{"id":"vidhyamitra:city-day:rishikesh:2045-06-13:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/rishikesh/2045-06-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"2045-06-13","date_display":"June 13, 2045 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":2045,"month":6,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2468144.770833,"kali_year":5147,"ahargana":1879679.2708,"sun":{"sidereal_longitude":57.6638,"rashi":2,"rashi_name":"Vṛṣabha"},"moon":{"sidereal_longitude":29.6501,"rashi":1,"rashi_name":"Meṣa"},"tithi":{"number":28,"name":"Trayodaśī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Trayodaśī","elongation_degrees":331.9863,"elapsed_within_tithi_degrees":7.9863},"nakshatra":{"number":3,"name":"Kṛttikā","pada":1,"moon_longitude":29.6501,"elapsed_within_degrees":2.9834},"yoga":{"number":7,"name":"Sukarma","sum_longitude":87.3139},"karana":{"half_tithi_index":55,"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":2045,"month":6,"day":13,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2468144.770833,"ahargana":1879679.2708,"kali_year":5147,"ayanamsa_lahiri":24.4879,"grahas":{"sun":{"sidereal_longitude":57.978076999999985,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":5,"name":"Mr̥gaśirā","pada":2},"retrograde":false},"moon":{"sidereal_longitude":30.094476999999983,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":3,"name":"Kṛttikā","pada":2},"retrograde":false,"latitude":4.4761},"mars":{"sidereal_longitude":47.152176999999995,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":4,"name":"Rohiṇī","pada":3},"retrograde":false},"mercury":{"sidereal_longitude":76.61877700000002,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":6,"name":"Ārdrā","pada":3},"retrograde":false},"jupiter":{"sidereal_longitude":317.426477,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":24,"name":"Śatabhiṣā","pada":4},"retrograde":false},"venus":{"sidereal_longitude":79.664377,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":6,"name":"Ārdrā","pada":4},"retrograde":false},"saturn":{"sidereal_longitude":222.02987699999994,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":17,"name":"Anurādhā","pada":3},"retrograde":true},"rahu":{"sidereal_longitude":305.5466,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":4},"retrograde":false},"ketu":{"sidereal_longitude":125.5466,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","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":"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":2045,"month":6,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2468144.770833,"kali_year":5147,"ahargana":1879679.2708,"sun":{"sidereal_longitude":57.6638,"rashi":2,"rashi_name":"Vṛṣabha"},"moon":{"sidereal_longitude":29.6501,"rashi":1,"rashi_name":"Meṣa"},"tithi":{"number":28,"name":"Trayodaśī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Trayodaśī","elongation_degrees":331.9863,"elapsed_within_tithi_degrees":7.9863},"nakshatra":{"number":3,"name":"Kṛttikā","pada":1,"moon_longitude":29.6501,"elapsed_within_degrees":2.9834},"yoga":{"number":7,"name":"Sukarma","sum_longitude":87.3139},"karana":{"half_tithi_index":55,"name":"Vaṇija"},"vara":{"number":4,"name":"Maṅgalavāra (Tuesday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":4.476,"elongation":28.014},"lunar":{"type":"lunar","occurs":false,"moon_latitude":4.476,"opposition_distance":151.986}},"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":"05:15","sunsetLocal":"19:19","solarNoonLocal":"12:17","dayLengthHours":14.063744023167832,"dayLengthDisplay":"14 Hours 03 Mins 49 Secs","nightLengthDisplay":"9 Hours 56 Mins 11 Secs","moonriseLocal":"03:36","moonsetLocal":"17:14","rahuKala":{"name":"Rāhu Kāla","start":"15:48","end":"17:33","startHours":15.79450967914861,"endHours":17.55247768204459,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"08:46","end":"10:31","startHours":8.762637667564693,"endHours":10.520605670460672,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"12:17","end":"14:02","startHours":12.27857367335665,"endHours":14.036541676252629,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"08:32","end":"09:00","startHours":8.52824193384523,"endHours":8.997033401284156,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"05:50","end":"06:12","startHours":5.832690996071395,"endHours":6.207724170022537,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:49","end":"12:45","startHours":11.809782205917724,"endHours":12.74736514079558,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"03:22","end":"04:19","