Indian Astronomy

Prähistorische Astronomie und Ethnoastronomie
Der Arbeitskreis Astronomiegeschichte hat im Zusammenhang mit der Tagung der Astronomischen Gesellschaft in Würzburg ein Kolloquium veranstaltet, das am Montag, den 24. September 2007, stattfand. Aus aktuellem Anlaß – im Jahr 2007 jährte sich der Geburtstag von Heinrich Hertz (1857–1894), dem Entdecker der elektromagnetischen Wellen, zum 150. Mal – wurde für diese Herbsttagung das Thema „Astronomie in neuen Wellenlängen“ gewählt. Als weiteres Thema wurde „Prähistorische Astronomie und Ethnoastronomie“ angeboten, das bisher beim Arbeitskreis Astronomiegeschichte noch überhaupt nicht berücksichtigt wurde und großen Zuspruch fand. Die Prähistorische Astronomie betrifft die astronomischen Aktivitäten in der Zeit vor der schriftlichen Aufzeichnung. Viele vor- und frühgeschichtliche Völker beschäftigten sich mit den Geheimnissen des Kosmos und überlieferten ihre Vorstellungen in eindrucksvollen Bauwerken. Grundlagen der prähistorischen Astronomie sind archäologische Ausgrabungen oder geodätische Vermessungen von Baudenkmälern (Gräber, Kultanlagen), um deren eventuelle astronomische Ausrichtung festzustellen und mit Hilfe astronomischen Fachwissens zu deuten und in einen historischen Kontext einzuordnen. Archäoastronomie ist ein sehr interdisziplinäres Thema; Archäologie, Kulturgeschichte, Geschichte der Naturwissenschaft und Technik, besonders Astronomiegeschichte spielen eine Rolle, aber auch Ethnographie, Anthropologie, Literatur- und Religionsgeschichte, um nur einige wichtige Wissengebiete zu nennen.

Das Spektrum der Vorträge – und der Artikel in diesem Buch – reicht von Astronomie der Steinzeit (Megalithkultur des Neolithikums) und Bronzezeit zur Astronomie bei den Germanen oder Kelten.
http://www.hs.uni-hamburg.de/DE/GNT/events/wbg-archaeo07.htm
Am bekanntesten in der Steinzeit ist natürlich Stonehenge, dessen astronomische Bedeutung erstmals ausführlich von Gerald Hawkins 1963 in seinem Buch Stonehenge decoded diskutiert wurde. Es gibt aber viele weitere Kreisgraben-Anlagen und einzelne Menhire oder Alignements (z.B. Carnac und Locmariaquer, Bretagne). Ferner ist das Ganggrab in Newgrange, Irland, zu erwähnen; tief in den Hügel hinein strahlt die Sonne am am 21. Dezember, am Tag der Wintersonnenwende, symbolisch die Wiedergeburt des Jahres. Diese prähistorischen Anlagen finden sich nicht nur in England, Deutschland und Frankreich, sondern in ganz Europa bis Nordafrika (Steinkreis von Nabta, Südägypten). Nicht vergessen sollte man die Tempel-Anlagen auf Malta und Gozo. Im Pazifischen Ozean gibt es neben den Steinkolossen auf der Osterinsel die Ruinenstadt Nan Madol auf der Insel Ponape in Mikronesien.

In der Bronzezeit sind besonders die Goldhüte oder die Scheibe von Nebra zu nennen, die im Zentrum des Interesses stehen, aber man könnte auch die Kreisgrabenanlagen in Goseck und Kyhna anführen und den Sonnenwagen von Trundholm (1500 v.Chr). Es wurde auch die Ethnoastronomie mit einbezogen, ein Artikel befaßt sich mit dem Himmel bei den australischen Aboriginals, ein anderer diskutiert astronomische Beobachtungstechniken im alten Indien, ein bisher zu wenig berücksichtigster Kulturkreis.
Gudrun Wolfschmidt

The astronomical dating of the Rāmāyaṇa to 12209 BCE by Oak is based on his claim of the shifting of lunisolar months from the seasons due to precession. Oak has claimed that a shift of one month occurs relative to the seasons every 2,000 years. Accordingly, Oak claims that during the time of the Rāmāyaṇa, Caitra was part of Śarad season. In this article, it is shown that Oak has used his unproven hypothesis and analogies to claim that the Caitra month was in the Śarad season. Against this claim of his I have provided clear and direct evidence that the Caitra month was in the Vasanta season during the Rāmāyaṇa time.

