Transit of sun through the seasonal nakṣatra cycle in the Vṛddha-Gārgīya Jyotiṣa (original) (raw)
Related papers
THE SOLAR INGRESS (SANKRĀNTI) ACCORDING TO THE MAKARANDASĀRIŅĪ AND OTHER INDIAN ASTRONOMICAL TEXTS
Journal of Astronomical History and Heritage
In the present paper we analyze the procedure for the computation of the sidereal solar ingress according to the popular Indian astronomical table, the Makarandasāriņī. The results are compared with those obtained from the basic treatise Sūryasiddhānta, from the Vākya and the Gaṇakānanda, and also from those based on modern computations. We have also discussed the varying durations of the solar months and the solar ingress to the twenty-seven nakșatras (zodiacal asterisms). A number of illustrative examples are also provided.
Indian J History of Science, 2023
The first theoretical system of tracking sun in the tropical annual cycle is cryptically mentioned in the Maitrāyaṇīya Āraṇyaka Upaniṣat (MAU) of the Kṛṣṇa Yajurveda, as the southern sojourn of sun starting at the summer solstice. This is called maghādyaṁ, the first point of the maghā nakṣatra, identified most likely with the early morning visibility of ε-Leo, near the azimuth of the sunrise point on the horizon as observed at Kurukshetra. Twenty seven equal nakṣatra sectors named in the traditional sequential order cover one tropical circuit of sun of 366 days with the winter solstice falling exactly at the middle of the śraviṣṭhā sector. Even though MAU mentions each nakṣatra to be made up of four quarters, no practical application of this ¼-nakṣatra sky part amounting to 3º20´ in longitude is seen in Vedic texts till we come to the Brahmāṇḍa Purāṇa, a text closer to the Vedas. This Purāṇa states, observed equinoctial full moon positions corresponding to spring equinox at ¼-kṛttikā and autumn equinox at ¾-viśākha exactly 180º apart as they should be. This statement is analysed in this paper by computer simulation of full moon time series for the years − 2400 to − 800 to show that the Purāṇa data would be realistically valid for the period 1980 BCE to 1610 BCE. It is further demonstrated that the Purāṇa has followed the maghādi system of solar nakṣatra system stated in the MAU. The central epoch circa 1800 BCE of this maghādi equal nakṣatra solar zodiac got modified, due to precession effects, to the śraviṣṭhādi scheme of Parāśara, Vṛddha Garga and Lagadha dateable to circa 1300 BCE.
Amrtotsavagranthamala , 2024
A question that often arises is about positive sciences of India before the Common Era and their links with the Vedas. As an answer, the present monograph brings out for the first time the Mahāsalilaṁ part of the Vṛddhagārgīya Jyotiṣa, critically edited from eleven hitherto unpublished manuscripts collected from libraries in India and abroad. Salilaṁ is the name of the primordial state of dark-matter called andhaṁ-tamaḥ out of which all creation including the celestial bodies emerged. The Mahāsalilaṁ in prose, introduces observations and quantification in terms of numbers, through a set of nearly one hundred questions and explanations, in a style that is archaic and original as emanating from the Vedic world view. Foundational concepts of astral sciences that over centuries evolved into full-fledged Indian astronomy and astrology can be traced to this source in seed form. Earliest description of the five planets in terms of their brightness, six monthly lunar eclipse period, classification of comets, a theory of rainfall, instant of full moon as pūrṇatithi, astronomical background of the Vedic sānnāyya, are here. The Prajāpati-Rohiṇī-Soma legend is explained in new light, leading to Soma as primal Time, moon being a proxy. The synchronization of the five-year solar cycle with the sixty-seven sidereal lunar cycle is given. The text belongs to the maghādi era (c 1800-1600 BCE) when the summer solstice was with the maghā nakṣatra, centuries before the śraviṣṭhādi winter solstice calendar of Lagadha.
Pañcasiddhāntikā of Varāhamihira Chapter Two: Vasishtha Siddhanta – Planetary Computations, etc.
2018
This translation contains Chapter Two of the Panchasiddhantika, a famous East Indian astrology text by Varahamihira (circa 6th century). The text is a compilation of five astronomical texts known to Varahamihira: the Paulisha, Romaka, Vasishtha, Saura, and Paitamaha. There are a total of 18 chapters in the Panchasiddhantika. The other chapters will be added as I complete them. My translation includes an outline of the major concepts for each chapter, a word for word translation from Sanskrit to English with parts of speech annotations. Chapter Two covers various calculations from the Vasishtha Siddhanta including the true position of the sun, true position of the moon, locating the nakshatra and tithi from the true positions of the sun and moon, duration of day and night time in the zodiac signs throughout the year, the twelve gnomonic shadow digits based on the position of the sun by tropical zodiac sign, position of the sun by tropical zodiac sign based on the twelve gnomonic shadow digits, position of the lagna from the shadow before noon and afternoon, and the position of the shadow from the lagna before noon and afternoon. I welcome any feedback. Thank you for your attention and support.
