{"id":"vidhyamitra:city-day:ranchi:2121-01-13:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/ranchi/2121-01-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"2121-01-13","date_display":"January 13, 2121 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":2121,"month":1,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2495751.770833,"kali_year":5222,"ahargana":1907286.2708,"sun":{"sidereal_longitude":266.8156,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":191.1452,"rashi":7,"rashi_name":"Tulā"},"tithi":{"number":24,"name":"Navamī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Navamī","elongation_degrees":284.3296,"elapsed_within_tithi_degrees":8.3296},"nakshatra":{"number":15,"name":"Svātī","pada":2,"moon_longitude":191.1452,"elapsed_within_degrees":4.4786},"yoga":{"number":8,"name":"Dhṛti","sum_longitude":97.9609},"karana":{"half_tithi_index":47,"name":"Gara"},"vara":{"number":3,"name":"Somavāra (Monday)"}},"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":2121,"month":1,"day":13,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2495751.770833,"ahargana":1907286.2708,"kali_year":5222,"ayanamsa_lahiri":25.5437,"grahas":{"sun":{"sidereal_longitude":267.24358699999993,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":1},"retrograde":false},"moon":{"sidereal_longitude":188.630087,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":15,"name":"Svātī","pada":1},"retrograde":false,"latitude":-4.4981},"mars":{"sidereal_longitude":122.142087,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","pada":1},"retrograde":false},"mercury":{"sidereal_longitude":277.46908699999994,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":4},"retrograde":true},"jupiter":{"sidereal_longitude":87.82498700000002,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":7,"name":"Punarvasu","pada":3},"retrograde":true},"venus":{"sidereal_longitude":308.14888700000006,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":24,"name":"Śatabhiṣā","pada":1},"retrograde":false},"saturn":{"sidereal_longitude":62.06208700000002,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":5,"name":"Mr̥gaśirā","pada":3},"retrograde":true},"rahu":{"sidereal_longitude":282.7949,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":22,"name":"Śravaṇa","pada":1},"retrograde":false},"ketu":{"sidereal_longitude":102.7949,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":8,"name":"Puṣya","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":2121,"month":1,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2495751.770833,"kali_year":5222,"ahargana":1907286.2708,"sun":{"sidereal_longitude":266.8156,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":191.1452,"rashi":7,"rashi_name":"Tulā"},"tithi":{"number":24,"name":"Navamī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Navamī","elongation_degrees":284.3296,"elapsed_within_tithi_degrees":8.3296},"nakshatra":{"number":15,"name":"Svātī","pada":2,"moon_longitude":191.1452,"elapsed_within_degrees":4.4786},"yoga":{"number":8,"name":"Dhṛti","sum_longitude":97.9609},"karana":{"half_tithi_index":47,"name":"Gara"},"vara":{"number":3,"name":"Somavāra (Monday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-4.498,"elongation":75.67},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-4.498,"opposition_distance":104.33}},"eclipse_window_40days":[{"offset_days":6,"type":"solar","occurs":true,"moon_latitude":-0.923,"elongation":2.346}]},"city":{"slug":"ranchi","name":"Ranchi, Jharkhand","lat":23.3441,"lon":85.3096,"tz_offset_hours":5.5,"state":"Jharkhand","country":"IN","tier":"tier-1"},"tier2":{"city":{"slug":"ranchi","name":"Ranchi, Jharkhand","lat":23.3441,"lon":85.3096,"tz_offset_hours":5.5,"state":"Jharkhand","country":"IN","tier":"tier-1"},"sunriseLocal":"06:33","sunsetLocal":"17:22","solarNoonLocal":"11:57","dayLengthHours":10.825899416019194,"dayLengthDisplay":"10 Hours 49 Mins 33 Secs","nightLengthDisplay":"13 Hours 10 Mins 27 Secs","moonriseLocal":"01:03","moonsetLocal":"12:23","rahuKala":{"name":"Rāhu