Oak claims that the Laṅkā of the Rāmāyaṇa was not Sri Lanka. There was no need for Rāma Setu in 12209 BCE as India and Sri Lanka were connected by land. This fact itself should have made it obvious to Oak that his dating of the Rāmāyaṇa is wrong. However, Oak claims that the Laṅkā of the Rāmāyaṇa was on the equator This is based on the description given in Indian astronomy texts. These texts also state that at 90° east of Laṅkā on the equator is the city called Yamakoṭi, at 90° west of Laṅkā on the equator is the city called Romaka, and directly opposite Laṅkā on the equator at 180° in either the east or west direction is the city called Siddhapurī (or Siddhapura). There never was any city at any of these locations. These were just four mathematically defined points.

From astronomical works in Sanskrit , location of Mayasura will be traced who is claimed to be in Kritayuga in famous Surya Siddhant . And from available research on Chitpavan Brahmins , connection of Chitpavans to Greek Egyptian settlement in Alexandria is further discussed

India has a long history of monuments built in stone—from prehistoric megaliths to later religious monuments like stupas, temples etc. covering a period of nearly four millennia. In this paper we discuss the influence of astronomy on the design and layout of some of these monuments, as well as depiction and incorporation of astronomical objects and phenomena in several of these or their components. In several instances, prehistoric rock art features Sun and Moon motifs, which are also seen in later sculptural art in temples, hero stones, etc. Megaliths, which are mostly the sepulchral and commemorative monuments of the Iron Age, have a variety of forms, ranging from the simple upright stone to relatively complex constructions like dolmens etc. We demonstrate that at least some megaliths have sightlines to astronomical phenomena on the local horizon deliberately incorporated into their layout. It is quite possible that these early monuments evolved into later monumental structures like stupas and temples. Temple architecture in southern India followed two main evolutionary trajectories that spanned roughly 800 years. Temples often feature sculptural panels of deities, myths and legends on their outer walls. We examine some of the legends, such as the Tripurantaka legend of Shiva, commonly depicted on temple walls, for astronomical symbolism. Heavenly bodies, such as the Sun, Moon and planets, are deified in traditions of the Indic religions, and we examine some of these deities depicted in temple sculptures. We also discuss the Dikpalas—guardians of the directions—often depicted to safeguard temple precincts. The phenomena of Sun Temples, depictions of eclipses, zodiacal stones and navagraha worship are also dealt with. Finally, we examine Sun-facing structures, such as rock-cut temples and structural temples, which are designed to interact with the rising or setting Sun on given days of the year.

The importance of Logic and its mathematical formulation can hardly be overstated in the modern age of Information Technology. Design, implementation and innovations of both computer hardware and software systems are dependent on Logic in different forms and formats. Digital logic is mainly used for hardware design. Symbolic logic and Propositional Calculus are essentially required for the design of Artificial Intelligence (AI) applications. Given the current level of understanding there is a need to review Logic from the perspective ancient wisdom. Can Indian Logic, both old and new systems, known as Puratana Nyaya (PN) and Nabya Nyaya (NN), help more efficient AI design process? This paper is an attempt in that direction. It will first review the origin of the concept of logic and thereafter it will propose the possible areas of application in modern context.

