{"id":"vidhyamitra:city-day:rishikesh:2051-12-07:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/rishikesh/2051-12-07","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"2051-12-07","date_display":"December 7, 2051 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":2051,"month":12,"day":7,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2470512.770833,"kali_year":5153,"ahargana":1882047.2708,"sun":{"sidereal_longitude":229.6992,"rashi":8,"rashi_name":"Vṛścika"},"moon":{"sidereal_longitude":273.4158,"rashi":10,"rashi_name":"Makara"},"tithi":{"number":4,"name":"Caturthī","paksha":"Śukla","full_name":"Śukla Caturthī","elongation_degrees":43.7166,"elapsed_within_tithi_degrees":7.7166},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":3,"moon_longitude":273.4158,"elapsed_within_degrees":6.7491},"yoga":{"number":11,"name":"Vṛddhi","sum_longitude":143.1149},"karana":{"half_tithi_index":7,"name":"Viṣṭi"},"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":2051,"month":12,"day":7,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2470512.770833,"ahargana":1882047.2708,"kali_year":5153,"ayanamsa_lahiri":24.5784,"grahas":{"sun":{"sidereal_longitude":230.28320199999996,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":2},"retrograde":false},"moon":{"sidereal_longitude":271.90780199999995,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":2},"retrograde":false,"latitude":4.4924},"mars":{"sidereal_longitude":199.68730200000005,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":15,"name":"Svātī","pada":4},"retrograde":false},"mercury":{"sidereal_longitude":210.63260200000002,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":16,"name":"Viśākhā","pada":4},"retrograde":false},"jupiter":{"sidereal_longitude":157.735902,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":12,"name":"Uttara Phalgunī","pada":4},"retrograde":false},"venus":{"sidereal_longitude":260.8590019999999,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":3},"retrograde":false},"saturn":{"sidereal_longitude":290.74340200000006,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":22,"name":"Śravaṇa","pada":4},"retrograde":false},"rahu":{"sidereal_longitude":180.0785,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":14,"name":"Citrā","pada":3},"retrograde":false},"ketu":{"sidereal_longitude":0.0785,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":1,"name":"Aśvinī","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":2051,"month":12,"day":7,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2470512.770833,"kali_year":5153,"ahargana":1882047.2708,"sun":{"sidereal_longitude":229.6992,"rashi":8,"rashi_name":"Vṛścika"},"moon":{"sidereal_longitude":273.4158,"rashi":10,"rashi_name":"Makara"},"tithi":{"number":4,"name":"Caturthī","paksha":"Śukla","full_name":"Śukla Caturthī","elongation_degrees":43.7166,"elapsed_within_tithi_degrees":7.7166},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":3,"moon_longitude":273.4158,"elapsed_within_degrees":6.7491},"yoga":{"number":11,"name":"Vṛddhi","sum_longitude":143.1149},"karana":{"half_tithi_index":7,"name":"Viṣṭi"},"vara":{"number":6,"name":"Guruvāra (Thursday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":4.492,"elongation":43.717},"lunar":{"type":"lunar","occurs":false,"moon_latitude":4.492,"opposition_distance":136.283}},"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":"07:01","sunsetLocal":"17:18","solarNoonLocal":"12:09","dayLengthHours":10.284270884963817,"dayLengthDisplay":"10 Hours 17 Mins 03 Secs","nightLengthDisplay":"13 Hours 42 Mins 57 Secs","moonriseLocal":"09:44","moonsetLocal":"20:08","rahuKala":{"name":"Rāhu