Kāla","start":"07:54","end":"09:15","startHours":7.8969132438490295,"endHours":9.25015067085143,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"10:36","end":"11:57","startHours":10.603388097853827,"endHours":11.956625524856227,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"13:19","end":"14:40","startHours":13.309862951858626,"endHours":14.663100378861024,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:04","end":"09:26","startHours":9.069719013917775,"endHours":9.430582327785082,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:00","end":"07:17","startHours":6.994754959180763,"endHours":7.283445610274608,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:36","end":"12:19","startHours":11.595762210988921,"endHours":12.317488838723532,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:06","end":"05:49","startHours":5.100222561377404,"endHours":5.821949189112017,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"05:38","end":"06:33","startHours":5.641517532178364,"endHours":6.54367581684663,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"13:46","end":"14:29","startHours":13.76094209419276,"endHours":14.482668721927373,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:10","end":"17:34","startHours":17.169575232865824,"endHours":17.569575232865823,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:22","end":"17:49","startHours":17.369575232865824,"endHours":17.820654375199958,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:07","end":"18:52","startHours":17.119575232865824,"endHours":18.869575232865824,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:36","end":"00:19","startHours":23.595762210988923,"endHours":24.317488838723534,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Amṛta","start":"06:33","end":"07:54","startHours":6.54367581684663,"endHours":7.8969132438490295,"quality":"auspicious"},{"name":"Kāla","start":"07:54","end":"09:15","startHours":7.8969132438490295,"endHours":9.25015067085143,"quality":"inauspicious"},{"name":"Śubha","start":"09:15","end":"10:36","startHours":9.25015067085143,"endHours":10.603388097853827,"quality":"auspicious"},{"name":"Roga","start":"10:36","end":"11:57","startHours":10.603388097853827,"endHours":11.956625524856227,"quality":"inauspicious"},{"name":"Udveg","start":"11:57","end":"13:19","startHours":11.956625524856227,"endHours":13.309862951858626,"quality":"inauspicious"},{"name":"Chala","start":"13:19","end":"14:40","startHours":13.309862951858626,"endHours":14.663100378861024,"quality":"neutral"},{"name":"Labha","start":"14:40","end":"16:01","startHours":14.663100378861024,"endHours":16.016337805863422,"quality":"auspicious"},{"name":"Amṛta","start":"16:01","end":"17:22","startHours":16.016337805863422,"endHours":17.369575232865824,"quality":"auspicious"}],"nightChoghadiyas":[{"name":"Chala","start":"17:22","end":"19:01","startHours":17.369575232865824,"endHours":19.016337805863426,"quality":"neutral"},{"name":"Labha","start":"19:01","end":"20:40","startHours":19.016337805863426,"endHours":20.663100378861024,"quality":"auspicious"},{"name":"Amṛta","start":"20:40","end":"22:19","startHours":20.663100378861024,"endHours":22.309862951858626,"quality":"auspicious"},{"name":"Kāla","start":"22:19","end":"23:57","startHours":22.309862951858626,"endHours":23.95662552485623,"quality":"inauspicious"},{"name":"Śubha","start":"23:57","end":"01:36","startHours":23.95662552485623,"endHours":25.603388097853827,"quality":"auspicious"},{"name":"Roga","start":"01:36","end":"03:15","startHours":25.603388097853827,"endHours":27.25015067085143,"quality":"inauspicious"},{"name":"Udveg","start":"03:15","end":"04:54","startHours":27.25015067085143,"endHours":28.896913243849028,"quality":"inauspicious"},{"name":"Chala","start":"04:54","end":"06:33","startHours":28.896913243849028,"endHours":30.54367581684663,"quality":"neutral"}],"horas":[{"name":"Hora 1","start":"06:33","end":"07:33","startHours":6.54367581684663,"endHours":7.54367581684663,"planetary_lord":"Moon"},{"name":"Hora 2","start":"07:33","end":"08:33","startHours":7.54367581684663,"endHours":8.54367581684663,"planetary_lord":"Mercury"},{"name":"Hora 3","start":"08:33","end":"09:33","startHours":8.54367581684663,"endHours":9.54367581684663,"planetary_lord":"Venus"},{"name":"Hora 4","start":"09:33","end":"10:33","startHours":9.54367581684663,"endHours":10.54367581684663,"planetary_lord":"Sun"},{"name":"Hora 5","start":"10:33","end":"11:33","startHours":10.54367581684663,"endHours":11.54367581684663,"planetary_lord":"Mars"},{"name":"Hora 6","start":"11:33","end":"12:33","startHours":11.54367581684663,"endHours":12.54367581684663,"planetary_lord":"Jupiter"},{"name":"Hora 7","start":"12:33","end":"13:33","startHours":12.54367581684663,"endHours":13.54367581684663,"planetary_lord":"Saturn"},{"name":"Hora 8","start":"13:33","end":"14:33","startHours":13.54367581684663,"endHours":14.54367581684663,"planetary_lord":"Moon"},{"name":"Hora 9","start":"14:33","end":"15:33","startHours":14.54367581684663,"endHours":15.54367581684663,"planetary_lord":"Mercury"},{"name":"Hora 