Among the bodies of auxiliary knowledge Buddhist missionaries brought to East Asia which had a lasting impact to the local cultures was the astral science. It comprises a broad range of related subjects such as cosmology, astronomy, metrology, calendrics, astrology and the worship of astral deities. The great interest in the subject is evinced by the fact that detailed accounts of these subjects found their way into a number of key Sanskrit Mahāyāna texts, as well as their Chinese translations such as the Śārdūlakarṇāvadāna, the Mahāsaṃnipātasūtra and Amoghavajra's Xiuyao jing. A comparison of the early Indian astral science and its East Asian version however reveals some key differences. In this paper, I will examine these differences and influences which may be attributed to Central Asian and other non-Indian sources.

The article presents the way in which al-Bīrūnī described the Indian calendrical system through three of his works, Al-ātār al-bāqiya, Tafhīm, and Taḥqīq mā li-l-Hind and how his knowledge evolved depending upon his sources of information. The interest of al-Bīrūnī in the Indian calendrical system led him to enumerate more than thirty Indian religious festivals fixed by the movements of the moon and the sun. The objective of this article is to offer an overview of these festivals as listed and described by him in his Taḥqīq mā li-l-Hind. This overview leads to some observations with regard to al-Bīrūnīʼs sources of information for his description of these religious celebrations. It appears that he chiefly based his depiction on oral reports. This orality is seen by the way in which Indic terms have been transliterated by al-Bīrūnī into Arabic. This article also highlights the connection between some categories of festivals celebrated by his Indian informants and the society he encountered in South Asia. A large variety of festivals were practiced as rituals, ranging from Dīpāvali and Śivarātri, to Tīj festivals, via celebrations dedicated to Brahmins and ancestors.

This article provides an updated English translation of Chapter 14 of al-Bīrūnī's Kitāb taḥqīq mā li-l-Hind, in which he lists and describes numerous Sanskrit works related to astronomy, astrology and mathematics, and a few books belonging to other genres. Chapter 14 of Kitāb taḥqīq mā li-l-Hind highlights several types of literature accessed by al-Bīrūnī in the north-west of the Subcontinent in the early eleventh century CE. Whenever possible the English translation is supplemented with annotations on the works mentioned by al-Bīrūnī, and the Appendix offers a comparison of the table of contents of the Brāhmasphutasiddhānta as reported by al-Bīrūnī (in Arabic) and that given in the edition by Dvivedin of the Sanskrit text.

Aryabhata I (b. 476 CE) enunciated the theory of diurnal rotation of the earth in his work Aryabhatiya. But scholars of astronomy like Varahamihira and Brahmagupta, who immediately followed Aryabhata, rebuked him for holding such a view. They vehemently attacked and refuted the theory. Their influence on the later scholars was so strong that even the followers of Aryabhata rejected the theory. For this, they misinterpreted  two passages of the text and changed (hampered) the text itself at two other instances.
(Some typographical errors that have crept into are regretted.)

Knowledge of Vedic time reckoning was preserved in the Ṛk- and Yajurveda recensions of the Jyotiṣavedāṅga. Most of the verses of the two treatises convey the same meaning and provide a lecture on the measurement of time and its division. Some basic mathematical operations are also applied in order to calculate specific data important for the performance of Vedic ritual. This paper discusses some of the stanzas
and examines the terminology applied for the sake of time reckoning.

"The Treatise on the Astral Science of the Buddhist Land" by the Japanese scholar-monk Entsū 円通 (1754-1834) is a work that deals with various topics concerning the astronomical knowledge transmitted from China, and the Islamic and European (Dutch Learning) traditions, and comments on them from the point of view of the “Buddhist Land,” or in other words, the Buddhist texts. While the “Buddhist Land” may be understood as equivalent to India, the Buddhist texts Entsū cited are numerous and their content heterogeneous, containing different and at times incompatible theories. How then did Entsū synthesize the Indian astral science in his Treatise based on the Buddhist texts and the astronomical references found in other historical works? To what extent did Entsū succeed in representing Indian astral science as it was? This paper focuses on these two questions in an attempt to understand the “Indian astral science” in Entsū’s astral masterpiece against the broader background of reception/rejection of European cosmology and astronomy in nineteenth century Japan.