Kāla","start":"13:26","end":"14:43","startHours":13.438965585231522,"endHours":14.724499445852,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"07:01","end":"08:18","startHours":7.011296282129137,"endHours":8.296830142749613,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"09:35","end":"10:52","startHours":9.582364003370092,"endHours":10.867897863990567,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:25","end":"09:45","startHours":9.410959488620694,"endHours":9.753768518119488,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:26","end":"07:43","startHours":7.439807569002629,"endHours":7.714054792601664,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:49","end":"12:30","startHours":11.810622695112253,"endHours":12.49624075410984,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:38","end":"06:20","startHours":5.640060164133962,"endHours":6.325678223131549,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"06:09","end":"07:01","startHours":6.154273708382152,"endHours":7.011296282129137,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"13:52","end":"14:33","startHours":13.867476872105016,"endHours":14.553094931102603,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:06","end":"17:30","startHours":17.095567167092955,"endHours":17.495567167092954,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:18","end":"17:43","startHours":17.295567167092955,"endHours":17.72407845396645,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:03","end":"18:48","startHours":17.045567167092955,"endHours":18.795567167092955,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:49","end":"00:30","startHours":23.81062269511225,"endHours":24.49624075410984,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Śubha","start":"07:01","end":"08:18","startHours":7.011296282129137,"endHours":8.296830142749613,"quality":"auspicious"},{"name":"Roga","start":"08:18","end":"09:35","startHours":8.296830142749613,"endHours":9.582364003370092,"quality":"inauspicious"},{"name":"Udveg","start":"09:35","end":"10:52","startHours":9.582364003370092,"endHours":10.867897863990567,"quality":"inauspicious"},{"name":"Chala","start":"10:52","end":"12:09","startHours":10.867897863990567,"endHours":12.153431724611046,"quality":"neutral"},{"name":"Labha","start":"12:09","end":"13:26","startHours":12.153431724611046,"endHours":13.438965585231522,"quality":"auspicious"},{"name":"Amṛta","start":"13:26","end":"14:43","startHours":13.438965585231522,"endHours":14.724499445852,"quality":"auspicious"},{"name":"Kāla","start":"14:43","end":"16:01","startHours":14.724499445852,"endHours":16.010033306472476,"quality":"inauspicious"},{"name":"Śubha","start":"16:01","end":"17:18","startHours":16.010033306472476,"endHours":17.295567167092955,"quality":"auspicious"}],"nightChoghadiyas":[{"name":"Amṛta","start":"17:18","end":"19:01","startHours":17.295567167092955,"endHours":19.01003330647248,"quality":"auspicious"},{"name":"Kāla","start":"19:01","end":"20:43","startHours":19.01003330647248,"endHours":20.724499445852,"quality":"inauspicious"},{"name":"Śubha","start":"20:43","end":"22:26","startHours":20.724499445852,"endHours":22.43896558523152,"quality":"auspicious"},{"name":"Roga","start":"22:26","end":"00:09","startHours":22.43896558523152,"endHours":24.153431724611046,"quality":"inauspicious"},{"name":"Udveg","start":"00:09","end":"01:52","startHours":24.153431724611046,"endHours":25.86789786399057,"quality":"inauspicious"},{"name":"Chala","start":"01:52","end":"03:35","startHours":25.86789786399057,"endHours":27.582364003370092,"quality":"neutral"},{"name":"Labha","start":"03:35","end":"05:18","startHours":27.582364003370092,"endHours":29.296830142749613,"quality":"auspicious"},{"name":"Amṛta","start":"05:18","end":"07:01","startHours":29.296830142749613,"endHours":31.011296282129138,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"07:01","end":"08:01","startHours":7.011296282129137,"endHours":8.011296282129138,"planetary_lord":"Jupiter"},{"name":"Hora 2","start":"08:01","end":"09:01","startHours":8.011296282129138,"endHours":9.011296282129138,"planetary_lord":"Saturn"},{"name":"Hora 3","start":"09:01","end":"10:01","startHours":9.011296282129138,"endHours":10.011296282129138,"planetary_lord":"Moon"},{"name":"Hora 4","start":"10:01","end":"11:01","startHours":10.011296282129138,"endHours":11.011296282129138,"planetary_lord":"Mercury"},{"name":"Hora 5","start":"11:01","end":"12:01","startHours":11.011296282129138,"endHours":12.011296282129138,"planetary_lord":"Venus"},{"name":"Hora 6","start":"12:01","end":"13:01","startHours":12.011296282129138,"endHours":13.011296282129138,"planetary_lord":"Sun"},{"name":"Hora 7","start":"13:01","end":"14:01","startHours":13.011296282129138,"endHours":14.011296282129138,"planetary_lord":"Mars"},{"name":"Hora 