{"id":"vidhyamitra:city-day:rishikesh:2041-12-20:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/rishikesh/2041-12-20","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"2041-12-20","date_display":"December 20, 2041 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":"Not independently benchmarked across the declared range","tradition_chain":"Āryabhaṭa(499) → Brahmagupta(628) → Bhāskara II(1150) → Mādhava(~1400) → Parameśvara(1430) → Nīlakaṇṭha(1501) → this","input":{"year":2041,"month":12,"day":20,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2466873.770833,"kali_year":5143,"ahargana":1878408.2708,"sun":{"sidereal_longitude":243.6301,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":203.0266,"rashi":7,"rashi_name":"Tulā"},"tithi":{"number":27,"name":"Dvādaśī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Dvādaśī","elongation_degrees":319.3965,"elapsed_within_tithi_degrees":7.3965},"nakshatra":{"number":16,"name":"Viśākhā","pada":1,"moon_longitude":203.0266,"elapsed_within_degrees":3.0266},"yoga":{"number":7,"name":"Sukarma","sum_longitude":86.6567},"karana":{"half_tithi_index":53,"name":"Taitila"},"vara":{"number":0,"name":"Śukravāra (Friday)"}},"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":2041,"month":12,"day":20,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2466873.770833,"ahargana":1878408.2708,"kali_year":5143,"ayanamsa_lahiri":24.4393,"grahas":{"sun":{"sidereal_longitude":244.07333900000003,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":2},"retrograde":false},"moon":{"sidereal_longitude":203.78593899999998,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":16,"name":"Viśākhā","pada":2},"retrograde":false,"latitude":-0.7912},"mars":{"sidereal_longitude":122.17453899999998,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","pada":1},"retrograde":false},"mercury":{"sidereal_longitude":258.03483900000003,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":2},"retrograde":false},"jupiter":{"sidereal_longitude":207.38173899999992,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":16,"name":"Viśākhā","pada":3},"retrograde":false},"venus":{"sidereal_longitude":240.50993900000003,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":1},"retrograde":false},"saturn":{"sidereal_longitude":188.756439,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":15,"name":"Svātī","pada":1},"retrograde":false},"rahu":{"sidereal_longitude":12.8903,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":1,"name":"Aśvinī","pada":4},"retrograde":false},"ketu":{"sidereal_longitude":192.8903,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":15,"name":"Svātī","pada":2},"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":"Not independently benchmarked across the declared range","tradition_chain":"Āryabhaṭa(499) → Brahmagupta(628) → Bhāskara II(1150) → Mādhava(~1400) → Parameśvara(1430) → Nīlakaṇṭha(1501) → this","input":{"year":2041,"month":12,"day":20,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2466873.770833,"kali_year":5143,"ahargana":1878408.2708,"sun":{"sidereal_longitude":243.6301,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":203.0266,"rashi":7,"rashi_name":"Tulā"},"tithi":{"number":27,"name":"Dvādaśī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Dvādaśī","elongation_degrees":319.3965,"elapsed_within_tithi_degrees":7.3965},"nakshatra":{"number":16,"name":"Viśākhā","pada":1,"moon_longitude":203.0266,"elapsed_within_degrees":3.0266},"yoga":{"number":7,"name":"Sukarma","sum_longitude":86.6567},"karana":{"half_tithi_index":53,"name":"Taitila"},"vara":{"number":0,"name":"Śukravāra (Friday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-0.791,"elongation":40.603},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-0.791,"opposition_distance":139.397}},"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":10.205509866412443,"dayLengthDisplay":"10 Hours 12 Mins 20 Secs","nightLengthDisplay":"13 Hours 47 Mins 40 Secs","moonriseLocal":"04:13","moonsetLocal":"14:55","rahuKala":{"name":"Rāhu