{"id":"vidhyamitra:city-day:phoenix:2021-07-13:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/phoenix/2021-07-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"2021-07-13","date_display":"July 13, 2021 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":2021,"month":7,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2459408.770833,"kali_year":5123,"ahargana":1870943.2708,"sun":{"sidereal_longitude":86.2724,"rashi":3,"rashi_name":"Mithuna"},"moon":{"sidereal_longitude":122.7085,"rashi":5,"rashi_name":"Siṃha"},"tithi":{"number":4,"name":"Caturthī","paksha":"Śukla","full_name":"Śukla Caturthī","elongation_degrees":36.4361,"elapsed_within_tithi_degrees":0.4361},"nakshatra":{"number":10,"name":"Maghā","pada":1,"moon_longitude":122.7085,"elapsed_within_degrees":2.7085},"yoga":{"number":16,"name":"Siddhi","sum_longitude":208.9809},"karana":{"half_tithi_index":6,"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":2021,"month":7,"day":13,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2459408.770833,"ahargana":1870943.2708,"kali_year":5123,"ayanamsa_lahiri":24.1538,"grahas":{"sun":{"sidereal_longitude":86.739756,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":7,"name":"Punarvasu","pada":3},"retrograde":false},"moon":{"sidereal_longitude":121.76975600000003,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","pada":1},"retrograde":false,"latitude":4.3315},"mars":{"sidereal_longitude":115.02205600000002,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":9,"name":"Aśleṣā","pada":3},"retrograde":false},"mercury":{"sidereal_longitude":67.15795600000001,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":6,"name":"Ārdrā","pada":1},"retrograde":false},"jupiter":{"sidereal_longitude":307.202356,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":24,"name":"Śatabhiṣā","pada":1},"retrograde":true},"venus":{"sidereal_longitude":114.737956,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":9,"name":"Aśleṣā","pada":3},"retrograde":false},"saturn":{"sidereal_longitude":287.50565600000004,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":22,"name":"Śravaṇa","pada":3},"retrograde":true},"rahu":{"sidereal_longitude":48.4219,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":4,"name":"Rohiṇī","pada":3},"retrograde":false},"ketu":{"sidereal_longitude":228.4219,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","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":2021,"month":7,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2459408.770833,"kali_year":5123,"ahargana":1870943.2708,"sun":{"sidereal_longitude":86.2724,"rashi":3,"rashi_name":"Mithuna"},"moon":{"sidereal_longitude":122.7085,"rashi":5,"rashi_name":"Siṃha"},"tithi":{"number":4,"name":"Caturthī","paksha":"Śukla","full_name":"Śukla Caturthī","elongation_degrees":36.4361,"elapsed_within_tithi_degrees":0.4361},"nakshatra":{"number":10,"name":"Maghā","pada":1,"moon_longitude":122.7085,"elapsed_within_degrees":2.7085},"yoga":{"number":16,"name":"Siddhi","sum_longitude":208.9809},"karana":{"half_tithi_index":6,"name":"Vaṇija"},"vara":{"number":4,"name":"Maṅgalavāra (Tuesday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":4.332,"elongation":36.436},"lunar":{"type":"lunar","occurs":false,"moon_latitude":4.332,"opposition_distance":143.564}},"eclipse_window_40days":[]},"city":{"slug":"phoenix","name":"Phoenix, USA","lat":33.4484,"lon":-112.074,"tz_offset_hours":-7,"country":"US","tier":"diaspora"},"tier2":{"city":{"slug":"phoenix","name":"Phoenix, USA","lat":33.4484,"lon":-112.074,"tz_offset_hours":-7,"country":"US","tier":"diaspora"},"sunriseLocal":"05:28","sunsetLocal":"19:39","solarNoonLocal":"12:34","dayLengthHours":14.193183873329737,"dayLengthDisplay":"14 Hours 11 Mins 35 Secs","nightLengthDisplay":"9 Hours 48 Mins 25 Secs","moonriseLocal":"08:16","moonsetLocal":"21:31","rahuKala":{"name":"Rāhu