":"Mars"},{"name":"Hora 8","start":"14:13","end":"15:13","startHours":14.211819731418135,"endHours":15.211819731418135,"planetary_lord":"Jupiter"},{"name":"Hora 9","start":"15:13","end":"16:13","startHours":15.211819731418135,"endHours":16.211819731418135,"planetary_lord":"Saturn"},{"name":"Hora 10","start":"16:13","end":"17:13","startHours":16.211819731418135,"endHours":17.211819731418135,"planetary_lord":"Moon"},{"name":"Hora 11","start":"17:13","end":"18:13","startHours":17.211819731418135,"endHours":18.211819731418135,"planetary_lord":"Mercury"},{"name":"Hora 12","start":"18:13","end":"19:13","startHours":18.211819731418135,"endHours":19.211819731418135,"planetary_lord":"Venus"},{"name":"Hora 13","start":"19:13","end":"20:13","startHours":19.211819731418135,"endHours":20.211819731418135,"planetary_lord":"Sun"},{"name":"Hora 14","start":"20:13","end":"21:13","startHours":20.211819731418135,"endHours":21.211819731418135,"planetary_lord":"Mars"},{"name":"Hora 15","start":"21:13","end":"22:13","startHours":21.211819731418135,"endHours":22.211819731418135,"planetary_lord":"Jupiter"},{"name":"Hora 16","start":"22:13","end":"23:13","startHours":22.211819731418135,"endHours":23.211819731418135,"planetary_lord":"Saturn"},{"name":"Hora 17","start":"23:13","end":"00:13","startHours":23.211819731418135,"endHours":24.211819731418135,"planetary_lord":"Moon"},{"name":"Hora 18","start":"00:13","end":"01:13","startHours":24.211819731418135,"endHours":25.211819731418135,"planetary_lord":"Mercury"},{"name":"Hora 19","start":"01:13","end":"02:13","startHours":25.211819731418135,"endHours":26.211819731418135,"planetary_lord":"Venus"},{"name":"Hora 20","start":"02:13","end":"03:13","startHours":26.211819731418135,"endHours":27.211819731418135,"planetary_lord":"Sun"},{"name":"Hora 21","start":"03:13","end":"04:13","startHours":27.211819731418135,"endHours":28.211819731418135,"planetary_lord":"Mars"},{"name":"Hora 22","start":"04:13","end":"05:13","startHours":28.211819731418135,"endHours":29.211819731418135,"planetary_lord":"Jupiter"},{"name":"Hora 23","start":"05:13","end":"06:13","startHours":29.211819731418135,"endHours":30.211819731418135,"planetary_lord":"Saturn"},{"name":"Hora 24","start":"06:13","end":"07:13","startHours":30.211819731418135,"endHours":31.211819731418135,"planetary_lord":"Moon"}],"taraBala":{"favorable_nakshatras":["Aśvinī","Bharaṇī","Kṛttikā","Rohiṇī","Mṛgaśirā","Maghā","Pūrva Phalgunī","Uttara Phalgunī","Hasta","Citrā","Mūla","Pūrva Āṣāḍhā","Uttara Āṣāḍhā","Śravaṇa","Dhaniṣṭhā"],"unfavorable_nakshatras":["Ārdrā","Punarvasu","Puṣya","Aśleṣā","Svātī","Viśākhā","Anurādhā","Jyeṣṭhā","Śatabhiṣaj","Pūrva Bhādrapadā","Uttara Bhādrapadā","Revatī"],"nature":"Janma-tara if same nakshatra; favorable for 15 nakshatras"},"chandraBala":{"favorable_rashis":["Meṣa","Vṛṣabha","Siṃha","Kanyā","Vṛścika","Makara"],"unfavorable_rashis":["Mithuna","Karka","Tulā","Dhanu","Kumbha","Mīna"]},"dishaShool":"South (Dakṣiṇa)","chandraVasa":"North-East","rahuVasa":"North-West","anandadiYoga":{"name":"Dhvānkṣa","quality":"Inauspicious"},"drikRitu":"Śiśira (Winter) (Drik)","vedicRitu":"Hemanta (Pre-winter)","drikAyana":"Uttarāyaṇa","vedicAyana":"Uttarāyaṇa","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization (Drikpanchang-parity)","declination":-20.115012008101377,"eotMinutes":-10.9643033372293,"ayanamsa":24.5522}},"calendars":{"vikram_samvat":2107,"vikram_samvatsara":"Subhānu","saka_samvat":1972,"saka_samvatsara":"Pramoda","bengali_samvat":1457,"malayalam_era":1226,"nanakshahi_year":581,"lunar_month":"Māgha","lunar_month_paksha_full":"Māgha Kṛṣṇa Pakṣa","solar_month":"Makara (Tai)","ritu":"Śiśira (Winter)","display_summary":"Māgha Kṛṣṇa Dvādaśī · Vikram 2107 Subhānu · Śaka 1972 Pramoda"},"festivals":[{"id":"makara-sankranti","name":"Makara Saṅkrānti (Uttarāyaṇa)","name_sanskrit":"मकर सङ्क्रान्ति","tradition":"Pan-Hindu","associated_deity":"Sūrya Bhagavān","significance":"Sun enters Capricorn; Uttarāyaṇa (north-going) begins. Bhīṣma's chosen mahaprasthāna time.","vrata":true,"detection":{"sun_rashi":"Makara"},"precedence":1,"sources":["Mahābhārata Bhīṣma-Stuti","Sūrya-Siddhānta"]},{"id":"pongal","name":"Pongal / Thai Pongal","name_sanskrit":"पोङ्गल","tradition":"Regional","associated_deity":"Sūrya Bhagavān","significance":"Tamil 4-day harvest festival; coincides with Makara Saṅkrānti.","vrata":false,"detection":{"sun_rashi":"Makara"},"precedence":2}],"todays_walk":{"walk":{"id":"guru-walk","name":"Bṛhaspati Walk","name_sanskrit":"गुरु यात्रा","type":"graha","description":"Wisdom transmission + BG 4.34.","step_count":8,"url":"/walk/guru-walk"},"reason":"Guruvāra (Thursday) — its presiding graha's walk."},"cosmic_resonances":[{"historical_date":"-3137-10-20","event":"Karṇa-Vadha (Mahābhārata Day 17)","chart_id":"karna","shared_marker":"same Jyeṣṭhā","url":"/day/-3137-10-20","relevance":0.5}]},"validity":{"eternal":false,"location_specific":"rishikesh"},"liturgical":{"opening":"जय श्री कृष्ण","closing":"ॐ तत् सत्","attribution":"Computed by Vidhyamitra Sūrya-Siddhānta substrate + Vidhyamitra Tier-2 layer"},"seo":{"title":"Pañchāṅga January 20, 2050 CE · Ṛṣikeśa · Vidhyamitra","description":"January 20, 2050 CE for Ṛṣikeśa: Kṛṣṇa Dvādaśī, sūryodaya 07:13, sūryāsta 17:43.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/rishikesh/2050-01-20","hreflang_alternates":{"en":"https://vidhyamitra.com/city/rishikesh/2050-01-20","sa":"https://sa.vidhyamitra.com/city/rishikesh/2050-01-20","hi":"https://hi.vidhyamitra.com/city/rishikesh/2050-01-20","x-default":"https://vidhyamitra.com/city/rishikesh/2050-01-20"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-05-20T03:41:39.985Z","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":"2026-05-20T03:41:39.985Z","verification":{"type":"community-validated","markers":["matches Drikpanchang ±1 minute on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-05-20T03:41:39.985Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"}}}