{"id":"vidhyamitra:city-day:rishikesh:2021-12-07:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/rishikesh/2021-12-07","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"2021-12-07","date_display":"December 7, 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":12,"day":7,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2459555.770833,"kali_year":5123,"ahargana":1871090.2708,"sun":{"sidereal_longitude":230.4797,"rashi":8,"rashi_name":"Vṛścika"},"moon":{"sidereal_longitude":266.6062,"rashi":9,"rashi_name":"Dhanu"},"tithi":{"number":4,"name":"Caturthī","paksha":"Śukla","full_name":"Śukla Caturthī","elongation_degrees":36.1265,"elapsed_within_tithi_degrees":0.1265},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":4,"moon_longitude":266.6062,"elapsed_within_degrees":13.2729},"yoga":{"number":11,"name":"Vṛddhi","sum_longitude":137.0859},"karana":{"half_tithi_index":6,"name":"Vaṇija"},"vara":{"number":4,"name":"Maṅgalavāra (Tuesday)"}},"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":12,"day":7,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2459555.770833,"ahargana":1871090.2708,"kali_year":5123,"ayanamsa_lahiri":24.1594,"grahas":{"sun":{"sidereal_longitude":230.98634000000004,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":2},"retrograde":false},"moon":{"sidereal_longitude":269.31683999999996,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":1},"retrograde":false,"latitude":-3.234},"mars":{"sidereal_longitude":211.10154,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":16,"name":"Viśākhā","pada":4},"retrograde":false},"mercury":{"sidereal_longitude":235.01084000000003,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":3},"retrograde":false},"jupiter":{"sidereal_longitude":302.05783999999994,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":3},"retrograde":false},"venus":{"sidereal_longitude":269.1793399999999,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":1},"retrograde":true},"saturn":{"sidereal_longitude":285.34704,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":22,"name":"Śravaṇa","pada":2},"retrograde":false},"rahu":{"sidereal_longitude":40.6331,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":4,"name":"Rohiṇī","pada":1},"retrograde":false},"ketu":{"sidereal_longitude":220.6331,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":17,"name":"Anurādhā","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":2021,"month":12,"day":7,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2459555.770833,"kali_year":5123,"ahargana":1871090.2708,"sun":{"sidereal_longitude":230.4797,"rashi":8,"rashi_name":"Vṛścika"},"moon":{"sidereal_longitude":266.6062,"rashi":9,"rashi_name":"Dhanu"},"tithi":{"number":4,"name":"Caturthī","paksha":"Śukla","full_name":"Śukla Caturthī","elongation_degrees":36.1265,"elapsed_within_tithi_degrees":0.1265},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":4,"moon_longitude":266.6062,"elapsed_within_degrees":13.2729},"yoga":{"number":11,"name":"Vṛddhi","sum_longitude":137.0859},"karana":{"half_tithi_index":6,"name":"Vaṇija"},"vara":{"number":4,"name":"Maṅgalavāra (Tuesday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-3.234,"elongation":36.127},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-3.234,"opposition_distance":143.873}},"eclipse_window_40days":[{"offset_days":-18,"type":"lunar","occurs":true,"moon_latitude":-0.942,"opposition_distance":2.637}]},"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":"07:01","sunsetLocal":"17:18","solarNoonLocal":"12:09","dayLengthHours":10.281359207265751,"dayLengthDisplay":"10 Hours 16 Mins 53 Secs","nightLengthDisplay":"13 Hours 43 Mins 07 Secs","moonriseLocal":"09:32","moonsetLocal":"19:53","rahuKala":{"name":"Rāhu Kāla","start":"14:43","end":"16:01","startHours":14.723771526427484,"endHours":16.008941427335703,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"09:35","end":"10:52","startHours":9.583091922794608,"endHours":10.868261823702827,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"12:09","end":"13:26","startHours":12.153431724611046,"endHours":13.438601625519265,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:25","end":"09:45","startHours":9.411735936006846,"endHours":9.75444790958237,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:26","end":"07:43","startHours":7.441142087947576,"endHours":7.715311666807995,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:49","end":"12:30","startHours":11.81071975103552,"endHours":12.496143698186572,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:39","end":"06:20","startHours":5.641904226676069,"endHours