{"id":"vidhyamitra:city-day:rishikesh:2166-12-20:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/rishikesh/2166-12-20","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"2166-12-20","date_display":"December 20, 2166 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":2166,"month":12,"day":20,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2512528.770833,"kali_year":5268,"ahargana":1924063.2708,"sun":{"sidereal_longitude":241.2229,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":211.9829,"rashi":8,"rashi_name":"Vṛścika"},"tithi":{"number":28,"name":"Trayodaśī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Trayodaśī","elongation_degrees":330.76,"elapsed_within_tithi_degrees":6.76},"nakshatra":{"number":16,"name":"Viśākhā","pada":4,"moon_longitude":211.9829,"elapsed_within_degrees":11.9829},"yoga":{"number":7,"name":"Sukarma","sum_longitude":93.2059},"karana":{"half_tithi_index":55,"name":"Vaṇija"},"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":2166,"month":12,"day":20,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2512528.770833,"ahargana":1924063.2708,"kali_year":5268,"ayanamsa_lahiri":26.1854,"grahas":{"sun":{"sidereal_longitude":241.98288200000002,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":1},"retrograde":false},"moon":{"sidereal_longitude":213.89138200000002,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":17,"name":"Anurādhā","pada":1},"retrograde":false,"latitude":4.4549},"mars":{"sidereal_longitude":237.80398200000002,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":4},"retrograde":false},"mercury":{"sidereal_longitude":253.929082,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":1},"retrograde":false},"jupiter":{"sidereal_longitude":35.15378199999998,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":3,"name":"Kṛttikā","pada":3},"retrograde":true},"venus":{"sidereal_longitude":264.487382,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":4},"retrograde":false},"saturn":{"sidereal_longitude":261.473982,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":3},"retrograde":false},"rahu":{"sidereal_longitude":113.8687,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":9,"name":"Āśleṣā","pada":3},"retrograde":false},"ketu":{"sidereal_longitude":293.8687,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":1},"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":2166,"month":12,"day":20,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2512528.770833,"kali_year":5268,"ahargana":1924063.2708,"sun":{"sidereal_longitude":241.2229,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":211.9829,"rashi":8,"rashi_name":"Vṛścika"},"tithi":{"number":28,"name":"Trayodaśī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Trayodaśī","elongation_degrees":330.76,"elapsed_within_tithi_degrees":6.76},"nakshatra":{"number":16,"name":"Viśākhā","pada":4,"moon_longitude":211.9829,"elapsed_within_degrees":11.9829},"yoga":{"number":7,"name":"Sukarma","sum_longitude":93.2059},"karana":{"half_tithi_index":55,"name":"Vaṇija"},"vara":{"number":1,"name":"Śanivāra (Saturday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":4.455,"elongation":29.24},"lunar":{"type":"lunar","occurs":false,"moon_latitude":4.455,"opposition_distance":150.76}},"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":"07:09","sunsetLocal":"17:21","solarNoonLocal":"12:15","dayLengthHours":10.205912984147657,"dayLengthDisplay":"10 Hours 12 Mins 21 Secs","nightLengthDisplay":"13 Hours 47 Mins 39 Secs","moonriseLocal":"05:09","moonsetLocal":"15:37","rahuKala":{"name":"Rāhu Kāla","start":"09:42","end":"10:59","startHours":9.699816461921943,"endHours":10.975555584940398,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"13:32","end":"14:48","startHours":13.527033830977313,"endHours":14.80277295399577,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"07:09","end":"08:25","startHours":7.148338215885028,"endHours":8.424077338903485,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:32","end":"09:52","startHours":9.529717912186147,"endHours":9.869915011657737,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:34","end":"07:51","startHours":7.573584590224514,"endHours":7.845742269801785,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:55","end":"12:35","startHours":11.911097608487268,"endHours":12.591491807430444,