Kāla","start":"10:59","end":"12:15","startHours":10.975605974657299,"endHours":12.251294707958856,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"14:48","end":"16:05","startHours":14.802672174561966,"endHours":16.07836090786352,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"08:25","end":"09:42","startHours":8.424228508054188,"endHours":9.699917241355744,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:32","end":"09:52","startHours":9.52982541024887,"endHours":9.870009072462619,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:34","end":"07:51","startHours":7.573769352519818,"endHours":7.845916282290816,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:55","end":"12:35","startHours":11.911111045745107,"endHours":12.591478370172604,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:47","end":"06:28","startHours":5.78780512589764,"endHours":6.468172450325137,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"06:18","end":"07:09","startHours":6.298080619218263,"endHours":7.148539774752633,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"13:57","end":"14:38","startHours":13.952213019027596,"endHours":14.632580343455093,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:09","end":"17:33","startHours":17.154049641165077,"endHours":17.554049641165076,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:21","end":"17:47","startHours":17.354049641165076,"endHours":17.779279218932263,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:06","end":"18:51","startHours":17.104049641165076,"endHours":18.854049641165076,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:55","end":"00:35","startHours":23.91111104574511,"endHours":24.591478370172602,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Chala","start":"07:09","end":"08:25","startHours":7.148539774752633,"endHours":8.424228508054188,"quality":"neutral"},{"name":"Labha","start":"08:25","end":"09:42","startHours":8.424228508054188,"endHours":9.699917241355744,"quality":"auspicious"},{"name":"Amṛta","start":"09:42","end":"10:59","startHours":9.699917241355744,"endHours":10.975605974657299,"quality":"auspicious"},{"name":"Kāla","start":"10:59","end":"12:15","startHours":10.975605974657299,"endHours":12.251294707958856,"quality":"inauspicious"},{"name":"Śubha","start":"12:15","end":"13:32","startHours":12.251294707958856,"endHours":13.526983441260409,"quality":"auspicious"},{"name":"Roga","start":"13:32","end":"14:48","startHours":13.526983441260409,"endHours":14.802672174561966,"quality":"inauspicious"},{"name":"Udveg","start":"14:48","end":"16:05","startHours":14.802672174561966,"endHours":16.07836090786352,"quality":"inauspicious"},{"name":"Chala","start":"16:05","end":"17:21","startHours":16.07836090786352,"endHours":17.354049641165076,"quality":"neutral"}],"nightChoghadiyas":[{"name":"Roga","start":"17:21","end":"19:05","startHours":17.354049641165076,"endHours":19.07836090786352,"quality":"inauspicious"},{"name":"Udveg","start":"19:05","end":"20:48","startHours":19.07836090786352,"endHours":20.802672174561966,"quality":"inauspicious"},{"name":"Chala","start":"20:48","end":"22:32","startHours":20.802672174561966,"endHours":22.52698344126041,"quality":"neutral"},{"name":"Labha","start":"22:32","end":"00:15","startHours":22.52698344126041,"endHours":24.251294707958856,"quality":"auspicious"},{"name":"Amṛta","start":"00:15","end":"01:59","startHours":24.251294707958856,"endHours":25.9756059746573,"quality":"auspicious"},{"name":"Kāla","start":"01:59","end":"03:42","startHours":25.9756059746573,"endHours":27.69991724135574,"quality":"inauspicious"},{"name":"Śubha","start":"03:42","end":"05:25","startHours":27.69991724135574,"endHours":29.42422850805419,"quality":"auspicious"},{"name":"Roga","start":"05:25","end":"07:09","startHours":29.42422850805419,"endHours":31.148539774752635,"quality":"inauspicious"}],"horas":[{"name":"Hora 1","start":"07:09","end":"08:09","startHours":7.148539774752633,"endHours":8.148539774752633,"planetary_lord":"Venus"},{"name":"Hora 2","start":"08:09","end":"09:09","startHours":8.148539774752633,"endHours":9.148539774752633,"planetary_lord":"Sun"},{"name":"Hora 3","start":"09:09","end":"10:09","startHours":9.148539774752633,"endHours":10.148539774752633,"planetary_lord":"Mars"},{"name":"Hora 4","start":"10:09","end":"11:09","startHours":10.148539774752633,"endHours":11.148539774752633,"planetary_lord":"Jupiter"},{"name":"Hora 5","start":"11:09","end":"12:09","startHours":11.148539774752633,"endHours":12.148539774752633,"planetary_lord":"Saturn"},{"name":"Hora 6","start":"12:09","end":"13:09","startHours":12.148539774752633,"endHours":13.148539774752633,"planetary_lord":"Moon"},{"name":"Hora 7","start":"13:09","end":"14:09","startHours":13.148539774752633,"endHours":14.148539774752633,"planetary_lord":"Mercury"},{"name":"Hora 8","start":"14:09","end":"15:09","startHours":14.148539774752633,"endHours":15.148539774752633,"planetary_lord":"Venus"},{"name":"Hora 9","start":"15:09","end":"16:09","startHours":15.148539774752633,"endHours":16.148539774752635,"planetary_lord":"Sun"},{"name":"Hora 10","start":"16:09","end":"17:09","startHours":16.148539774752635,"endHours":17.148539774752635,"planetary_lord":"Mars"},{"name":"Hora 11","start":"17:09","end":"18:09","startHours":17.148539774752635,"endHours":18.148539774752635,"planetary_lord":"Jupiter"},{"name":"Hora 