Since its discovery by scholars in the late nineteenth century, the last chapter of Sphujidhvaja's Yavanajātaka has been known as one of the earliest extant specimens of Indian astronomical works composed in Sanskrit. Subsequently, thanks to David Pingree's 1978 edition of the text, this chapter became widely recognized as one of the earliest Greek astronomical texts translated into Sanskrit, revealing the remarkable connection between the Greco-Babylonian astral science and the Indian one. However, some of Pingree's claims had been disputed by scholars and Pingree's reading and interpretation of the primary materials have been challenged by scholars such as Shukla (1989) and Falk (2001). In the light of the discovery of a new Nepalese paper manuscript and some other additional materials, some of the lacunae may now be filled and the additional variant readings have given us further clues to an improved interpretation of the text. The present study provides a summary of all the new findings concerning the last chapter of the Yavanajātaka, together with a revised, annotated critical edition.

The astronomical dating of the Rāmāyaṇa to 12209 BCE by Oak is based on his claim of the shifting of lunisolar months from the seasons due to precession. Oak has claimed that a shift of one month occurs relative to the seasons every 2,000 years. Accordingly, Oak claims that during the time of the Rāmāyaṇa, Āśvina and Kārttika were part of Vasanta season, and Caitra and Vaiśākha were part of Śarad season. In this article, the assumptions behind the hypothesis proposed by Oak are clarified and the proposed shifting of months relative to seasons is explained by means of illustrations. It is pointed out that there is no evidence for this hypothesis in the Rāmāyaṇa.

In same timespan , astronomer mathematician person likely to be astrophysicist & aeronautical engineer as both space & aircraft design & astronomy are closely related . So Lalla quoted in Vaimanika Shastra must be the same author of Shishya-Dhi-Vriddhi Tantra , treatise on astronomy .

Oak has misinterpreted the meaning of the Rāmāyaṇa verses to create the evidence he needs and called them 'Astronomy Poison Pills'. He has come up with a time period between 17500 BCE and 10000 BCE spanning 7,500 years, when these supposed Astronomy Poison Pills were valid. Oak claims to have found a unique observation during those 7,500 years. Oak's claim is based on the Comet 2P/Encke being visible in the Mūla nakshatra only in 12209 BCE. However, comets lose mass as they pass near the Sun, while they gain mass when they pass through the Kuiper Belt. As the mass and shape of a comet changes with time, neither its time of arrival nor its brightness can be predicted with accuracy. Comet 2P/Encke had a maximum brightness of 3.5 in 1829 CE. According to Voyager 4.5, the maximum brightness of Comet 2P/Encke in 1829 CE was 7.1, while according to Stellarium, the maximum brightness of Comet 2P/Encke in 1829 CE was 6.57. None of them has the value close to the observed value of 3.5 in 1829 CE. Though the Comet 2P/Encke was in the Mūla nakshatra on 9 September, 12209 BCE according to Voyager 4.5 simulation, it was nowhere near the Mūla nakshatra on that day according to Stellarium simulation. Instead, Comet 2P/Encke was closest to earth on 17 April, 12210 BCE in the Stellarium simulation. This shows that the trajectory and brightness of comets shown in astronomy software are completely unreliable. Thus 12209 BCE dating of the Rāmāyaṇa is based on astronomy software generated illusion.

