{"id":"vidhyamitra:day:2040-08-13:en","page_class":"VM-1-day","url":"https://vidhyamitra.com/day/2040-08-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"2040-08-13","date_display":"August 13, 2040 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":2040,"month":8,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2466379.770833,"kali_year":5142,"ahargana":1877914.2708,"sun":{"sidereal_longitude":115.8052,"rashi":4,"rashi_name":"Karka"},"moon":{"sidereal_longitude":175.9004,"rashi":6,"rashi_name":"Kanyā"},"tithi":{"number":6,"name":"Ṣaṣṭhī","paksha":"Śukla","full_name":"Śukla Ṣaṣṭhī","elongation_degrees":60.0952,"elapsed_within_tithi_degrees":0.0952},"nakshatra":{"number":14,"name":"Citrā","pada":1,"moon_longitude":175.9004,"elapsed_within_degrees":2.5671},"yoga":{"number":22,"name":"Sādhya","sum_longitude":291.7056},"karana":{"half_tithi_index":10,"name":"Kaulava"},"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":2040,"month":8,"day":13,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2466379.770833,"ahargana":1877914.2708,"kali_year":5142,"ayanamsa_lahiri":24.4204,"grahas":{"sun":{"sidereal_longitude":116.50631299999998,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":9,"name":"Aśleṣā","pada":3},"retrograde":false},"moon":{"sidereal_longitude":173.45661300000006,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":14,"name":"Citrā","pada":1},"retrograde":false,"latitude":3.0767},"mars":{"sidereal_longitude":154.085513,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":12,"name":"Uttara Phalgunī","pada":3},"retrograde":false},"mercury":{"sidereal_longitude":115.73501299999998,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":9,"name":"Aśleṣā","pada":3},"retrograde":false},"jupiter":{"sidereal_longitude":156.31771300000003,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":12,"name":"Uttara Phalgunī","pada":3},"retrograde":false},"venus":{"sidereal_longitude":136.103113,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":11,"name":"Pūrva Phalgunī","pada":1},"retrograde":false},"saturn":{"sidereal_longitude":163.55281300000001,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":13,"name":"Hasta","pada":2},"retrograde":false},"rahu":{"sidereal_longitude":39.0648,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":3,"name":"Kṛttikā","pada":4},"retrograde":false},"ketu":{"sidereal_longitude":219.0648,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":17,"name":"Anurādhā","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":2040,"month":8,"day":13,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2466379.770833,"kali_year":5142,"ahargana":1877914.2708,"sun":{"sidereal_longitude":115.8052,"rashi":4,"rashi_name":"Karka"},"moon":{"sidereal_longitude":175.9004,"rashi":6,"rashi_name":"Kanyā"},"tithi":{"number":6,"name":"Ṣaṣṭhī","paksha":"Śukla","full_name":"Śukla Ṣaṣṭhī","elongation_degrees":60.0952,"elapsed_within_tithi_degrees":0.0952},"nakshatra":{"number":14,"name":"Citrā","pada":1,"moon_longitude":175.9004,"elapsed_within_degrees":2.5671},"yoga":{"number":22,"name":"Sādhya","sum_longitude":291.7056},"karana":{"half_tithi_index":10,"name":"Kaulava"},"vara":{"number":3,"name":"Somavāra (Monday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":3.077,"elongation":60.095},"lunar":{"type":"lunar","occurs":false,"moon_latitude":3.077,"opposition_distance":119.905}},"eclipse_window_40days":[]},"calendars":{"vikram_samvat":2097,"vikram_samvatsara":"Śrīmukha","saka_samvat":1962,"saka_samvatsara":"Raudra","bengali_samvat":1447,"malayalam_era":1216,"nanakshahi_year":571,"lunar_month":"Śrāvaṇa","lunar_month_paksha_full":"Śrāvaṇa Śukla Pakṣa","solar_month":"Karkaṭa (Āḍi)","ritu":"Varṣā (Monsoon)","display_summary":"Śrāvaṇa Śukla Ṣaṣṭhī · Vikram 2097 Śrīmukha · Śaka 1962 Raudra"},"festivals":[{"id":"karka-sankranti","name":"Karka Saṅkrānti (Dakṣiṇāyana)","name_sanskrit":"कर्क सङ्क्रान्ति","tradition":"Pan-Hindu","associated_deity":"Sūrya Bhagavān","significance":"Sun enters Cancer; Dakṣiṇāyana (south-going) begins. Devatā-rātri begins.","vrata":true,"detection":{"sun_rashi":"Karka"},"precedence":2},{"id":"kalki-jayanti","name":"Kalki Jayantī","name_sanskrit":"कल्कि जयन्ती","tradition":"Vaishnava","associated_deity":"Kalki (10th daśāvatāra of Krishna)","deity_avatara_index":22,"significance":"Future Kalki avatāra — to manifest at end of Kali Yuga; observed Śrāvaṇa Śukla 6.","vrata":false,"detection":{"tithi_number":6,"tithi_paksha":"Śukla","lunar_month":"Śrāvaṇa"},"precedence":4,"sources":["Bhāgavata 12.2.18-20","Kalki Purāṇa"]}],"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,"valid_from":"2040-08-13T00:00:00Z"},"liturgical":{"opening":"जय श्री कृष्ण","closing":"ॐ तत् सत्","attribution":"Computed by Vidhyamitra Sūrya-Siddhānta substrate; Vidhyamitra substrate"},"seo":{"title":"Pañchāṅga August 13, 2040 CE · Vidhyamitra","description":"Vedic pañchāṅga for August 13, 2040 CE: Śukla Ṣaṣṭhī · Citrā.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/day/2040-08-13","hreflang_alternates":{"en":"https://vidhyamitra.com/day/2040-08-13","sa":"https://sa.vidhyamitra.com/day/2040-08-13","hi":"https://hi.vidhyamitra.com/day/2040-08-13","x-default":"https://vidhyamitra.com/day/2040-08-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-05-14T16:08:37.307Z","verification":{"type":"multi-marker","confidence":"canonical"}}],"meta":{"generated_at":"2026-05-14T16:08:37.307Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa"}}}