":6.327328173827119,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"06:09","end":"07:01","startHours":6.155972187039357,"endHours":7.01275212097817,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"13:52","end":"14:33","startHours":13.86699159248867,"endHours":14.55241553963972,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:06","end":"17:30","startHours":17.094111328243923,"endHours":17.49411132824392,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:18","end":"17:43","startHours":17.294111328243922,"endHours":17.722501295213327,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:03","end":"18:48","startHours":17.044111328243922,"endHours":18.794111328243922,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:49","end":"00:30","startHours":23.81071975103552,"endHours":24.49614369818657,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Roga","start":"07:01","end":"08:18","startHours":7.01275212097817,"endHours":8.29792202188639,"quality":"inauspicious"},{"name":"Udveg","start":"08:18","end":"09:35","startHours":8.29792202188639,"endHours":9.583091922794608,"quality":"inauspicious"},{"name":"Chala","start":"09:35","end":"10:52","startHours":9.583091922794608,"endHours":10.868261823702827,"quality":"neutral"},{"name":"Labha","start":"10:52","end":"12:09","startHours":10.868261823702827,"endHours":12.153431724611046,"quality":"auspicious"},{"name":"Amṛta","start":"12:09","end":"13:26","startHours":12.153431724611046,"endHours":13.438601625519265,"quality":"auspicious"},{"name":"Kāla","start":"13:26","end":"14:43","startHours":13.438601625519265,"endHours":14.723771526427484,"quality":"inauspicious"},{"name":"Śubha","start":"14:43","end":"16:01","startHours":14.723771526427484,"endHours":16.008941427335703,"quality":"auspicious"},{"name":"Roga","start":"16:01","end":"17:18","startHours":16.008941427335703,"endHours":17.294111328243922,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Kāla","start":"17:18","end":"19:01","startHours":17.294111328243922,"endHours":19.008941427335703,"quality":"inauspicious"},{"name":"Śubha","start":"19:01","end":"20:43","startHours":19.008941427335703,"endHours":20.723771526427484,"quality":"auspicious"},{"name":"Roga","start":"20:43","end":"22:26","startHours":20.723771526427484,"endHours":22.438601625519265,"quality":"inauspicious"},{"name":"Udveg","start":"22:26","end":"00:09","startHours":22.438601625519265,"endHours":24.153431724611046,"quality":"inauspicious"},{"name":"Chala","start":"00:09","end":"01:52","startHours":24.153431724611046,"endHours":25.868261823702827,"quality":"neutral"},{"name":"Labha","start":"01:52","end":"03:35","startHours":25.868261823702827,"endHours":27.58309192279461,"quality":"auspicious"},{"name":"Amṛta","start":"03:35","end":"05:18","startHours":27.58309192279461,"endHours":29.29792202188639,"quality":"auspicious"},{"name":"Kāla","start":"05:18","end":"07:01","startHours":29.29792202188639,"endHours":31.01275212097817,"quality":"inauspicious"}],"horas":[{"name":"Hora 1","start":"07:01","end":"08:01","startHours":7.01275212097817,"endHours":8.01275212097817,"planetary_lord":"Mars"},{"name":"Hora 2","start":"08:01","end":"09:01","startHours":8.01275212097817,"endHours":9.01275212097817,"planetary_lord":"Jupiter"},{"name":"Hora 3","start":"09:01","end":"10:01","startHours":9.01275212097817,"endHours":10.01275212097817,"planetary_lord":"Saturn"},{"name":"Hora 4","start":"10:01","end":"11:01","startHours":10.01275212097817,"endHours":11.01275212097817,"planetary_lord":"Moon"},{"name":"Hora 5","start":"11:01","end":"12:01","startHours":11.01275212097817,"endHours":12.01275212097817,"planetary_lord":"Mercury"},{"name":"Hora 6","start":"12:01","end":"13:01","startHours":12.01275212097817,"endHours":13.01275212097817,"planetary_lord":"Venus"},{"name":"Hora 7","start":"13:01","end":"14:01","startHours":13.01275212097817,"endHours":14.01275212097817,"planetary_lord":"Sun"},{"name":"Hora 8","start":"14:01","end":"15:01","startHours":14.01275212097817,"endHours":15.01275212097817,"planetary_lord":"Mars"},{"name":"Hora 9","start":"15:01","end":"16:01","startHours":15.01275212097817,"endHours":16.01275212097817,"planetary_lord":"Jupiter"},{"name":"Hora 10","start":"16:01","end":"17:01","startHours":16.01275212097817,"endHours":17.01275212097817,"planetary_lord":"Saturn"},{"name":"Hora 11","start":"17:01","end":"18:01","startHours":17.01275212097817,"endHours":18.01275212097817,"planetary_lord":"Moon"},{"name":"Hora 12","start":"18:01","end":"19:01","startHours":18.01275212097817,"endHours":19.01275212097817,"planetary_lord":"Mercury"},{"name":"Hora 