startHours":3.371535792017024,"endHours":4.30911872689488,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"04:04","end":"05:15","startHours":4.074722993175415,"endHours":5.246701661772735,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:37","end":"15:34","startHours":14.622531010551292,"endHours":15.560113945429148,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"19:07","end":"19:31","startHours":19.11044568494057,"endHours":19.510445684940567,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"19:19","end":"19:54","startHours":19.310445684940568,"endHours":19.896435019239227,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"19:04","end":"20:49","startHours":19.060445684940568,"endHours":20.810445684940568,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:49","end":"00:45","startHours":23.809782205917728,"endHours":24.74736514079558,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Roga","start":"05:15","end":"07:00","startHours":5.246701661772735,"endHours":7.0046696646687145,"quality":"inauspicious"},{"name":"Udveg","start":"07:00","end":"08:46","startHours":7.0046696646687145,"endHours":8.762637667564693,"quality":"inauspicious"},{"name":"Chala","start":"08:46","end":"10:31","startHours":8.762637667564693,"endHours":10.520605670460672,"quality":"neutral"},{"name":"Labha","start":"10:31","end":"12:17","startHours":10.520605670460672,"endHours":12.27857367335665,"quality":"auspicious"},{"name":"Amṛta","start":"12:17","end":"14:02","startHours":12.27857367335665,"endHours":14.036541676252629,"quality":"auspicious"},{"name":"Kāla","start":"14:02","end":"15:48","startHours":14.036541676252629,"endHours":15.79450967914861,"quality":"inauspicious"},{"name":"Śubha","start":"15:48","end":"17:33","startHours":15.79450967914861,"endHours":17.55247768204459,"quality":"auspicious"},{"name":"Roga","start":"17:33","end":"19:19","startHours":17.55247768204459,"endHours":19.310445684940568,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Kāla","start":"19:19","end":"20:33","startHours":19.310445684940568,"endHours":20.55247768204459,"quality":"inauspicious"},{"name":"Śubha","start":"20:33","end":"21:48","startHours":20.55247768204459,"endHours":21.79450967914861,"quality":"auspicious"},{"name":"Roga","start":"21:48","end":"23:02","startHours":21.79450967914861,"endHours":23.036541676252632,"quality":"inauspicious"},{"name":"Udveg","start":"23:02","end":"00:17","startHours":23.036541676252632,"endHours":24.278573673356654,"quality":"inauspicious"},{"name":"Chala","start":"00:17","end":"01:31","startHours":24.278573673356654,"endHours":25.520605670460675,"quality":"neutral"},{"name":"Labha","start":"01:31","end":"02:46","startHours":25.520605670460675,"endHours":26.762637667564693,"quality":"auspicious"},{"name":"Amṛta","start":"02:46","end":"04:00","startHours":26.762637667564693,"endHours":28.004669664668715,"quality":"auspicious"},{"name":"Kāla","start":"04:00","end":"05:15","startHours":28.004669664668715,"endHours":29.246701661772736,"quality":"inauspicious"}],"horas":[{"name":"Hora 1","start":"05:15","end":"06:15","startHours":5.246701661772735,"endHours":6.246701661772735,"planetary_lord":"Mars"},{"name":"Hora 2","start":"06:15","end":"07:15","startHours":6.246701661772735,"endHours":7.246701661772735,"planetary_lord":"Jupiter"},{"name":"Hora 3","start":"07:15","end":"08:15","startHours":7.246701661772735,"endHours":8.246701661772736,"planetary_lord":"Saturn"},{"name":"Hora 4","start":"08:15","end":"09:15","startHours":8.246701661772736,"endHours":9.246701661772736,"planetary_lord":"Moon"},{"name":"Hora 5","start":"09:15","end":"10:15","startHours":9.246701661772736,"endHours":10.246701661772736,"planetary_lord":"Mercury"},{"name":"Hora 6","start":"10:15","end":"11:15","startHours":10.246701661772736,"endHours":11.246701661772736,"planetary_lord":"Venus"},{"name":"Hora 7","start":"11:15","end":"12:15","startHours":11.246701661772736,"endHours":12.246701661772736,"planetary_lord":"Sun"},{"name":"Hora 8","start":"12:15","end":"13:15","startHours":12.246701661772736,"endHours":13.246701661772736,"planetary_lord":"Mars"},{"name":"Hora 9","start":"13:15","end":"14:15","startHours":13.246701661772736,"endHours":14.246701661772736,"planetary_lord":"Jupiter"},{"name":"Hora 10","start":"14:15","end":"15:15","startHours":14.246701661772736,"endHours":15.246701661772736,"planetary_lord":"Saturn"},{"name":"Hora 11","start":"15:15","end":"16:15","startHours":15.246701661772736,"endHours":16.246701661772736,"planetary_lord":"Moon"},{"name":"Hora 