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:47","end":"06:28","startHours":5.7875498179986735,"endHours":6.467944016941851,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"06:18","end":"07:09","startHours":6.297845467206057,"endHours":7.148338215885028,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"13:57","end":"14:38","startHours":13.9522802053168,"endHours":14.632674404259976,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:09","end":"17:33","startHours":17.154251200032686,"endHours":17.554251200032684,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:21","end":"17:47","startHours":17.354251200032685,"endHours":17.779497574372172,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:06","end":"18:51","startHours":17.104251200032685,"endHours":18.854251200032685,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:55","end":"00:35","startHours":23.911097608487268,"endHours":24.591491807430444,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Kāla","start":"07:09","end":"08:25","startHours":7.148338215885028,"endHours":8.424077338903485,"quality":"inauspicious"},{"name":"Śubha","start":"08:25","end":"09:42","startHours":8.424077338903485,"endHours":9.699816461921943,"quality":"auspicious"},{"name":"Roga","start":"09:42","end":"10:59","startHours":9.699816461921943,"endHours":10.975555584940398,"quality":"inauspicious"},{"name":"Udveg","start":"10:59","end":"12:15","startHours":10.975555584940398,"endHours":12.251294707958856,"quality":"inauspicious"},{"name":"Chala","start":"12:15","end":"13:32","startHours":12.251294707958856,"endHours":13.527033830977313,"quality":"neutral"},{"name":"Labha","start":"13:32","end":"14:48","startHours":13.527033830977313,"endHours":14.80277295399577,"quality":"auspicious"},{"name":"Amṛta","start":"14:48","end":"16:05","startHours":14.80277295399577,"endHours":16.078512077014228,"quality":"auspicious"},{"name":"Kāla","start":"16:05","end":"17:21","startHours":16.078512077014228,"endHours":17.354251200032685,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Labha","start":"17:21","end":"19:05","startHours":17.354251200032685,"endHours":19.078512077014228,"quality":"auspicious"},{"name":"Amṛta","start":"19:05","end":"20:48","startHours":19.078512077014228,"endHours":20.80277295399577,"quality":"auspicious"},{"name":"Kāla","start":"20:48","end":"22:32","startHours":20.80277295399577,"endHours":22.527033830977313,"quality":"inauspicious"},{"name":"Śubha","start":"22:32","end":"00:15","startHours":22.527033830977313,"endHours":24.251294707958856,"quality":"auspicious"},{"name":"Roga","start":"00:15","end":"01:59","startHours":24.251294707958856,"endHours":25.975555584940402,"quality":"inauspicious"},{"name":"Udveg","start":"01:59","end":"03:42","startHours":25.975555584940402,"endHours":27.69981646192194,"quality":"inauspicious"},{"name":"Chala","start":"03:42","end":"05:25","startHours":27.69981646192194,"endHours":29.424077338903487,"quality":"neutral"},{"name":"Labha","start":"05:25","end":"07:09","startHours":29.424077338903487,"endHours":31.148338215885026,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"07:09","end":"08:09","startHours":7.148338215885028,"endHours":8.148338215885028,"planetary_lord":"Saturn"},{"name":"Hora 2","start":"08:09","end":"09:09","startHours":8.148338215885028,"endHours":9.148338215885028,"planetary_lord":"Moon"},{"name":"Hora 3","start":"09:09","end":"10:09","startHours":9.148338215885028,"endHours":10.148338215885028,"planetary_lord":"Mercury"},{"name":"Hora 4","start":"10:09","end":"11:09","startHours":10.148338215885028,"endHours":11.148338215885028,"planetary_lord":"Venus"},{"name":"Hora 5","start":"11:09","end":"12:09","startHours":11.148338215885028,"endHours":12.148338215885028,"planetary_lord":"Sun"},{"name":"Hora 6","start":"12:09","end":"13:09","startHours":12.148338215885028,"endHours":13.148338215885028,"planetary_lord":"Mars"},{"name":"Hora 7","start":"13:09","end":"14:09","startHours":13.148338215885028,"endHours":14.148338215885028,"planetary_lord":"Jupiter"},{"name":"Hora 8","start":"14:09","end":"15:09","startHours":14.148338215885028,"endHours":15.148338215885028,"planetary_lord":"Saturn"},{"name":"Hora 9","start":"15:09","end":"16:09","startHours":15.148338215885028,"endHours":16.148338215885026,"planetary_lord":"Moon"},{"name":"Hora 