According to Oak, the astronomical observation of the Sun setting near Puṣya nakṣatra during the Hemant season fixes the date of the Rāmāyaṇa between 11500 BCE and 17500 BCE. My calculations show that there is a time interval of 12500 BCE to 19000 BCE, when the Sun was in the Puṣya nakṣatra during the Hemanta season. Oak quotes Araṇyakāṇḍa 16.12 as the basis of his claim. He has given no justification for the claim that the Sun was near Puṣya nakṣatra during the Hemanta season. I have checked six different translations of Araṇyakāṇḍa 16.12 and none of them say anything about the Sun being near Puṣya nakṣatra during the Hemanta season. The verse Araṇyakāṇḍa 16.12 is about the nights, which are becoming longer and colder due to which people cannot sleep outside. Since it is referring to the nights, obviously it is not about the position of the Sun. Regarding Puṣya, the translations either say that it refers to the month of Pauṣa or Puṣya nakṣatra being visible at night. Oak has misinterpreted the verse Araṇyakāṇḍa 16.12 to suit his fanciful timeline.

The seven articles in this series of ten articles make it clear that the Rāmāyaṇa did not take place in 12209 BCE as proposed by Oak. If that is so, then there can be no corroboration for this date in the Rāmāyaṇa. However, Oak claims over 575 corroborations for the 12209 BCE date in the Rāmāyaṇa. Oak divides his claim of over 575 corroborations in two categories: 1. Effects due to precession of equinoxes and 2. Effects due to near earth phenomena. The corroborations under the category "effects due to near earth phenomena" are refuted based on their periodic nature as the 12209 BCE date of the Rāma-Rāvaṇa yuddha has been refuted and the four astronomy poison pills which placed this event between 17500 BCE and 10000 BCE according to Oak have also been refuted. Oak claims 225+ corroborations for seasons. He has not provided full details of these corroborations. The partial list provided includes analogies which cannot count as astronomical observations. Furthermore, he has counted interconnected evidence as independent evidence. As shown in Part 2 and Part 4, there is extensive evidence in the Rāmāyaṇa for standard seasons and months. Oak's claim of 225+ corroboration for seasons in the Rāmāyaṇa is completely bogus and he has exactly ZERO corroborations in the Rāmāyaṇa for 12209 BCE.

This paper attempts to compare the astronomical content of the Chinese Buddhist texts with the extant Indian astronomical works in Sanskrit, and to thereby analyze the development of Indian astronomy from a historical and text-critical perspective. Based on this analysis, the author points out that Indian astronomy may be divided largely into three periods: 1) Old (Vedic period to 3rd century CE); 2) Transitional (ca. 6th century), and; 3) New (8th century onward). Within the Chinese Buddhist corpus, each of these three periods is characterized by different equinoctial coordinate (vernal equinox), astral system and descriptions of asterisms and planets and so on. This paper focuses in particular on the Mahāsaṃnipātasūtra which demonstrates the transitional nature of Indian astronomy between the 4th and 6th century and how such transformation might have taken place.

In Chapter X.6 of Al-Bı̄rūnı̄’s astronomical opus magnum Al-Qānūn al-Mas‘ūdı̄ , Al-Bı̄rūnı̄ investigates on several methods, based on different paradigms, concerning the determination of distances between Earth and the wandering stars. In this article I will especially focus on Al-Bı̄rūnı̄’s evaluation of arguments strenght regarding wether they are observationnally based or not.

Dans le chapitre X.6 de son traité majeur d’astronomie, Al-Qānūn al-Mas‘ūdı̄, Al-Bı̄rūnı̄ discute plusieurs méthodes, basées sur des paradigmes distincts, traitant de la détermination de la distance des astres errants à la Terre. On étudiera ses arguments en prêtant une attention particulière aux nuances de statut qu’il leur accorde en fonction de leur proximité vis-à-vis de données d’observation.

