{"id":"vidhyamitra:city-day:vrindavan:2168-12-20:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/vrindavan/2168-12-20","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"2168-12-20","date_display":"December 20, 2168 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":2168,"month":12,"day":20,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2513259.770833,"kali_year":5270,"ahargana":1924794.2708,"sun":{"sidereal_longitude":241.7182,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":129.0075,"rashi":5,"rashi_name":"Siṃha"},"tithi":{"number":21,"name":"Ṣaṣṭhī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Ṣaṣṭhī","elongation_degrees":247.2893,"elapsed_within_tithi_degrees":7.2893},"nakshatra":{"number":10,"name":"Maghā","pada":3,"moon_longitude":129.0075,"elapsed_within_degrees":9.0075},"yoga":{"number":1,"name":"Viṣkambha","sum_longitude":10.7257},"karana":{"half_tithi_index":41,"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":2168,"month":12,"day":20,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2513259.770833,"ahargana":1924794.2708,"kali_year":5270,"ayanamsa_lahiri":26.2134,"grahas":{"sun":{"sidereal_longitude":242.478652,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":1},"retrograde":false},"moon":{"sidereal_longitude":133.17985199999998,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","pada":4},"retrograde":false,"latitude":3.6333},"mars":{"sidereal_longitude":253.0426520000001,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":4},"retrograde":false},"mercury":{"sidereal_longitude":236.1721520000001,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":3},"retrograde":true},"jupiter":{"sidereal_longitude":109.23815200000001,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":9,"name":"Aśleṣā","pada":1},"retrograde":true},"venus":{"sidereal_longitude":285.39515200000005,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":22,"name":"Śravaṇa","pada":2},"retrograde":false},"saturn":{"sidereal_longitude":282.099152,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":22,"name":"Śravaṇa","pada":1},"retrograde":false},"rahu":{"sidereal_longitude":75.1368,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":6,"name":"Ārdrā","pada":3},"retrograde":false},"ketu":{"sidereal_longitude":255.1368,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","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":2168,"month":12,"day":20,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2513259.770833,"kali_year":5270,"ahargana":1924794.2708,"sun":{"sidereal_longitude":241.7182,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":129.0075,"rashi":5,"rashi_name":"Siṃha"},"tithi":{"number":21,"name":"Ṣaṣṭhī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Ṣaṣṭhī","elongation_degrees":247.2893,"elapsed_within_tithi_degrees":7.2893},"nakshatra":{"number":10,"name":"Maghā","pada":3,"moon_longitude":129.0075,"elapsed_within_degrees":9.0075},"yoga":{"number":1,"name":"Viṣkambha","sum_longitude":10.7257},"karana":{"half_tithi_index":41,"name":"Vaṇija"},"vara":{"number":4,"name":"Maṅgalavāra (Tuesday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":3.633,"elongation":112.711},"lunar":{"type":"lunar","occurs":false,"moon_latitude":3.633,"opposition_distance":67.289}},"eclipse_window_40days":[{"offset_days":-5,"type":"lunar","occurs":true,"moon_latitude":-1.424,"opposition_distance":0.344},{"offset_days":9,"type":"solar","occurs":true,"moon_latitude":0.456,"elongation":2.131}]},"city":{"slug":"vrindavan","name":"Vṛndāvana","lat":27.565,"lon":77.6593,"tz_offset_hours":5.5,"state":"Uttar Pradesh","country":"IN","tier":"tirtha"},"tier2":{"city":{"slug":"vrindavan","name":"Vṛndāvana","lat":27.565,"lon":77.6593,"tz_offset_hours":5.5,"state":"Uttar Pradesh","country":"IN","tier":"tirtha"},"sunriseLocal":"07:06","sunsetLocal":"17:29","solarNoonLocal":"12:18","dayLengthHours":10.396613217520795,"dayLengthDisplay":"10 Hours 23 Mins 48 Secs","nightLengthDisplay":"13 Hours 36 Mins 12 Secs","moonriseLocal":"22:41","moonsetLocal":"11:20","rahuKala":{"name":"Rāhu