The reason for the selection of the original lists of 28 nakatras or lunar mansions for the lunar zodiac of ancient India and China has remained an unexplained mystery for more than 2,000 years. This paper sets out to explain when and why these 28 divisions of the lunar zodiac were initially selected and show how they were linked to the Indian and Chinese Bronze Age calendars and the Vedic year of 360 days. It has been almost universally presumed by modern astronomers and assyriologists that this early 360 day year or calendar adopted by the ancient cultures from Egypt and Mesopotamia to the Orient was merely used as a schematic guide for calculations and astrological predictions but with little impact on more general day to day life and with no proper link to the correct movements in the ancient skies of the sun or moon or stars. However this study of early Vedic Indian astronomical systems will show that the development of their unique set of nakatras, tithis, and other systems for keeping track of the moment of Moonrise were all founded on and related to an acceptance that the Vedic calendar of 12 months of exactly 30 days did reflect a virtual or true astronomical reality. Once it is understood that their astronomical developments were based directly on a 360 day year it can be seen that their systems were both accurate and precise. Please note that references made to monthly and daily movements of the Moon will relate only to average movements, and not to exact daily movements which are quite variable.
The Origin of the 28 Nakshatras in Early Indian Astronomy and Astrology, Howard D. Jones
The reason for the selection of the original lists of 28 nakatras or lunar mansions for the lunar zodiac of ancient India and China has remained an unexplained mystery for more than 2,000 years. This paper sets out to explain when and why these 28 divisions of the lunar zodiac were initially selected and show how they were linked to the Indian and Chinese Bronze Age calendars and the Vedic year of 360 days. It has been almost universally presumed by modern astronomers and assyriologists that this early 360 day year or calendar adopted by the ancient cultures from Egypt and Mesopotamia to the Orient was merely used as a schematic guide for calculations and astrological predictions but with little impact on more general day to day life and with no proper link to the correct movements in the ancient skies of the sun or moon or stars. However this study of early Vedic Indian astronomical systems will show that the development of their unique set of nakatras, tithis, and other systems for keeping track of the moment of Moonrise were all founded on and related to an acceptance that the Vedic calendar of 12 months of exactly 30 days did reflect a virtual or true astronomical reality. Once it is understood that their astronomical developments were based directly on a 360 day year it can be seen that their systems were both accurate and precise. Please note that references made to monthly and daily movements of the Moon will relate only to average movements, and not to exact daily movements which are quite variable.
Ancient Indian Astronomy in Vedic Texts
Astronomy in popular perception is about stars, planets, sun, moon, eclipses, comets, meteorites and associated observable phenomena. Something of all of these was known to our ancients though not in the same form and detail as it is available now. In the context of India, the question is what was known, in what detail and when. For the siddhānta period, roughly starting with the Common Era, (CE) such questions have been fairly well answered. This has been possible since several texts of the period, specifically devoted to astronomy are available for systematic study. But for the more ancient period we have no exclusive texts other than Lagadha’s Vedānga Jyotiṣa (c 1400 BCE) which is a calendar with no reference to eclipses or planets. Hence when one talks of Vedic Times several precautions are necessary..... In the following articles we investigate briefly how comets, meteorites, and eclipses were experienced and pictured in the Vedic texts. Over a long period of time the effect of precession was also felt as with the loss of importance for the constellation Śiśumāra (Draco) and shifting of the Pole Star Dhruva. The astral descriptions and the religious lore behind the above astronomical entities provided the inspiration for the development of observational and mathematical astronomy in India. Some portion of the present study has appeared in the Indian Journal of History of Science (2005, 2009, 2010, 2011 and 2012) in the form of papers. However, considerable new information, beyond the published material, can be found in the following pages