According to Oak, Āśvina month was part of the Vasanta season during the time of Rāmāyaṇa, which fixes the date of the Rāmāyaṇa between 11800 BCE and 16500 BCE. Oak's claim is based on a verse in Kiṣkindhākāṇḍa, Sarga 53. It is number 9 in some versions and number 22 in other versions. The translation by Oak is not only a gross misinterpretation but contradictory in itself. I have checked six different translations of Kiṣkindhākāṇḍa, 53.9/53.22 and none of them match Oak's translation. The key word is "prasthitā" in the verse and there can be no doubt that it means departure. This is the way it has been translated by all six translators. Oak has deliberately mistranslated the verse to claim that the current month was Āśvina instead of the month when Vānara army was sent out to look for Sītā. Oak has misinterpreted the meaning of Rāmāyaṇa verses to create the evidence he needs and called them "Astronomy Poison Pills".

Time is perceived through movements of objects in sky, seasonal cycles, and biological changes, which appear to be universal and every society makes their sense. Studying change in the temporal models therefore provides understanding about cultural change in a broader context (Geertz, 1966: 389-409). Temporal organization represents the relationship between culture and ecology through different informal and formal markers in the same way as space is linked with the environment (Engel-Frisch, 1943). Calendars are one of the temporal markers, which represent the people’s association with and understanding of their environment both in ecological and astronomical sense.

One’s life in ancient India was centered around Vedic rites. In order for the ritual to be celebrated correctly, it was necessary to know the appropriate time for that, that is, to determine the propitious time for it drawing upon the position of moon and the sun in the (night)sky. The treatise Ṛgvedajyotiṣavedāṅga is the oldest preserved work containing not only passages proving that astronomical observations were applied at those times, but also that some complex mathematical instructions were employed, especially on the division of time and the setting of meaningful moments of the day depending also on the position of the sun and the moon in the horizon. These times of the day, determined by the calculations and observations, were foundation for determining the appropriate time for the celebration of the Vedic ritual.

आर्यभटीय is the first Indian work dealing exclusively with Mathematics and Astronomy in a systematic manner. It is a small work in Sanskrit. Contains 121 verses. The date of composition is recorded by author himself - Kali 3601 = 499 CE. Work contains many bold statements like  भूगोळः सर्वतो वृत्तः, प्राणेनैति कलां भूः, भूग्रहभानां गोळार्धानि स्वच्छायया विवर्णानि.

Vartak proposed that the grouping of seasons and lunar months changes by one month every 2,160 years due to precession, which was adopted by Oak, who uses a period of 2,000 years for the change of one lunar month. I have called this hypothesis the "Vartak-Oak hypothesis". According to this hypothesis, seasons consist of different pairs of luni-solar months as time changes. To confirm this hypothesis, the combinations of months and seasons were searched in the Indian texts going back to the Vedas. The listings of explicit mentions of seasons and months conform to the standard configuration from the earliest times till now. However, the combination has changed in East Indian calendars. According to the "Vartak-Oak hypothesis," the grouping of seasons and lunar months should have changed by one month every 2,000 years due to precession. There is no evidence of it in the Indian literature.

In Geo centric universe of classical indian astronomers , earth was stationary . Even Aryabhatt had same view as per his followers . Only 19th century british Indologist and later indian historians started saying that Aryabhatt was in favor of the rotation of the earth . Along with this most ancient astronomers were against precession of equinox . Since when this view changed is question . Was Surya Siddhant of Maya or Ptolemy changed this view of indian astronomers ? As they gave divine status to Ptolemy's book Great Treaties or Surya Siddhant