Kāla","start":"14:53","end":"16:11","startHours":14.891001345672386,"endHours":16.190577997862487,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"09:42","end":"11:00","startHours":9.692694736911989,"endHours":10.99227138910209,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"12:18","end":"13:35","startHours":12.291848041292187,"endHours":13.591424693482288,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:31","end":"09:52","startHours":9.51941784995331,"endHours":9.865971623870669,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:32","end":"07:48","startHours":7.526733649928491,"endHours":7.803976669062378,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:57","end":"12:38","startHours":11.945294267374827,"endHours":12.638401815209548,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:42","end":"06:24","startHours":5.7073263368623515,"endHours":6.400433884697072,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"06:14","end":"07:06","startHours":6.227156997738391,"endHours":7.093541432531791,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:01","end":"14:43","startHours":14.024616910878986,"endHours":14.717724458713706,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:17","end":"17:41","startHours":17.290154650052585,"endHours":17.690154650052584,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:29","end":"17:55","startHours":17.490154650052585,"endHours":17.923346867449283,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:14","end":"18:59","startHours":17.240154650052585,"endHours":18.990154650052585,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:57","end":"00:38","startHours":23.945294267374827,"endHours":24.638401815209548,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Roga","start":"07:06","end":"08:24","startHours":7.093541432531791,"endHours":8.393118084721891,"quality":"inauspicious"},{"name":"Udveg","start":"08:24","end":"09:42","startHours":8.393118084721891,"endHours":9.692694736911989,"quality":"inauspicious"},{"name":"Chala","start":"09:42","end":"11:00","startHours":9.692694736911989,"endHours":10.99227138910209,"quality":"neutral"},{"name":"Labha","start":"11:00","end":"12:18","startHours":10.99227138910209,"endHours":12.291848041292187,"quality":"auspicious"},{"name":"Amṛta","start":"12:18","end":"13:35","startHours":12.291848041292187,"endHours":13.591424693482288,"quality":"auspicious"},{"name":"Kāla","start":"13:35","end":"14:53","startHours":13.591424693482288,"endHours":14.891001345672386,"quality":"inauspicious"},{"name":"Śubha","start":"14:53","end":"16:11","startHours":14.891001345672386,"endHours":16.190577997862487,"quality":"auspicious"},{"name":"Roga","start":"16:11","end":"17:29","startHours":16.190577997862487,"endHours":17.490154650052585,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Kāla","start":"17:29","end":"19:11","startHours":17.490154650052585,"endHours":19.190577997862484,"quality":"inauspicious"},{"name":"Śubha","start":"19:11","end":"20:53","startHours":19.190577997862484,"endHours":20.891001345672386,"quality":"auspicious"},{"name":"Roga","start":"20:53","end":"22:35","startHours":20.891001345672386,"endHours":22.59142469348229,"quality":"inauspicious"},{"name":"Udveg","start":"22:35","end":"00:18","startHours":22.59142469348229,"endHours":24.291848041292187,"quality":"inauspicious"},{"name":"Chala","start":"00:18","end":"02:00","startHours":24.291848041292187,"endHours":25.992271389102086,"quality":"neutral"},{"name":"Labha","start":"02:00","end":"03:42","startHours":25.992271389102086,"endHours":27.69269473691199,"quality":"auspicious"},{"name":"Amṛta","start":"03:42","end":"05:24","startHours":27.69269473691199,"endHours":29.39311808472189,"quality":"auspicious"},{"name":"Kāla","start":"05:24","end":"07:06","startHours":29.39311808472189,"endHours":31.09354143253179,"quality":"inauspicious"}],"horas":[{"name":"Hora 1","start":"07:06","end":"08:06","startHours":7.093541432531791,"endHours":8.09354143253179,"planetary_lord":"Mars"},{"name":"Hora 2","start":"08:06","end":"09:06","startHours":8.09354143253179,"endHours":9.09354143253179,"planetary_lord":"Jupiter"},{"name":"Hora 3","start":"09:06","end":"10:06","startHours":9.09354143253179,"endHours":10.09354143253179,"planetary_lord":"Saturn"},{"name":"Hora 4","start":"10:06","end":"11:06","startHours":10.09354143253179,"endHours":11.09354143253179,"planetary_lord":"Moon"},{"name":"Hora 5","start":"11:06","end":"12:06","startHours":11.09354143253179,"endHours":12.09354143253179,"planetary_lord":"Mercury"},{"name":"Hora 6","start":"12:06","end":"13:06","startHours":12.09354143253179,"endHours":13.09354143253179,"planetary_lord":"Venus"},{"name":"Hora 7","start":"13:06","end":"14:06","startHours":13.09354143253179,"endHours":14.09354143253179,"planetary_lord":"Sun"},{"name":"Hora 