{"id":"vidhyamitra:city-day:mathura:-3180-01-13:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3180-01-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3180-01-13","date_display":"January 13, 3181 BCE","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":-3180,"month":1,"day":13,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":559574.770833,"kali_year":-79,"ahargana":-28890.7292,"sun":{"sidereal_longitude":327.4541,"rashi":11,"rashi_name":"Kumbha"},"moon":{"sidereal_longitude":201.652,"rashi":7,"rashi_name":"Tulā"},"tithi":{"number":20,"name":"Pañcamī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Pañcamī","elongation_degrees":234.1979,"elapsed_within_tithi_degrees":6.1979},"nakshatra":{"number":16,"name":"Viśākhā","pada":1,"moon_longitude":201.652,"elapsed_within_degrees":1.652},"yoga":{"number":13,"name":"Vyāghāta","sum_longitude":169.106},"karana":{"half_tithi_index":39,"name":"Taitila"},"vara":{"number":5,"name":"Budhavāra (Wednesday)"}},"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":-3180,"month":1,"day":13,"hour":6,"minute":30,"calendar":"julian"},"julian_day":559574.770833,"ahargana":-28890.7292,"kali_year":-79,"ayanamsa_lahiri":-48.5078,"grahas":{"sun":{"sidereal_longitude":327.4541,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":25,"name":"Pūrva Bhādrapadā","pada":3},"retrograde":false},"moon":{"sidereal_longitude":201.652,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":16,"name":"Viśākhā","pada":1},"retrograde":false,"latitude":-4.2039},"mars":{"sidereal_longitude":337.9995,"rashi":{"number":12,"name":"Mīna"},"nakshatra":{"number":26,"name":"Uttara Bhādrapadā","pada":2},"retrograde":false},"mercury":{"sidereal_longitude":298.8105,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":2},"retrograde":false},"jupiter":{"sidereal_longitude":117.1333,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":9,"name":"Āśleṣā","pada":4},"retrograde":true},"venus":{"sidereal_longitude":311.9177,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":24,"name":"Śatabhiṣā","pada":2},"retrograde":true},"saturn":{"sidereal_longitude":118.4794,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":9,"name":"Āśleṣā","pada":4},"retrograde":true},"rahu":{"sidereal_longitude":270.7699,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":2},"retrograde":false},"ketu":{"sidereal_longitude":90.7699,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":7,"name":"Punarvasu","pada":4},"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":-3180,"month":1,"day":13,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":559574.770833,"kali_year":-79,"ahargana":-28890.7292,"sun":{"sidereal_longitude":327.4541,"rashi":11,"rashi_name":"Kumbha"},"moon":{"sidereal_longitude":201.652,"rashi":7,"rashi_name":"Tulā"},"tithi":{"number":20,"name":"Pañcamī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Pañcamī","elongation_degrees":234.1979,"elapsed_within_tithi_degrees":6.1979},"nakshatra":{"number":16,"name":"Viśākhā","pada":1,"moon_longitude":201.652,"elapsed_within_degrees":1.652},"yoga":{"number":13,"name":"Vyāghāta","sum_longitude":169.106},"karana":{"half_tithi_index":39,"name":"Taitila"},"vara":{"number":5,"name":"Budhavāra (Wednesday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-4.204,"elongation":125.802},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-4.204,"opposition_distance":54.198}},"eclipse_window_40days":[]},"city":{"slug":"mathura","name":"Mathurā","lat":27.4924,"lon":77.6737,"tz_offset_hours":5.5,"state":"Uttar Pradesh","country":"IN","tier":"tirtha"},"tier2":{"city":{"slug":"mathura","name":"Mathurā","lat":27.4924,"lon":77.6737,"tz_offset_hours":5.5,"state":"Uttar Pradesh","country":"IN","tier":"tirtha"},"sunriseLocal":"07:15","sunsetLocal":"17:41","solarNoonLocal":"12:28","dayLengthHours":10.426486217961356,"dayLengthDisplay":"10 Hours 25 Mins 35 Secs","nightLengthDisplay":"13 Hours 34 Mins 25 Secs","moonriseLocal":"21:40","moonsetLocal":"10:29","rahuKala":{"name":"Rāhu