पद्यकाव्यानि च्छन्दोबद्धान्येव प्रणीतानि पूर्वैः कवीश्वरैः । काले काले श्रवणसुभगताहेतोः मात्राविन्यासविशेषैः तालानुकूलान्यपि वृत्तानि सृष्टानि गोचरीभवन्ति । अनेनैव हेतुना गीतिमार्गोऽपि आविष्कृतो भूयोभिः । सर्वा इमा आविष्कृतयः समुचिताः सहृदयाभ्युपगताश्च । तदनेन महता वृत्तवैविध्येन बन्धबान्धुर्येण च परिपुष्टः पद्यकाव्यप्रपञ्चः । छन्दोविचितिरेषा पद्यानि हृद्गतानि विधातुम् अतितमाम् उपकुर्वते । तान्येतानि कालान्तरे स्मृतिपथम् आगतान्यपि रसम् अनुभावयन्ति सहृदयम् । काव्येषु रसभावादीनां स्फुटाभिव्यञ्जनार्थमपि वृत्तविशेषा उपात्ताः सन्ति कविभिः । तद्यथा – सङ्ग्रामवर्णने तत्संवादे वा स्रग्धरा प्रभावातिशयाय कल्पते । प्रोषितभर्तृकावर्णने तु शिखरिणी शिरोमणीभवति । वियोगप्रसङ्गेषु वियोगिन्यपि हृद्यतां भजते । अत्र मन्दाक्रान्ताप्रभावस्तु सुविदित एव सहृदयानां यश्च मेघदूते सुप्रतिष्ठापितः । ’न खलु न खलु बाणः सन्निपात्योऽयमस्मिन्’ इत्यस्मिन् शाकुन्तलीये पद्ये राजानं बाणप्रयोगाद् वारयतस्त्वरा मालिन्या सुव्यक्ता । एवं छन्दोवैविध्यं बहुप्रयोजनकम् आदरास्पदं चेति निश्चप्रचम् ।
किञ्चाधुनिके काव्यप्रपञ्चे अन्येऽपि केचन पन्थानः प्राप्तावताराः सन्ति । भाषान्तरीयाः हायिकु-गलज्जलिकाप्रभृतयो बन्धविशेषाः संस्कृतेऽपि दृग्गोचराः साम्प्रतम् । मुक्तच्छन्दोरूपोऽपि कश्चित् प्रकार इह सुप्रतिष्ठितोऽधुना योऽसावपि भाषान्तरप्रभावपरिणत इति निश्चप्रचम् ।
तदेवम् इह छन्दोविषये प्रकथितानां प्रकाराणाम् आधुनिकेषु काव्येषु सत्यामपि सत्तायां तत्र गुणवत्तायां संख्यायां च वर्तत एव तारतम्यम् । सोऽयमंशो न तथा विद्वद्भिर्विमृष्टो विलोक्यते । अतस्तदेतत् सकलं समाहृत्य समीक्ष्य च आधुनिके संस्कृतकाव्यप्रपञ्चे छन्दोविषये कवीनाम् आस्था का? तत्र प्रतिप्रकारं कवीनां कियान् श्रमः? चेत्यादिको विचार इह चिकीर्षितोऽस्ति । यथा, आर्यायाम् अर्धसमवृत्तेषु च कवयितारः सम्प्रति विरला एव । पूर्वकविसमादृतेषु हरिण्यादिषु ईषदप्रसिद्धेषु वृत्तेषु पाटवं केषुचिदेवावलोक्यते । वृत्तौचित्यविवेकवन्तोऽपि नाधिकं विलोक्यन्ते । मुक्तच्छन्दोमार्गो गीतिमार्गश्च बहुमतो जायमानोऽस्ति ।

कालस्य प्रमुखेषु अवयवेषु अयनम् अन्यतमं वर्तते, केषाञ्चन श्रौतस्मार्तकर्मणाम् अनुष्ठानयोग्यकालनिर्णये तस्यावश्यकत्वात्, सर्वेषां कर्मणामनुष्ठाने तत्सङ्कीर्तनाच्च । अतस्तदारम्भादिविषये शास्त्रसम्मतो निर्णयः अत्यावश्यकः । किञ्चात्र मतद्वितयं वरीवर्ति साम्प्रतम् । केचिदत्र सायनं पक्षम् ऊरीकुर्वते परे तु निरयणम् । तयोः कतरन्मतं श्रुतिसम्मतिं शास्त्रयुक्तिं प्रत्यक्षाविरोधं च समर्हति इत्येतं विषयं साधारं प्रस्तौति पत्रमिदम् ।

Time is perceived through movements of objects in sky, seasonal cycles, and biological changes, which appear to be universal and every society makes their sense. Studying change in the temporal models therefore provides understanding about cultural change in a broader context (Geertz, 1966: 389-409). Temporal organization represents the relationship between culture and ecology through different informal and formal markers in the same way as space is linked with the environment (Engel-Frisch, 1943). Calendars are one of the temporal markers, which represent the people’s association with and understanding of their environment both in ecological and astronomical sense.