13","start":"19:01","end":"20:01","startHours":19.01275212097817,"endHours":20.01275212097817,"planetary_lord":"Venus"},{"name":"Hora 14","start":"20:01","end":"21:01","startHours":20.01275212097817,"endHours":21.01275212097817,"planetary_lord":"Sun"},{"name":"Hora 15","start":"21:01","end":"22:01","startHours":21.01275212097817,"endHours":22.01275212097817,"planetary_lord":"Mars"},{"name":"Hora 16","start":"22:01","end":"23:01","startHours":22.01275212097817,"endHours":23.01275212097817,"planetary_lord":"Jupiter"},{"name":"Hora 17","start":"23:01","end":"00:01","startHours":23.01275212097817,"endHours":24.01275212097817,"planetary_lord":"Saturn"},{"name":"Hora 18","start":"00:01","end":"01:01","startHours":24.01275212097817,"endHours":25.01275212097817,"planetary_lord":"Moon"},{"name":"Hora 19","start":"01:01","end":"02:01","startHours":25.01275212097817,"endHours":26.01275212097817,"planetary_lord":"Mercury"},{"name":"Hora 20","start":"02:01","end":"03:01","startHours":26.01275212097817,"endHours":27.01275212097817,"planetary_lord":"Venus"},{"name":"Hora 21","start":"03:01","end":"04:01","startHours":27.01275212097817,"endHours":28.01275212097817,"planetary_lord":"Sun"},{"name":"Hora 22","start":"04:01","end":"05:01","startHours":28.01275212097817,"endHours":29.01275212097817,"planetary_lord":"Mars"},{"name":"Hora 23","start":"05:01","end":"06:01","startHours":29.01275212097817,"endHours":30.01275212097817,"planetary_lord":"Jupiter"},{"name":"Hora 24","start":"06:01","end":"07:01","startHours":30.01275212097817,"endHours":31.01275212097817,"planetary_lord":"Saturn"}],"taraBala":{"favorable_nakshatras":["Kṛttikā","Rohiṇī","Mṛgaśirā","Ārdrā","Punarvasu","Uttara Phalgunī","Hasta","Citrā","Svātī","Viśākhā","Uttara Āṣāḍhā","Śravaṇa","Dhaniṣṭhā","Śatabhiṣaj","Pūrva Bhādrapadā"],"unfavorable_nakshatras":["Aśvinī","Bharaṇī","Puṣya","Aśleṣā","Maghā","Pūrva Phalgunī","Anurādhā","Jyeṣṭhā","Mūla","Pūrva Āṣāḍhā","Uttara Bhādrapadā","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":"North","anandadiYoga":{"name":"Dhātṛ","quality":"Auspicious"},"drikRitu":"Hemanta (Pre-winter) (Drik)","vedicRitu":"Śarad (Autumn)","drikAyana":"Dakṣiṇāyana","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization (Drikpanchang-parity)","declination":-22.609019990944695,"eotMinutes":7.723696523337262,"ayanamsa":24.1594}},"calendars":{"vikram_samvat":2078,"vikram_samvatsara":"Ānanda","saka_samvat":1943,"saka_samvatsara":"Plava","bengali_samvat":1428,"malayalam_era":1197,"nanakshahi_year":552,"lunar_month":"Mārgaśīrṣa","lunar_month_paksha_full":"Mārgaśīrṣa Śukla Pakṣa","solar_month":"Vṛścika (Kārttikai)","ritu":"Hemanta (Pre-winter)","display_summary":"Mārgaśīrṣa Śukla Caturthī · Vikram 2078 Ānanda · Śaka 1943 Plava"},"festivals":[{"id":"angarika-chaturthi","name":"Aṅgāraka Caturthī (Tuesday Caturthī)","name_sanskrit":"अङ्गारक चतुर्थी","tradition":"Pan-Hindu","associated_deity":"Gaṇeśa + Maṅgala","significance":"Tuesday-Caturthī (rare); supremely auspicious for Maṅgala-doṣa-nivāraṇa.","vrata":true,"detection":{"any_of":[{"tithi_number":4,"vara_name":"Maṅgalavāra (Tuesday)"},{"tithi_number":19,"vara_name":"Maṅgalavāra (Tuesday)"}]},"precedence":3},{"id":"vrischika-sankranti","name":"Vṛścika Saṅkrānti","name_sanskrit":"वृश्चिक सङ्क्रान्ति","tradition":"Pan-Hindu","significance":"Sun enters Scorpio.","vrata":false,"detection":{"sun_rashi":"Vṛścika"},"precedence":5},{"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":"mangala-walk","name":"Maṅgala Walk","name_sanskrit":"मङ्गल यात्रा","type":"graha","description":"Right action + BG 2.31-38 (kṣatriya-dharma).","step_count":7,"url":"/walk/mangala-walk"},"reason":"Maṅgalavāra (Tuesday) — its presiding graha's walk."},"cosmic_resonances":[]},"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 7, 2021 CE · Ṛṣikeśa · Vidhyamitra","description":"December 7, 2021 CE for Ṛṣikeśa: Śukla Caturthī, sūryodaya 07:01, sūryāsta 17:18.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/rishikesh/2021-12-07","hreflang_alternates":{"en":"https://vidhyamitra.com/city/rishikesh/2021-12-07","sa":"https://sa.vidhyamitra.com/city/rishikesh/2021-12-07","hi":"https://hi.vidhyamitra.com/city/rishikesh/2021-12-07","x-default":"https://vidhyamitra.com/city/rishikesh/2021-12-07"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-05-15T06:54:55.621Z","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":"2026-05-15T06:54:55.621Z","verification":{"type":"community-validated","markers":["matches Drikpanchang ±1 minute on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-05-15T06:54:55.621Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"}}}