Kāla","start":"12:28","end":"13:46","startHours":12.465685524856227,"endHours":13.768996302101396,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"08:33","end":"09:52","startHours":8.555753193120717,"endHours":9.859063970365886,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"11:10","end":"12:28","startHours":11.162374747611057,"endHours":12.465685524856227,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:41","end":"10:02","startHours":9.685289200066531,"endHours":10.032838740665243,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:41","end":"07:58","startHours":7.686879341623937,"endHours":7.964918974102907,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"12:07","end":"12:49","startHours":12.118135984257515,"endHours":12.813235065454938,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:52","end":"06:33","startHours":5.8622442534807,"endHours":6.557343334678124,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"06:23","end":"07:15","startHours":6.383568564378768,"endHours":7.252442415875548,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:12","end":"14:54","startHours":14.203433227849786,"endHours":14.898532309047209,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:29","end":"17:53","startHours":17.478928633836905,"endHours":17.878928633836903,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:41","end":"18:07","startHours":17.678928633836904,"endHours":18.113365559585294,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:26","end":"19:11","startHours":17.428928633836904,"endHours":19.178928633836904,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"00:07","end":"00:49","startHours":24.118135984257513,"endHours":24.81323506545494,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Labha","start":"07:15","end":"08:33","startHours":7.252442415875548,"endHours":8.555753193120717,"quality":"auspicious"},{"name":"Amṛta","start":"08:33","end":"09:52","startHours":8.555753193120717,"endHours":9.859063970365886,"quality":"auspicious"},{"name":"Kāla","start":"09:52","end":"11:10","startHours":9.859063970365886,"endHours":11.162374747611057,"quality":"inauspicious"},{"name":"Śubha","start":"11:10","end":"12:28","startHours":11.162374747611057,"endHours":12.465685524856227,"quality":"auspicious"},{"name":"Roga","start":"12:28","end":"13:46","startHours":12.465685524856227,"endHours":13.768996302101396,"quality":"inauspicious"},{"name":"Udveg","start":"13:46","end":"15:04","startHours":13.768996302101396,"endHours":15.072307079346565,"quality":"inauspicious"},{"name":"Chala","start":"15:04","end":"16:23","startHours":15.072307079346565,"endHours":16.375617856591735,"quality":"neutral"},{"name":"Labha","start":"16:23","end":"17:41","startHours":16.375617856591735,"endHours":17.678928633836904,"quality":"auspicious"}],"nightChoghadiyas":[{"name":"Udveg","start":"17:41","end":"19:23","startHours":17.678928633836904,"endHours":19.375617856591735,"quality":"inauspicious"},{"name":"Chala","start":"19:23","end":"21:04","startHours":19.375617856591735,"endHours":21.072307079346565,"quality":"neutral"},{"name":"Labha","start":"21:04","end":"22:46","startHours":21.072307079346565,"endHours":22.768996302101396,"quality":"auspicious"},{"name":"Amṛta","start":"22:46","end":"00:28","startHours":22.768996302101396,"endHours":24.465685524856227,"quality":"auspicious"},{"name":"Kāla","start":"00:28","end":"02:10","startHours":24.465685524856227,"endHours":26.162374747611054,"quality":"inauspicious"},{"name":"Śubha","start":"02:10","end":"03:52","startHours":26.162374747611054,"endHours":27.859063970365888,"quality":"auspicious"},{"name":"Roga","start":"03:52","end":"05:33","startHours":27.859063970365888,"endHours":29.555753193120715,"quality":"inauspicious"},{"name":"Udveg","start":"05:33","end":"07:15","startHours":29.555753193120715,"endHours":31.25244241587555,"quality":"inauspicious"}],"horas":[{"name":"Hora 1","start":"07:15","end":"08:15","startHours":7.252442415875548,"endHours":8.252442415875548,"planetary_lord":"Mercury"},{"name":"Hora 2","start":"08:15","end":"09:15","startHours":8.252442415875548,"endHours":9.252442415875548,"planetary_lord":"Venus"},{"name":"Hora 3","start":"09:15","end":"10:15","startHours":9.252442415875548,"endHours":10.252442415875548,"planetary_lord":"Sun"},{"name":"Hora 4","start":"10:15","end":"11:15","startHours":10.252442415875548,"endHours":11.252442415875548,"planetary_lord":"Mars"},{"name":"Hora 5","start":"11:15","end":"12:15","startHours":11.252442415875548,"endHours":12.252442415875548,"planetary_lord":"Jupiter"},{"name":"Hora 6","start":"12:15","end":"13:15","startHours":12.252442415875548,"endHours":13.252442415875548,"planetary_lord":"Saturn"},{"name":"Hora 7","start":"13:15","end":"14:15","startHours":13.252442415875548,"endHours":14.252442415875548,"planetary_lord":"Moon"},{"name":"Hora 