Kāla","start":"16:07","end":"17:53","startHours":16.109253115768443,"endHours":17.883401099934662,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"09:01","end":"10:47","startHours":9.012661179103574,"endHours":10.786809163269792,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"12:34","end":"14:20","startHours":12.56095714743601,"endHours":14.335105131602226,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"08:47","end":"09:15","startHours":8.77610811454808,"endHours":9.24921424365907,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:03","end":"06:26","startHours":6.05574787215988,"endHours":6.434232775448673,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"12:05","end":"13:02","startHours":12.087851018325019,"endHours":13.034063276547002,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"03:34","end":"04:31","startHours":3.571940694327176,"endHours":4.518152952549158,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"04:17","end":"05:28","startHours":4.2815998879936625,"endHours":5.464365210771141,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:56","end":"15:52","startHours":14.926487792990965,"endHours":15.872700051212947,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"19:27","end":"19:51","startHours":19.45754908410088,"endHours":19.857549084100878,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"19:39","end":"20:15","startHours":19.65754908410088,"endHours":20.248931745489617,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"19:24","end":"21:09","startHours":19.40754908410088,"endHours":21.15754908410088,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"00:05","end":"01:02","startHours":24.08785101832502,"endHours":25.034063276547002,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Roga","start":"05:28","end":"07:14","startHours":5.464365210771141,"endHours":7.238513194937358,"quality":"inauspicious"},{"name":"Udveg","start":"07:14","end":"09:01","startHours":7.238513194937358,"endHours":9.012661179103574,"quality":"inauspicious"},{"name":"Chala","start":"09:01","end":"10:47","startHours":9.012661179103574,"endHours":10.786809163269792,"quality":"neutral"},{"name":"Labha","start":"10:47","end":"12:34","startHours":10.786809163269792,"endHours":12.56095714743601,"quality":"auspicious"},{"name":"Amṛta","start":"12:34","end":"14:20","startHours":12.56095714743601,"endHours":14.335105131602226,"quality":"auspicious"},{"name":"Kāla","start":"14:20","end":"16:07","startHours":14.335105131602226,"endHours":16.109253115768443,"quality":"inauspicious"},{"name":"Śubha","start":"16:07","end":"17:53","startHours":16.109253115768443,"endHours":17.883401099934662,"quality":"auspicious"},{"name":"Roga","start":"17:53","end":"19:39","startHours":17.883401099934662,"endHours":19.65754908410088,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Kāla","start":"19:39","end":"20:53","startHours":19.65754908410088,"endHours":20.883401099934662,"quality":"inauspicious"},{"name":"Śubha","start":"20:53","end":"22:07","startHours":20.883401099934662,"endHours":22.109253115768446,"quality":"auspicious"},{"name":"Roga","start":"22:07","end":"23:20","startHours":22.109253115768446,"endHours":23.335105131602226,"quality":"inauspicious"},{"name":"Udveg","start":"23:20","end":"00:34","startHours":23.335105131602226,"endHours":24.56095714743601,"quality":"inauspicious"},{"name":"Chala","start":"00:34","end":"01:47","startHours":24.56095714743601,"endHours":25.786809163269794,"quality":"neutral"},{"name":"Labha","start":"01:47","end":"03:01","startHours":25.786809163269794,"endHours":27.012661179103574,"quality":"auspicious"},{"name":"Amṛta","start":"03:01","end":"04:14","startHours":27.012661179103574,"endHours":28.238513194937358,"quality":"auspicious"},{"name":"Kāla","start":"04:14","end":"05:28","startHours":28.238513194937358,"endHours":29.464365210771142,"quality":"inauspicious"}],"horas":[{"name":"Hora 1","start":"05:28","end":"06:28","startHours":5.464365210771141,"endHours":6.464365210771141,"planetary_lord":"Mars"},{"name":"Hora 2","start":"06:28","end":"07:28","startHours":6.464365210771141,"endHours":7.464365210771141,"planetary_lord":"Jupiter"},{"name":"Hora 3","start":"07:28","end":"08:28","startHours":7.464365210771141,"endHours":8.464365210771142,"planetary_lord":"Saturn"},{"name":"Hora 4","start":"08:28","end":"09:28","startHours":8.464365210771142,"endHours":9.464365210771142,"planetary_lord":"Moon"},{"name":"Hora 5","start":"09:28","end":"10:28","startHours":9.464365210771142,"endHours":10.464365210771142,"planetary_lord":"Mercury"},{"name":"Hora 6","start":"10:28","end":"11:28","startHours":10.464365210771142,"endHours":11.464365210771142,"planetary_lord":"Venus"},{"name":"Hora 7","start":"11:28","end":"12:28","startHours":11.464365210771142,"endHours":12.464365210771142,"planetary_lord":"Sun"},{"name":"Hora 8","start":"12:28","end":"13:28","startHours":12.464365210771142,"endHours":13.464365210771142,"planetary_lord":"Mars"},{"name":"Hora 9","start":"13:28","end":"14:28","startHours":13.464365210771142,"endHours":14.464365210771142,"planetary_lord":"Jupiter"},{"name":"Hora 