12","start":"16:15","end":"17:15","startHours":16.246701661772736,"endHours":17.246701661772736,"planetary_lord":"Mercury"},{"name":"Hora 13","start":"17:15","end":"18:15","startHours":17.246701661772736,"endHours":18.246701661772736,"planetary_lord":"Venus"},{"name":"Hora 14","start":"18:15","end":"19:15","startHours":18.246701661772736,"endHours":19.246701661772736,"planetary_lord":"Sun"},{"name":"Hora 15","start":"19:15","end":"20:15","startHours":19.246701661772736,"endHours":20.246701661772736,"planetary_lord":"Mars"},{"name":"Hora 16","start":"20:15","end":"21:15","startHours":20.246701661772736,"endHours":21.246701661772736,"planetary_lord":"Jupiter"},{"name":"Hora 17","start":"21:15","end":"22:15","startHours":21.246701661772736,"endHours":22.246701661772736,"planetary_lord":"Saturn"},{"name":"Hora 18","start":"22:15","end":"23:15","startHours":22.246701661772736,"endHours":23.246701661772736,"planetary_lord":"Moon"},{"name":"Hora 19","start":"23:15","end":"00:15","startHours":23.246701661772736,"endHours":24.246701661772736,"planetary_lord":"Mercury"},{"name":"Hora 20","start":"00:15","end":"01:15","startHours":24.246701661772736,"endHours":25.246701661772736,"planetary_lord":"Venus"},{"name":"Hora 21","start":"01:15","end":"02:15","startHours":25.246701661772736,"endHours":26.246701661772736,"planetary_lord":"Sun"},{"name":"Hora 22","start":"02:15","end":"03:15","startHours":26.246701661772736,"endHours":27.246701661772736,"planetary_lord":"Mars"},{"name":"Hora 23","start":"03:15","end":"04:15","startHours":27.246701661772736,"endHours":28.246701661772736,"planetary_lord":"Jupiter"},{"name":"Hora 24","start":"04:15","end":"05:15","startHours":28.246701661772736,"endHours":29.246701661772736,"planetary_lord":"Saturn"}],"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":["Vṛṣabha","Karka","Tulā","Vṛścika","Kumbha","Mīna"],"unfavorable_rashis":["Meṣa","Mithuna","Siṃha","Kanyā","Dhanu","Makara"]},"dishaShool":"North (Uttara)","chandraVasa":"South-East","rahuVasa":"North","anandadiYoga":{"name":"Chatra","quality":"Auspicious"},"drikRitu":"Grīṣma (Summer) (Drik)","vedicRitu":"Vasanta (Spring)","drikAyana":"Uttarāyaṇa","vedicAyana":"Uttarāyaṇa","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization (Drikpanchang-parity)","declination":23.222255909268785,"eotMinutes":0.2151795986009022,"ayanamsa":24.4879}},"calendars":{"vikram_samvat":2102,"vikram_samvatsara":"Bahudhānya","saka_samvat":1967,"saka_samvatsara":"Krodhana","bengali_samvat":1452,"malayalam_era":1221,"nanakshahi_year":576,"lunar_month":"Jyeṣṭha","lunar_month_paksha_full":"Jyeṣṭha Kṛṣṇa Pakṣa","solar_month":"Vṛṣabha (Vaikāsi)","ritu":"Grīṣma (Summer)","display_summary":"Jyeṣṭha Kṛṣṇa Trayodaśī · Vikram 2102 Bahudhānya · Śaka 1967 Krodhana"},"festivals":[{"id":"vrishabha-sankranti","name":"Vṛṣabha Saṅkrānti","name_sanskrit":"वृषभ सङ्क्रान्ति","tradition":"Pan-Hindu","significance":"Sun enters Taurus.","vrata":false,"detection":{"sun_rashi":"Vṛṣabha"},"precedence":5},{"id":"pradosha-vrata","name":"Pradoṣa Vrata","name_sanskrit":"प्रदोष व्रत","tradition":"Shaiva","associated_deity":"Śiva","significance":"Twilight worship of Śiva on Trayodaśī.","vrata":true,"detection":{"any_of":[{"tithi_number":13},{"tithi_number":28}]},"precedence":7}],"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":[{"historical_date":"-3137-10-04","event":"Mahābhārata Day 1 (Bhagavad Gītā delivered)","chart_id":"krishna","shared_marker":"same Kṛttikā","url":"/day/-3137-10-04","relevance":0.5},{"historical_date":"-3137-12-25","event":"Bhīṣma's Mahaprasthan","chart_id":"bhishma","shared_marker":"same Kṛttikā","url":"/day/-3137-12-25","relevance":0.5}]},"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 June 13, 2045 CE · Ṛṣikeśa · Vidhyamitra","description":"June 13, 2045 CE for Ṛṣikeśa: Kṛṣṇa Trayodaśī, sūryodaya 05:15, sūryāsta 19:19.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/rishikesh/2045-06-13","hreflang_alternates":{"en":"https://vidhyamitra.com/city/rishikesh/2045-06-13","sa":"https://sa.vidhyamitra.com/city/rishikesh/2045-06-13","hi":"https://hi.vidhyamitra.com/city/rishikesh/2045-06-13","x-default":"https://vidhyamitra.com/city/rishikesh/2045-06-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-05-16T11:11:11.159Z","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":"2026-05-16T11:11:11.159Z","verification":{"type":"community-validated","markers":["matches Drikpanchang ±1 minute on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-05-16T11:11:11.159Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"}}}