Gāndhāri's curse specifying 36th year for Yadava Civil War counted from 3067 BCE date of the Great War is the clearest evidence of the knowledge of Viśvedevā विश्वेदेवा Eclipse Cycle of 36 years from Rgveda times. This is later referred to as the 36-year Saros Eclipse Cycle. --kālasya paryayam, 'reverses of Time', concept of अनुषङ्गः anuṣaṅgaḥ, the foundation of Hindu astronomy --यज्ञो वै विष्णुर्यदत्र नापि क्रियते तद्विष्णुना यज्ञेनापि करोति -- Viṣṇu is the yajna (Pañcaviṃśa-Brāhmaṇa XIII.5.5) and Gāndhāri's curse --varṣe ṣaṭtriṃśe, declares Gāndhāri; i.e. in the 36th Solar Year (the destruction of Yadava will occur), which is a metaphor for the occurrence of Eclipse Season Cycle after 36 years; these are Viśvedevā विश्वेदेवा Eclipse Cycles of 6678 Viśvedevā विश्वेदेवा visits every 371 tithi OR 18 Solar years (varṣa); varṣa a year (commonly applied to age), Br. (ā varṣāt, for a whole year; varṣāt, after a year; varṣeṇa within a year; varṣe every year); a day (?), R. vii, 73, 5 (Sch.)(Monier-Williams) Varṣa (वर्ष) refers to the “rainy” season and represents the months Āṣāḍha to Bhādrapadā (mid July to mid September) and is one of the six “seasons” (ṛtu).—According to the Vedic calendar, there are six different seasons, which correspond to the twelve months of the year. Varṣa (वर्ष) refers to 1 (one) solar year, according to the Bṛhatsaṃhitā (chapter 2), an encyclopedic Sanskrit work written by Varāhamihira mainly focusing on the science of ancient Indian astronomy astronomy (Jyotiṣa).—Accordingly, “We shall now proceed to give a brief description of (the qualifications of) a jyotiṣaka. [...] He must have a correct, knowledge of a yuga (43,20,000 Solar years), varṣa (a solar year), āyana (6 solar months), ṛtu (2 solar months), māsa (a solar month), pakṣa (15 solar days), ahorātra (a solar day), yama (one-eighth of a solar day), muhūrta (one-thirtieth of a solar day), nāḍī (one-sixtieth of a solar day or 24 minutes), vināḍi (one sixtieth of a nāḍī or 24 seconds), prāṇa (4 seconds) truṭi (33, 75th of a second) and parts of a truṭi and other divisions of time and also of divisions of space”.(Brihat Samhita by Varahamihira) The concept of varṣa a Solar year is traced to Rgveda times: Rgveda 1.25.8 वेद मासो धृतव्रतो द्वादश प्रजावतः । वेदा य उपजायते ॥ veda māso dhṛtavrato dvādaśa prajāvataḥ | vedā ya upajāyate || English translation: “He, who accepting the rites (dedicated to him) knows the twelve months and their productions and that which is supplementarily engendered.” Commentary by Sāyaṇa: Ṛgveda-bhāṣya An allusion to the thirteenth, the supplementary or intercalary month of the Hindu unisolar year and to the transition to the lunar year from the solar year; 'that thirteenth or additional month which is produced of itself, in connection with the year', yaḥ trayodaśo adhikamāsa upajāyate saṃvatsarasamīpe svayam evotpadyate. Rig Veda 1.164.48 द्वादश प्रधयश्चक्रमेकं त्रीणि नभ्यानि क उ तच्चिकेत । तस्मिन्त्साकं त्रिशता न शङ्कवोऽर्पिताः षष्टिर्न चलाचलासः ॥ dvādaśa pradhayaś cakram ekaṃ trīṇi nabhyāni ka u tac ciketa | tasmin sākaṃ triśatā na śaṅkavo 'rpitāḥ ṣaṣṭir na calācalāsaḥ || English translation: “The fellies are twelve; the wheel is one; three are the axles; but who knows it? within it are collected 360 (spokes), which are, as it were, moveable and immoveable.” Commentary by Sāyaṇa: Ṛgveda-bhāṣya The wheel is the year of twelve months; the three axles are the three doubble seasons, or hot, wet and cold; and the three hundred and sixty spokes are the days of the lunar-solar year; stanaḥ śaśayaḥ, śayāna, sleeping; dehe vartamānaḥ, abiding in the body. Rig Veda 2.40.3 सोमापूषणा रजसो विमानं सप्तचक्रं रथमविश्वमिन्वम् । विषूवृतं मनसा युज्यमानं तं जिन्वथो वृषणा पञ्चरश्मिम् ॥ somāpūṣaṇā rajaso vimānaṃ saptacakraṃ ratham aviśvaminvam | viṣūvṛtam manasā yujyamānaṃ taṃ jinvatho vṛṣaṇā pañcaraśmim || English translation: “Soma and Pūṣaṇ, showerers (of benefits)m direct towards us the seven-wheeled car, the measure of the spheres, undistinguishable from the universe, everywhere existing, (guided) by five reins, and to be harnessed by the mind.” Commentary by Sāyaṇa: Ṛgveda-bhāṣya The seven-wheeled car: sapra-cakra, the year, of seven seasons, reckoning the intercalary month as an additional ṛtu or season; five reins: again, a reference to the solar year, reduced by the amalgamation of the cold and dewy seasons into one, to five seasons: dvādaśa vai māsāḥ pañcartavo hemantaśiśirayoḥ samāsena, the twelve months are verily five seasons by the combination of the cold and dewy seasons. -- Viṣṇu is the yajna; inexorable time recurs in 3339 Viśvedevā विश्वेदेवा Eclipse Cycles -- In days after the 18-day Great War which began on 22 November, 3067 BCE, Śrī Kr̥ṣṇa meets Gāndhāri who is consumed by the wrath of the death of her sons and Kaurava soldiers in the war and who curses Śrī Kr̥ṣṇa that his Yadava clan will perish after 36 years. The specification of 36 years for the date of the Yadava Civil War (3031 BCE) is related to the next Eclipse Cycle season after 3067 BCE Great War. This inevitabilityh of the occurrence of the next Eclipse Cycle season is the clearest evidence that people of the Mahabharata times knew the astronomical detrminant of the Viśvedevā विश्वेदेवा count of 3339 divinities and the related metaphor of 36-Year Eclipse Cycles; counting the visits of the divinities in the bright fortnight and dark fortnight of the phases of the Moon, the 6678 visits occur in the metaphorical equivalence of 36 X 371 tithi (since 371 tithi constitute a Solar Year and after 36 years, the next eclipse season will recur). -- Concept of अनुषङ्गः anuṣaṅgaḥ in Hindu astronomy which explains the Viśvedevā विश्वेदेवा count of 3339 divinities (RV 3.9.9) and the occurrence of identical eclipse sequences which occur in a Time-span of 36 years, i.e. in 3067 BCE and in 3031 BCE This is an addendum to: Viśvedevā विश्वेदेवा count of 3339 divinities (Rgveda 3.9.9) is a celestial eclipse measure, a Vedic metaphor of identical-eclipse-sequence 3067&3031 BCE https://tinyurl.com/55h8c5fu Pañcaviṃśa-Brāhmaṇa XIII.5.5 of वर्गः: सामवेदः clearly explains the metaphor of the Veda divinity: Viṣṇu is the yajna. This is the clearest evidence for linking a celestial divinity with the time of performance of an iṣṭi an oblation consisting of butter, fruits, &c., opposed to the yajna of an animal or Soma, RV. i, 166, 14; x, 169, 2; ŚBr. ; ĀśvŚr. ; Yājñ. ; Mn. ; Śak. ; Ragh.(Monier-Williams). Brahmāṇḍa Purāṇa Section 2 - Anuṣaṅga-pāda Chapter 23 - Information about Heavenly bodies (stars, planets etc.) explains how the celestial events related to the Sun developing the Moon into the Full Moon day when Devas are propitiated by means of the Soma nectar; thus, there is a clear correlation between the Cyclical Motion of Time and the role of Divinities in the celestial sphere which impact earthly events. See, for example, the link between Divinities and Time explained in verses 38 and 39 of Anuṣaṅga-pāda of Brahmāṇḍa Purāṇa; अनुषङ्गः anuṣaṅgaḥ 1 Close adherence or attendance; connection, conjunction, association; तस्य वैरानुषङ्गस्य गन्ताऽस्म्यन्तं सुदुर्गमम् Mb.5.162.35. सानुषङ्गाणि कल्याणानि U.7. good things closely follow one another (come close upon one another). -2 Coalition, commixture. -3 Connection of word with word. -4 A word or words repeated from the context to supply an ellipsis. cf. अनुषङ्गश्च फलवचनमभविष्यत् ŚB. on MS.6.1.5. -5 Necessary consequence, inevitable result. -6 Connection of a subsequent with a previous act. अनुषङ्गिक anuṣaṅgika a. Following as a necessary result, consequent; concomitant, adhering to, connected with.अनुषङ्गिन् anuṣaṅgin a. 1 Connected with, adhering or sticking to; अनीकजे रजसि मुखानुषङ्गिणि Śi.17.57. -2 Following as a necessary consequence; यस्यानुषङ्गिण इमे भोगादयो भवन्ति Bh.3.76. -3 Related or applicable to, common, prevailing (अनुक्षणं प्रसक्त); सप्तकस्यास्य वर्गस्य सर्वत्रैवानुषङ्गिणः Ms.7.52; विभुतानुषङ्गि भयमेति जनः Ki.6.35 connected with, natural to, greatness. -4 Addicted to, devoted or attached to, fond of.(Apte). Thus, there is a clear अनुषङ्गः anuṣaṅgaḥ between celestial events observed on skymaps and events which occur on the earth.
HISTORICAL NOTES Measurement of coordinates of Nakśatras in Indian astronomy
It is well known that ancient Indian calendar dwelled on the 27 nakśatra system for fixing the positions of the sun, moon and the planets. Several attempts to identify these 27 stars in the sky have yielded very precise results for stars bright enough not to be misidentified, which is not so for the fainter ones. The basis for identification is the coordinate system available in the texts. Here, we try to understand the ambiguity and offer a possible solution by using the measured coordinates, which have not been utilized for this purpose so far. This also provides clues on the techniques used for measuring the coordinates.