12","start":"18:09","end":"19:09","startHours":18.148539774752635,"endHours":19.148539774752635,"planetary_lord":"Saturn"},{"name":"Hora 13","start":"19:09","end":"20:09","startHours":19.148539774752635,"endHours":20.148539774752635,"planetary_lord":"Moon"},{"name":"Hora 14","start":"20:09","end":"21:09","startHours":20.148539774752635,"endHours":21.148539774752635,"planetary_lord":"Mercury"},{"name":"Hora 15","start":"21:09","end":"22:09","startHours":21.148539774752635,"endHours":22.148539774752635,"planetary_lord":"Venus"},{"name":"Hora 16","start":"22:09","end":"23:09","startHours":22.148539774752635,"endHours":23.148539774752635,"planetary_lord":"Sun"},{"name":"Hora 17","start":"23:09","end":"00:09","startHours":23.148539774752635,"endHours":24.148539774752635,"planetary_lord":"Mars"},{"name":"Hora 18","start":"00:09","end":"01:09","startHours":24.148539774752635,"endHours":25.148539774752635,"planetary_lord":"Jupiter"},{"name":"Hora 19","start":"01:09","end":"02:09","startHours":25.148539774752635,"endHours":26.148539774752635,"planetary_lord":"Saturn"},{"name":"Hora 20","start":"02:09","end":"03:09","startHours":26.148539774752635,"endHours":27.148539774752635,"planetary_lord":"Moon"},{"name":"Hora 21","start":"03:09","end":"04:09","startHours":27.148539774752635,"endHours":28.148539774752635,"planetary_lord":"Mercury"},{"name":"Hora 22","start":"04:09","end":"05:09","startHours":28.148539774752635,"endHours":29.148539774752635,"planetary_lord":"Venus"},{"name":"Hora 23","start":"05:09","end":"06:09","startHours":29.148539774752635,"endHours":30.148539774752635,"planetary_lord":"Sun"},{"name":"Hora 24","start":"06:09","end":"07:09","startHours":30.148539774752635,"endHours":31.148539774752635,"planetary_lord":"Mars"}],"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","Karka","Siṃha","Tulā","Dhanu","Mīna"],"unfavorable_rashis":["Vṛṣabha","Mithuna","Kanyā","Vṛścika","Makara","Kumbha"]},"dishaShool":"West (Paścim)","chandraVasa":"North","rahuVasa":"South-East","anandadiYoga":{"name":"Śrīvatsa","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":-23.42813191081941,"eotMinutes":1.851917522468745,"ayanamsa":24.4393}},"calendars":{"vikram_samvat":2098,"vikram_samvatsara":"Bhāva","saka_samvat":1963,"saka_samvatsara":"Durmati","bengali_samvat":1448,"malayalam_era":1217,"nanakshahi_year":572,"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 Dvādaśī · Vikram 2098 Bhāva · Śaka 1963 Durmati"},"festivals":[],"todays_walk":{"walk":{"id":"shukra-walk","name":"Śukra Walk","name_sanskrit":"शुक्र यात्रा","type":"graha","description":"Beauty + creativity in dharma + BG 10.36.","step_count":5,"url":"/walk/shukra-walk"},"reason":"Śukravāra (Friday) — 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 20, 2041 CE · Ṛṣikeśa · Vidhyamitra","description":"December 20, 2041 CE for Ṛṣikeśa: Kṛṣṇa Dvādaśī, sūryodaya 07:09, sūryāsta 17:21.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/rishikesh/2041-12-20","hreflang_alternates":{"en":"https://vidhyamitra.com/city/rishikesh/2041-12-20","sa":"https://sa.vidhyamitra.com/city/rishikesh/2041-12-20","hi":"https://hi.vidhyamitra.com/city/rishikesh/2041-12-20","x-default":"https://vidhyamitra.com/city/rishikesh/2041-12-20"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-10T02:55:39.528Z","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":"2026-08-10T02:55:39.528Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-10T02:55:39.528Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"},"reader_local_antaryami":{"reader_geography":"Every reader enters from their own kṣetra anywhere on Bhūmi; no single city is the universal center.","purna_chain":["Goloka/Vraja Rādhā-Krishna","Vaikuṇṭha Lakṣmī-Nārāyaṇa","Mahāviṣṇu/Kāraṇodakaśāyī Viṣṇu","Garbhodakaśāyī Viṣṇu","Brahmā","Kṣīrodaka Paramātmā/Antaryāmī (Kṣīrodakaśāyī Viṣṇu)","Bhūmi","reader's own kṣetra anywhere on Bhūmi","exact reading kṣetra","reader-bhakta","chitta/vāṇī/aṅgulī","keyboard-silicon-pathways","Vidhyāmitra substrate","reader/seer","Krishna"],"antaryami_responsibility_formula":"Kṣīrodakaśāyī Viṣṇu = Paramātmā = Antaryāmī. Jīva desires. Prakṛti executes through guṇas. Paramātmā witnesses, permits, remembers, guides, and sustains. Bhagavān is the ultimate source.","source_anchors":[{"label":"BG 13.23","path":"/bhagavad-gita/13/23","meaning":"upadraṣṭā-anumantā · witness-permitter"},{"label":"BG 15.15","path":"/bhagavad-gita/15/15","meaning":"the Lord seated in every heart as memory, knowledge, and forgetting"},{"label":"BG 18.61","path":"/bhagavad-gita/18/61","meaning":"Īśvara seated in the heart of all beings"}],"nama_seal":"Hare Krishna Hare Krishna · Krishna Krishna Hare Hare · Hare Rama Hare Rama · Rama Rama Hare Hare"}}}