10","start":"16:09","end":"17:09","startHours":16.148338215885026,"endHours":17.148338215885026,"planetary_lord":"Mercury"},{"name":"Hora 11","start":"17:09","end":"18:09","startHours":17.148338215885026,"endHours":18.148338215885026,"planetary_lord":"Venus"},{"name":"Hora 12","start":"18:09","end":"19:09","startHours":18.148338215885026,"endHours":19.148338215885026,"planetary_lord":"Sun"},{"name":"Hora 13","start":"19:09","end":"20:09","startHours":19.148338215885026,"endHours":20.148338215885026,"planetary_lord":"Mars"},{"name":"Hora 14","start":"20:09","end":"21:09","startHours":20.148338215885026,"endHours":21.148338215885026,"planetary_lord":"Jupiter"},{"name":"Hora 15","start":"21:09","end":"22:09","startHours":21.148338215885026,"endHours":22.148338215885026,"planetary_lord":"Saturn"},{"name":"Hora 16","start":"22:09","end":"23:09","startHours":22.148338215885026,"endHours":23.148338215885026,"planetary_lord":"Moon"},{"name":"Hora 17","start":"23:09","end":"00:09","startHours":23.148338215885026,"endHours":24.148338215885026,"planetary_lord":"Mercury"},{"name":"Hora 18","start":"00:09","end":"01:09","startHours":24.148338215885026,"endHours":25.148338215885026,"planetary_lord":"Venus"},{"name":"Hora 19","start":"01:09","end":"02:09","startHours":25.148338215885026,"endHours":26.148338215885026,"planetary_lord":"Sun"},{"name":"Hora 20","start":"02:09","end":"03:09","startHours":26.148338215885026,"endHours":27.148338215885026,"planetary_lord":"Mars"},{"name":"Hora 21","start":"03:09","end":"04:09","startHours":27.148338215885026,"endHours":28.148338215885026,"planetary_lord":"Jupiter"},{"name":"Hora 22","start":"04:09","end":"05:09","startHours":28.148338215885026,"endHours":29.148338215885026,"planetary_lord":"Saturn"},{"name":"Hora 23","start":"05:09","end":"06:09","startHours":29.148338215885026,"endHours":30.148338215885026,"planetary_lord":"Moon"},{"name":"Hora 24","start":"06:09","end":"07:09","startHours":30.148338215885026,"endHours":31.148338215885026,"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","Vṛṣabha","Siṃha","Kanyā","Vṛścika","Makara"],"unfavorable_rashis":["Mithuna","Karka","Tulā","Dhanu","Kumbha","Mīna"]},"dishaShool":"East (Pūrva)","chandraVasa":"North-East","rahuVasa":"East","anandadiYoga":{"name":"Maitra","quality":"Auspicious"},"tropicalRitu":"Hemanta (Pre-winter)","vedicRitu":"Hemanta (Pre-winter)","tropicalAyana":"Dakṣiṇāyana","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":-23.423809140191135,"eotMinutes":1.851917522468745,"ayanamsa":26.1854}},"calendars":{"vikram_samvat":2223,"vikram_samvatsara":"Pramāthi","saka_samvat":2088,"saka_samvatsara":"Akṣaya","bengali_samvat":1573,"malayalam_era":1342,"nanakshahi_year":697,"lunar_month":"Pauṣa","lunar_month_paksha_full":"Pauṣa Kṛṣṇa Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Pauṣa","lunar_month_amanta":"Mārgaśīrṣa","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Dhanus (Mārgaḻi)","ritu":"Hemanta (Pre-winter)","display_summary":"Pauṣa Kṛṣṇa Trayodaśī · Vikram 2223 Pramāthi · Śaka 2088 Akṣaya"},"festivals":[{"id":"pradosha-vrata","name":"Pradoṣa Vrata","name_sanskrit":"प्रदोष व्रत","tradition":"Shaiva","associated_deity":"Śiva","significance":"Twilight worship of Śiva on Trayodaśī.","vrata":true,"detection":{"any_of":[{"tithi_number":13},{"tithi_number":28}]},"precedence":7}],"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":[{"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":"rishikesh"},"liturgical":{"opening":"जय श्री कृष्ण","closing":"ॐ तत् सत्","attribution":"Computed by Vidhyamitra Sūrya-Siddhānta substrate + Vidhyamitra Tier-2 layer"},"seo":{"title":"Pañchāṅga December 20, 2166 CE · Ṛṣikeśa · Vidhyamitra","description":"December 20, 2166 CE for Ṛṣikeśa: Kṛṣṇa Trayodaśī, sūryodaya 07:09, sūryāsta 17:21.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/rishikesh/2166-12-20","hreflang_alternates":{"en":"https://vidhyamitra.com/city/rishikesh/2166-12-20","sa":"https://sa.vidhyamitra.com/city/rishikesh/2166-12-20","hi":"https://hi.vidhyamitra.com/city/rishikesh/2166-12-20","x-default":"https://vidhyamitra.com/city/rishikesh/2166-12-20"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-05-31T21:20:27.041Z","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":"2026-05-31T21:20:27.041Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-05-31T21:20:27.041Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"}}}