8","start":"14:15","end":"15:15","startHours":14.252442415875548,"endHours":15.252442415875548,"planetary_lord":"Mercury"},{"name":"Hora 9","start":"15:15","end":"16:15","startHours":15.252442415875548,"endHours":16.25244241587555,"planetary_lord":"Venus"},{"name":"Hora 10","start":"16:15","end":"17:15","startHours":16.25244241587555,"endHours":17.25244241587555,"planetary_lord":"Sun"},{"name":"Hora 11","start":"17:15","end":"18:15","startHours":17.25244241587555,"endHours":18.25244241587555,"planetary_lord":"Mars"},{"name":"Hora 12","start":"18:15","end":"19:15","startHours":18.25244241587555,"endHours":19.25244241587555,"planetary_lord":"Jupiter"},{"name":"Hora 13","start":"19:15","end":"20:15","startHours":19.25244241587555,"endHours":20.25244241587555,"planetary_lord":"Saturn"},{"name":"Hora 14","start":"20:15","end":"21:15","startHours":20.25244241587555,"endHours":21.25244241587555,"planetary_lord":"Moon"},{"name":"Hora 15","start":"21:15","end":"22:15","startHours":21.25244241587555,"endHours":22.25244241587555,"planetary_lord":"Mercury"},{"name":"Hora 16","start":"22:15","end":"23:15","startHours":22.25244241587555,"endHours":23.25244241587555,"planetary_lord":"Venus"},{"name":"Hora 17","start":"23:15","end":"00:15","startHours":23.25244241587555,"endHours":24.25244241587555,"planetary_lord":"Sun"},{"name":"Hora 18","start":"00:15","end":"01:15","startHours":24.25244241587555,"endHours":25.25244241587555,"planetary_lord":"Mars"},{"name":"Hora 19","start":"01:15","end":"02:15","startHours":25.25244241587555,"endHours":26.25244241587555,"planetary_lord":"Jupiter"},{"name":"Hora 20","start":"02:15","end":"03:15","startHours":26.25244241587555,"endHours":27.25244241587555,"planetary_lord":"Saturn"},{"name":"Hora 21","start":"03:15","end":"04:15","startHours":27.25244241587555,"endHours":28.25244241587555,"planetary_lord":"Moon"},{"name":"Hora 22","start":"04:15","end":"05:15","startHours":28.25244241587555,"endHours":29.25244241587555,"planetary_lord":"Mercury"},{"name":"Hora 23","start":"05:15","end":"06:15","startHours":29.25244241587555,"endHours":30.25244241587555,"planetary_lord":"Venus"},{"name":"Hora 24","start":"06:15","end":"07:15","startHours":30.25244241587555,"endHours":31.25244241587555,"planetary_lord":"Sun"}],"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":"North (Uttara)","chandraVasa":"North","rahuVasa":"South-West","anandadiYoga":{"name":"Dhātṛ","quality":"Auspicious"},"tropicalRitu":"Hemanta (Pre-winter) (tropical)","vedicRitu":"Śiśira (Winter)","tropicalAyana":"Uttarāyaṇa","vedicAyana":"Uttarāyaṇa","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":-23.134683857176707,"eotMinutes":-8.635931491373626,"ayanamsa":-48.5078}},"calendars":{"vikram_samvat":-3123,"saka_samvat":-3258,"bengali_samvat":-3773,"malayalam_era":-4004,"nanakshahi_year":-4649,"lunar_month":"Phālguna","lunar_month_paksha_full":"Phālguna Kṛṣṇa Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Phālguna","lunar_month_amanta":"Phālguna","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Kumbha (Māsi)","ritu":"Śiśira (Winter)","display_summary":"Phālguna Kṛṣṇa Pañcamī · Vikram -3123 undefined · Śaka -3258 undefined"},"festivals":[],"todays_walk":{"walk":{"id":"budha-walk","name":"Budha Walk","name_sanskrit":"बुध यात्रा","type":"graha","description":"Discrimination + BG 2.41 (vyavasāyātmikā buddhi).","step_count":6,"url":"/walk/budha-walk"},"reason":"Budhavāra (Wednesday) — its presiding graha's walk."},"cosmic_resonances":[]},"validity":{"eternal":true,"location_specific":"mathura"},"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, 3181 BCE · Mathurā · Vidhyamitra","description":"January 13, 3181 BCE for Mathurā: Kṛṣṇa Pañcamī, sūryodaya 07:15, sūryāsta 17:41.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3180-01-13","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3180-01-13","sa":"https://sa.vidhyamitra.com/city/mathura/-3180-01-13","hi":"https://hi.vidhyamitra.com/city/mathura/-3180-01-13","x-default":"https://vidhyamitra.com/city/mathura/-3180-01-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-12T05:26:35.087Z","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":"2026-08-12T05:26:35.087Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-12T05:26:35.087Z","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"}}}