8","start":"14:01","end":"15:01","startHours":14.011296282129138,"endHours":15.011296282129138,"planetary_lord":"Jupiter"},{"name":"Hora 9","start":"15:01","end":"16:01","startHours":15.011296282129138,"endHours":16.011296282129138,"planetary_lord":"Saturn"},{"name":"Hora 10","start":"16:01","end":"17:01","startHours":16.011296282129138,"endHours":17.011296282129138,"planetary_lord":"Moon"},{"name":"Hora 11","start":"17:01","end":"18:01","startHours":17.011296282129138,"endHours":18.011296282129138,"planetary_lord":"Mercury"},{"name":"Hora 12","start":"18:01","end":"19:01","startHours":18.011296282129138,"endHours":19.011296282129138,"planetary_lord":"Venus"},{"name":"Hora 13","start":"19:01","end":"20:01","startHours":19.011296282129138,"endHours":20.011296282129138,"planetary_lord":"Sun"},{"name":"Hora 14","start":"20:01","end":"21:01","startHours":20.011296282129138,"endHours":21.011296282129138,"planetary_lord":"Mars"},{"name":"Hora 15","start":"21:01","end":"22:01","startHours":21.011296282129138,"endHours":22.011296282129138,"planetary_lord":"Jupiter"},{"name":"Hora 16","start":"22:01","end":"23:01","startHours":22.011296282129138,"endHours":23.011296282129138,"planetary_lord":"Saturn"},{"name":"Hora 17","start":"23:01","end":"00:01","startHours":23.011296282129138,"endHours":24.011296282129138,"planetary_lord":"Moon"},{"name":"Hora 18","start":"00:01","end":"01:01","startHours":24.011296282129138,"endHours":25.011296282129138,"planetary_lord":"Mercury"},{"name":"Hora 19","start":"01:01","end":"02:01","startHours":25.011296282129138,"endHours":26.011296282129138,"planetary_lord":"Venus"},{"name":"Hora 20","start":"02:01","end":"03:01","startHours":26.011296282129138,"endHours":27.011296282129138,"planetary_lord":"Sun"},{"name":"Hora 21","start":"03:01","end":"04:01","startHours":27.011296282129138,"endHours":28.011296282129138,"planetary_lord":"Mars"},{"name":"Hora 22","start":"04:01","end":"05:01","startHours":28.011296282129138,"endHours":29.011296282129138,"planetary_lord":"Jupiter"},{"name":"Hora 23","start":"05:01","end":"06:01","startHours":29.011296282129138,"endHours":30.011296282129138,"planetary_lord":"Saturn"},{"name":"Hora 24","start":"06:01","end":"07:01","startHours":30.011296282129138,"endHours":31.011296282129138,"planetary_lord":"Moon"}],"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":["Mithuna","Karka","Tulā","Vṛścika","Makara","Mīna"],"unfavorable_rashis":["Meṣa","Vṛṣabha","Siṃha","Kanyā","Dhanu","Kumbha"]},"dishaShool":"South (Dakṣiṇa)","chandraVasa":"South-East","rahuVasa":"North-West","anandadiYoga":{"name":"Vajra","quality":"Inauspicious"},"tropicalRitu":"Hemanta (Pre-winter) (tropical)","vedicRitu":"Śarad (Autumn)","tropicalAyana":"Dakṣiṇāyana","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":-22.57734691941268,"eotMinutes":7.723696523337262,"ayanamsa":24.5784}},"calendars":{"vikram_samvat":2108,"vikram_samvatsara":"Tāraṇa","saka_samvat":1973,"saka_samvatsara":"Prajāpati","bengali_samvat":1458,"malayalam_era":1227,"nanakshahi_year":582,"lunar_month":"Mārgaśīrṣa","lunar_month_paksha_full":"Mārgaśīrṣa Śukla Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Mārgaśīrṣa","lunar_month_amanta":"Mārgaśīrṣa","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Vṛścika (Kārttikai)","ritu":"Hemanta (Pre-winter)","display_summary":"Mārgaśīrṣa Śukla Caturthī · Vikram 2108 Tāraṇa · Śaka 1973 Prajāpati"},"festivals":[{"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":"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":[]},"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, 2051 CE · Ṛṣikeśa · Vidhyamitra","description":"December 7, 2051 CE for Ṛṣikeśa: Śukla Caturthī, sūryodaya 07:01, sūryāsta 17:18.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/rishikesh/2051-12-07","hreflang_alternates":{"en":"https://vidhyamitra.com/city/rishikesh/2051-12-07","sa":"https://sa.vidhyamitra.com/city/rishikesh/2051-12-07","hi":"https://hi.vidhyamitra.com/city/rishikesh/2051-12-07","x-default":"https://vidhyamitra.com/city/rishikesh/2051-12-07"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-06-01T00:45:26.529Z","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":"2026-06-01T00:45:26.529Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-06-01T00:45:26.529Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"}}}