{"id":"vidhyamitra:day:2040-10-21:en","page_class":"VM-1-day","url":"https://vidhyamitra.com/day/2040-10-21","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"2040-10-21","date_display":"October 21, 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":10,"day":21,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2466448.770833,"kali_year":5142,"ahargana":1877983.2708,"sun":{"sidereal_longitude":183.019,"rashi":7,"rashi_name":"Tulā"},"moon":{"sidereal_longitude":15.2953,"rashi":1,"rashi_name":"Meṣa"},"tithi":{"number":17,"name":"Dvitīyā","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Dvitīyā","elongation_degrees":192.2763,"elapsed_within_tithi_degrees":0.2763},"nakshatra":{"number":2,"name":"Bharaṇī","pada":1,"moon_longitude":15.2953,"elapsed_within_degrees":1.962},"yoga":{"number":15,"name":"Vajra","sum_longitude":198.3144},"karana":{"half_tithi_index":32,"name":"Taitila"},"vara":{"number":2,"name":"Ravivāra (Sunday)"}},"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":10,"day":21,"hour":6,"minute":30,"calendar":"gregorian"},"julian_day":2466448.770833,"ahargana":1877983.2708,"kali_year":5142,"ayanamsa_lahiri":24.423,"grahas":{"sun":{"sidereal_longitude":183.83867699999996,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":14,"name":"Citrā","pada":4},"retrograde":false},"moon":{"sidereal_longitude":14.317177000000015,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":2,"name":"Bharaṇī","pada":1},"retrograde":false,"latitude":-1.5461},"mars":{"sidereal_longitude":199.75237700000002,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":15,"name":"Svātī","pada":4},"retrograde":false},"mercury":{"sidereal_longitude":184.336277,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":14,"name":"Citrā","pada":4},"retrograde":true},"jupiter":{"sidereal_longitude":170.78677700000003,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":13,"name":"Hasta","pada":4},"retrograde":false},"venus":{"sidereal_longitude":220.06607699999995,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":17,"name":"Anurādhā","pada":3},"retrograde":false},"saturn":{"sidereal_longitude":171.48907699999995,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":13,"name":"Hasta","pada":4},"retrograde":false},"rahu":{"sidereal_longitude":35.4088,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":3,"name":"Kṛttikā","pada":3},"retrograde":false},"ketu":{"sidereal_longitude":215.4088,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":17,"name":"Anurādhā","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":2040,"month":10,"day":21,"hour":6,"minute":30,"second":0,"calendar":"gregorian"},"julian_day":2466448.770833,"kali_year":5142,"ahargana":1877983.2708,"sun":{"sidereal_longitude":183.019,"rashi":7,"rashi_name":"Tulā"},"moon":{"sidereal_longitude":15.2953,"rashi":1,"rashi_name":"Meṣa"},"tithi":{"number":17,"name":"Dvitīyā","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Dvitīyā","elongation_degrees":192.2763,"elapsed_within_tithi_degrees":0.2763},"nakshatra":{"number":2,"name":"Bharaṇī","pada":1,"moon_longitude":15.2953,"elapsed_within_degrees":1.962},"yoga":{"number":15,"name":"Vajra","sum_longitude":198.3144},"karana":{"half_tithi_index":32,"name":"Taitila"},"vara":{"number":2,"name":"Ravivāra (Sunday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-1.546,"elongation":167.724},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-1.546,"opposition_distance":12.276}},"eclipse_window_40days":[{"offset_days":15,"type":"solar","occurs":true,"moon_latitude":1.132,"elongation":1.981}]},"calendars":{"vikram_samvat":2097,"vikram_samvatsara":"Śrīmukha","saka_samvat":1962,"saka_samvatsara":"Raudra","bengali_samvat":1447,"malayalam_era":1216,"nanakshahi_year":571,"lunar_month":"Kārtika","lunar_month_paksha_full":"Kārtika Kṛṣṇa Pakṣa","solar_month":"Tulā (Aippasi)","ritu":"Śarad (Autumn)","display_summary":"Kārtika Kṛṣṇa Dvitīyā · Vikram 2097 Śrīmukha · Śaka 1962 Raudra"},"festivals":[{"id":"tula-sankranti","name":"Tulā Saṅkrānti","name_sanskrit":"तुला सङ्क्रान्ति","tradition":"Pan-Hindu","significance":"Sun enters Libra.","vrata":false,"detection":{"sun_rashi":"Tulā"},"precedence":5}],"todays_walk":{"walk":{"id":"surya-walk","name":"Sūrya Walk","name_sanskrit":"सूर्य यात्रा","type":"graha","description":"Self-illumination + BG 4.1 (Sun-lineage of Gītā transmission).","step_count":6,"url":"/walk/surya-walk"},"reason":"Ravivāra (Sunday) — its presiding graha's walk."},"cosmic_resonances":[]},"validity":{"eternal":false,"valid_from":"2040-10-21T00:00:00Z"},"liturgical":{"opening":"जय श्री कृष्ण","closing":"ॐ तत् सत्","attribution":"Computed by Vidhyamitra Sūrya-Siddhānta substrate; Vidhyamitra substrate"},"seo":{"title":"Pañchāṅga October 21, 2040 CE · Vidhyamitra","description":"Vedic pañchāṅga for October 21, 2040 CE: Kṛṣṇa Dvitīyā · Bharaṇī.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/day/2040-10-21","hreflang_alternates":{"en":"https://vidhyamitra.com/day/2040-10-21","sa":"https://sa.vidhyamitra.com/day/2040-10-21","hi":"https://hi.vidhyamitra.com/day/2040-10-21","x-default":"https://vidhyamitra.com/day/2040-10-21"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-05-14T12:47:15.653Z","verification":{"type":"multi-marker","confidence":"canonical"}}],"meta":{"generated_at":"2026-05-14T12:47:15.653Z","pillar_versions":{"BOB-History":"Pūrṇa"}}}