8","start":"14:06","end":"15:06","startHours":14.09354143253179,"endHours":15.09354143253179,"planetary_lord":"Mars"},{"name":"Hora 9","start":"15:06","end":"16:06","startHours":15.09354143253179,"endHours":16.09354143253179,"planetary_lord":"Jupiter"},{"name":"Hora 10","start":"16:06","end":"17:06","startHours":16.09354143253179,"endHours":17.09354143253179,"planetary_lord":"Saturn"},{"name":"Hora 11","start":"17:06","end":"18:06","startHours":17.09354143253179,"endHours":18.09354143253179,"planetary_lord":"Moon"},{"name":"Hora 12","start":"18:06","end":"19:06","startHours":18.09354143253179,"endHours":19.09354143253179,"planetary_lord":"Mercury"},{"name":"Hora 13","start":"19:06","end":"20:06","startHours":19.09354143253179,"endHours":20.09354143253179,"planetary_lord":"Venus"},{"name":"Hora 14","start":"20:06","end":"21:06","startHours":20.09354143253179,"endHours":21.09354143253179,"planetary_lord":"Sun"},{"name":"Hora 15","start":"21:06","end":"22:06","startHours":21.09354143253179,"endHours":22.09354143253179,"planetary_lord":"Mars"},{"name":"Hora 16","start":"22:06","end":"23:06","startHours":22.09354143253179,"endHours":23.09354143253179,"planetary_lord":"Jupiter"},{"name":"Hora 17","start":"23:06","end":"00:06","startHours":23.09354143253179,"endHours":24.09354143253179,"planetary_lord":"Saturn"},{"name":"Hora 18","start":"00:06","end":"01:06","startHours":24.09354143253179,"endHours":25.09354143253179,"planetary_lord":"Moon"},{"name":"Hora 19","start":"01:06","end":"02:06","startHours":25.09354143253179,"endHours":26.09354143253179,"planetary_lord":"Mercury"},{"name":"Hora 20","start":"02:06","end":"03:06","startHours":26.09354143253179,"endHours":27.09354143253179,"planetary_lord":"Venus"},{"name":"Hora 21","start":"03:06","end":"04:06","startHours":27.09354143253179,"endHours":28.09354143253179,"planetary_lord":"Sun"},{"name":"Hora 22","start":"04:06","end":"05:06","startHours":28.09354143253179,"endHours":29.09354143253179,"planetary_lord":"Mars"},{"name":"Hora 23","start":"05:06","end":"06:06","startHours":29.09354143253179,"endHours":30.09354143253179,"planetary_lord":"Jupiter"},{"name":"Hora 24","start":"06:06","end":"07:06","startHours":30.09354143253179,"endHours":31.09354143253179,"planetary_lord":"Saturn"}],"taraBala":{"favorable_nakshatras":["Bharaṇī","Kṛttikā","Rohiṇī","Mṛgaśirā","Ārdrā","Pūrva Phalgunī","Uttara Phalgunī","Hasta","Citrā","Svātī","Pūrva Āṣāḍhā","Uttara Āṣāḍhā","Śravaṇa","Dhaniṣṭhā","Śatabhiṣaj"],"unfavorable_nakshatras":["Aśvinī","Punarvasu","Puṣya","Aśleṣā","Maghā","Viśākhā","Anurādhā","Jyeṣṭhā","Mūla","Pūrva Bhādrapadā","Uttara Bhādrapadā","Revatī"],"nature":"Janma-tara if same nakshatra; favorable for 15 nakshatras"},"chandraBala":{"favorable_rashis":["Vṛṣabha","Mithuna","Siṃha","Tulā","Makara","Kumbha"],"unfavorable_rashis":["Meṣa","Karka","Kanyā","Vṛścika","Dhanu","Mīna"]},"dishaShool":"North (Uttara)","chandraVasa":"West","rahuVasa":"North","anandadiYoga":{"name":"Kāṇa","quality":"Inauspicious"},"tropicalRitu":"Hemanta (Pre-winter)","vedicRitu":"Hemanta (Pre-winter)","tropicalAyana":"Dakṣiṇāyana","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":-23.430028825343946,"eotMinutes":1.851917522468745,"ayanamsa":26.2134}},"calendars":{"vikram_samvat":2225,"vikram_samvatsara":"Vṛṣa","saka_samvat":2090,"saka_samvatsara":"Vibhava","bengali_samvat":1575,"malayalam_era":1344,"nanakshahi_year":699,"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 Ṣaṣṭhī · Vikram 2225 Vṛṣa · Śaka 2090 Vibhava"},"festivals":[],"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":"vrindavan"},"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, 2168 CE · Vṛndāvana · Vidhyamitra","description":"December 20, 2168 CE for Vṛndāvana: Kṛṣṇa Ṣaṣṭhī, sūryodaya 07:06, sūryāsta 17:29.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/vrindavan/2168-12-20","hreflang_alternates":{"en":"https://vidhyamitra.com/city/vrindavan/2168-12-20","sa":"https://sa.vidhyamitra.com/city/vrindavan/2168-12-20","hi":"https://hi.vidhyamitra.com/city/vrindavan/2168-12-20","x-default":"https://vidhyamitra.com/city/vrindavan/2168-12-20"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-06-01T06:03:18.695Z","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":"2026-06-01T06:03:18.695Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-06-01T06:03:18.695Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"}}}