10","start":"15:33","end":"16:33","startHours":15.54367581684663,"endHours":16.54367581684663,"planetary_lord":"Venus"},{"name":"Hora 11","start":"16:33","end":"17:33","startHours":16.54367581684663,"endHours":17.54367581684663,"planetary_lord":"Sun"},{"name":"Hora 12","start":"17:33","end":"18:33","startHours":17.54367581684663,"endHours":18.54367581684663,"planetary_lord":"Mars"},{"name":"Hora 13","start":"18:33","end":"19:33","startHours":18.54367581684663,"endHours":19.54367581684663,"planetary_lord":"Jupiter"},{"name":"Hora 14","start":"19:33","end":"20:33","startHours":19.54367581684663,"endHours":20.54367581684663,"planetary_lord":"Saturn"},{"name":"Hora 15","start":"20:33","end":"21:33","startHours":20.54367581684663,"endHours":21.54367581684663,"planetary_lord":"Moon"},{"name":"Hora 16","start":"21:33","end":"22:33","startHours":21.54367581684663,"endHours":22.54367581684663,"planetary_lord":"Mercury"},{"name":"Hora 17","start":"22:33","end":"23:33","startHours":22.54367581684663,"endHours":23.54367581684663,"planetary_lord":"Venus"},{"name":"Hora 18","start":"23:33","end":"00:33","startHours":23.54367581684663,"endHours":24.54367581684663,"planetary_lord":"Sun"},{"name":"Hora 19","start":"00:33","end":"01:33","startHours":24.54367581684663,"endHours":25.54367581684663,"planetary_lord":"Mars"},{"name":"Hora 20","start":"01:33","end":"02:33","startHours":25.54367581684663,"endHours":26.54367581684663,"planetary_lord":"Jupiter"},{"name":"Hora 21","start":"02:33","end":"03:33","startHours":26.54367581684663,"endHours":27.54367581684663,"planetary_lord":"Saturn"},{"name":"Hora 22","start":"03:33","end":"04:33","startHours":27.54367581684663,"endHours":28.54367581684663,"planetary_lord":"Moon"},{"name":"Hora 23","start":"04:33","end":"05:33","startHours":28.54367581684663,"endHours":29.54367581684663,"planetary_lord":"Mercury"},{"name":"Hora 24","start":"05:33","end":"06:33","startHours":29.54367581684663,"endHours":30.54367581684663,"planetary_lord":"Venus"}],"taraBala":{"favorable_nakshatras":["Aśvinī","Bharaṇī","Punarvasu","Puṣya","Aśleṣā","Maghā","Pūrva Phalgunī","Viśākhā","Anurādhā","Jyeṣṭhā","Mūla","Pūrva Āṣāḍhā","Pūrva Bhādrapadā","Uttara Bhādrapadā","Revatī"],"unfavorable_nakshatras":["Kṛttikā","Rohiṇī","Mṛgaśirā","Ārdrā","Uttara Phalgunī","Hasta","Citrā","Svātī","Uttara Āṣāḍhā","Śravaṇa","Dhaniṣṭhā","Śatabhiṣaj"],"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":"East (Pūrva)","chandraVasa":"North","rahuVasa":"North-East","anandadiYoga":{"name":"Siddhi","quality":"Auspicious"},"tropicalRitu":"Hemanta (Pre-winter) (tropical)","vedicRitu":"Hemanta (Pre-winter)","tropicalAyana":"Uttarāyaṇa","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":-21.511569184407577,"eotMinutes":-8.635931491373626,"ayanamsa":25.5437}},"calendars":{"vikram_samvat":2178,"vikram_samvatsara":"Jaya","saka_samvat":2043,"saka_samvatsara":"Vṛṣa","bengali_samvat":1528,"malayalam_era":1297,"nanakshahi_year":652,"lunar_month":"Māgha","lunar_month_paksha_full":"Māgha Kṛṣṇa Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Māgha","lunar_month_amanta":"Pauṣa","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Dhanus (Mārgaḻi)","ritu":"Śiśira (Winter)","display_summary":"Māgha Kṛṣṇa Navamī · Vikram 2178 Jaya · Śaka 2043 Vṛṣa"},"festivals":[],"todays_walk":{"walk":{"id":"chandra-walk","name":"Candra Walk","name_sanskrit":"चन्द्र यात्रा","type":"graha","description":"Manas-control + BG 6.5-7.","step_count":5,"url":"/walk/chandra-walk"},"reason":"Somavāra (Monday) — its presiding graha's walk."},"cosmic_resonances":[]},"validity":{"eternal":false,"location_specific":"ranchi"},"liturgical":{"opening":"जय श्री कृष्ण","closing":"ॐ तत् सत्","attribution":"Computed by Vidhyamitra Sūrya-Siddhānta substrate + Vidhyamitra Tier-2 layer"},"seo":{"title":"Pañchāṅga January 13, 2121 CE · Ranchi, Jharkhand · Vidhyamitra","description":"January 13, 2121 CE for Ranchi, Jharkhand: Kṛṣṇa Navamī, sūryodaya 06:33, sūryāsta 17:22.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/ranchi/2121-01-13","hreflang_alternates":{"en":"https://vidhyamitra.com/city/ranchi/2121-01-13","sa":"https://sa.vidhyamitra.com/city/ranchi/2121-01-13","hi":"https://hi.vidhyamitra.com/city/ranchi/2121-01-13","x-default":"https://vidhyamitra.com/city/ranchi/2121-01-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-06-01T02:45:02.787Z","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":"2026-06-01T02:45:02.787Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-06-01T02:45:02.787Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"}}}