10","start":"14:28","end":"15:28","startHours":14.464365210771142,"endHours":15.464365210771142,"planetary_lord":"Saturn"},{"name":"Hora 11","start":"15:28","end":"16:28","startHours":15.464365210771142,"endHours":16.464365210771142,"planetary_lord":"Moon"},{"name":"Hora 12","start":"16:28","end":"17:28","startHours":16.464365210771142,"endHours":17.464365210771142,"planetary_lord":"Mercury"},{"name":"Hora 13","start":"17:28","end":"18:28","startHours":17.464365210771142,"endHours":18.464365210771142,"planetary_lord":"Venus"},{"name":"Hora 14","start":"18:28","end":"19:28","startHours":18.464365210771142,"endHours":19.464365210771142,"planetary_lord":"Sun"},{"name":"Hora 15","start":"19:28","end":"20:28","startHours":19.464365210771142,"endHours":20.464365210771142,"planetary_lord":"Mars"},{"name":"Hora 16","start":"20:28","end":"21:28","startHours":20.464365210771142,"endHours":21.464365210771142,"planetary_lord":"Jupiter"},{"name":"Hora 17","start":"21:28","end":"22:28","startHours":21.464365210771142,"endHours":22.464365210771142,"planetary_lord":"Saturn"},{"name":"Hora 18","start":"22:28","end":"23:28","startHours":22.464365210771142,"endHours":23.464365210771142,"planetary_lord":"Moon"},{"name":"Hora 19","start":"23:28","end":"00:28","startHours":23.464365210771142,"endHours":24.464365210771142,"planetary_lord":"Mercury"},{"name":"Hora 20","start":"00:28","end":"01:28","startHours":24.464365210771142,"endHours":25.464365210771142,"planetary_lord":"Venus"},{"name":"Hora 21","start":"01:28","end":"02:28","startHours":25.464365210771142,"endHours":26.464365210771142,"planetary_lord":"Sun"},{"name":"Hora 22","start":"02:28","end":"03:28","startHours":26.464365210771142,"endHours":27.464365210771142,"planetary_lord":"Mars"},{"name":"Hora 23","start":"03:28","end":"04:28","startHours":27.464365210771142,"endHours":28.464365210771142,"planetary_lord":"Jupiter"},{"name":"Hora 24","start":"04:28","end":"05:28","startHours":28.464365210771142,"endHours":29.464365210771142,"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"},"drikRitu":"Grīṣma (Summer) (Drik)","vedicRitu":"Grīṣma (Summer)","drikAyana":"Dakṣiṇāyana","vedicAyana":"Uttarāyaṇa","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization (Drikpanchang-parity)","declination":21.81305600736251,"eotMinutes":-5.361428846160681,"ayanamsa":24.1538}},"calendars":{"vikram_samvat":2078,"vikram_samvatsara":"Ānanda","saka_samvat":1943,"saka_samvatsara":"Plava","bengali_samvat":1428,"malayalam_era":1197,"nanakshahi_year":552,"lunar_month":"Āṣāḍha","lunar_month_paksha_full":"Āṣāḍha Śukla Pakṣa","solar_month":"Mithuna (Āni)","ritu":"Grīṣma (Summer)","display_summary":"Āṣāḍha Śukla Caturthī · Vikram 2078 Ānanda · Śaka 1943 Plava"},"festivals":[{"id":"angarika-chaturthi","name":"Aṅgāraka Caturthī (Tuesday Caturthī)","name_sanskrit":"अङ्गारक चतुर्थी","tradition":"Pan-Hindu","associated_deity":"Gaṇeśa + Maṅgala","significance":"Tuesday-Caturthī (rare); supremely auspicious for Maṅgala-doṣa-nivāraṇa.","vrata":true,"detection":{"any_of":[{"tithi_number":4,"vara_name":"Maṅgalavāra (Tuesday)"},{"tithi_number":19,"vara_name":"Maṅgalavāra (Tuesday)"}]},"precedence":3},{"id":"mithuna-sankranti","name":"Mithuna Saṅkrānti","name_sanskrit":"मिथुन सङ्क्रान्ति","tradition":"Pan-Hindu","significance":"Sun enters Gemini.","vrata":false,"detection":{"sun_rashi":"Mithuna"},"precedence":5},{"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":"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":"phoenix"},"liturgical":{"opening":"जय श्री कृष्ण","closing":"ॐ तत् सत्","attribution":"Computed by Vidhyamitra Sūrya-Siddhānta substrate + Vidhyamitra Tier-2 layer"},"seo":{"title":"Pañchāṅga July 13, 2021 CE · Phoenix, USA · Vidhyamitra","description":"July 13, 2021 CE for Phoenix, USA: Śukla Caturthī, sūryodaya 05:28, sūryāsta 19:39.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/phoenix/2021-07-13","hreflang_alternates":{"en":"https://vidhyamitra.com/city/phoenix/2021-07-13","sa":"https://sa.vidhyamitra.com/city/phoenix/2021-07-13","hi":"https://hi.vidhyamitra.com/city/phoenix/2021-07-13","x-default":"https://vidhyamitra.com/city/phoenix/2021-07-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-05-14T23:54:40.759Z","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":"2026-05-14T23:54:40.759Z","verification":{"type":"community-validated","markers":["matches Drikpanchang ±1 minute on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-05-14T23:54:40.759Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"}}}