Among their many passages describing the details of rituals and sacrifices, the Dharmasūtras contain sections which make the time of the performance of ritual activities dependent on observable phenomena in the sky, such as lunar phases, eclipses or the journey of the Sun along its ecliptics (ṛta). These connections appear in some verses on ancestral offerings, purification rites and penances, rules for Vedic recitation and its suspension or Vedic studies in general. The knowledge of Vedāṅgas, as expressed in Dharmasūtras, is said to have purificatory qualities, which is especially important when eating food in the company of an impure or sinful person (Gautama Dharmasūtra 15.28, Baudhāyana Dharmasūtra 2:14.2, Vāsiṣṭha Dharmasūtra 3.19). What actually enables a sacrificer to understand the sacrifice itself is the knowledge and comprehension of jyotiṣa (Ṛgvedajyotiṣavedāṅga 3, Yajurvedajyotiṣavedāṅga 36), i.e. the science of heavenly bodies and their movements, sometimes equated with astronomy. This astronomical knowledge (gaṇita) has been preserved in two treatises of the Jyotiṣavedāṅga (V-III BC), specifically in the Ṛgveda recension and the Yajurveda recension. The aim of this paper is to examine selected passages of astronomical nature given in Dharmasūtras regarding relation to the Jyotiṣavedāṅga treatises and their prescriptive character.

Dans le chapitre X.6 de son traite majeur d’astronomie, Al-Qānūn al-Mas‘ūdi, Al-Birūni discute plusieurs methodes, basees sur des paradigmes distincts, traitant de la determination de la distance des astres errants a la Terre. On etudiera ses arguments en pretant une attention particuliere aux nuances de statut qu’il leur accorde en fonction de leur proximite vis-a-vis de donnees d’observation.

Oak claims that based on the Rāmāyaṇa Yuddha Kāṇḍa 4.48 Brahmarāśi/Vega/Abhijit was the Pole Star and this astronomical observation can be dated to 12000 BCE. The assertion "Brahmarāśi/Vega/Abhijit was the Pole Star in 12000 BCE as per Rāmāyaṇa" by Oak rests on two assumptions: 1. Brahmarāśi was the Pole Star according to Rāmāyaṇa and 2. Brahmarāśi is same as Abhijit (Vega) star according to Rāmāyaṇa. Brahmarāśi is made by joining Brahma and Rāśi. Brahmarāśi cannot mean Pole Star as Pole Star at any time can be only one star, while rāśi means a collection. Even if Brahmarāśi is taken as Dhruva or Pole Star, the claim of Oak needs the equivalence of Brahmarāśi and Abhijit (Vega) star. Oak's claim is based on Mahābhārata, Bhīṣma Parva 3.18. Oak uses only longitude to show that Mars was close to the yogatārās of Abhijit, Śravaṇa and Dhaniṣṭhā, thereby satisfying his interpretation of the Mahābhārata. However, both longitude and latitude must be taken into account. Mars is a planet and planets stay close to the ecliptic. If Mars is always close to the ecliptic and Vega is always close to 62° away from the ecliptic, then there is no way Mars was closer to the yogatārā of Abhijit (Vega) at any time. This proves that the equivalence of Brahmarāśi and the yogatārā of Abhijit (Vega) is false.

Indian treatises on astronomy as one of the first attracted the attention of Western scholars, at time when Sanskrit literature began to be known by them at the end of the eighteenth century. The reasons for this interest were, among others, the nakshatras as well as the problem of the precession of the equinoxes, both included, in the oldest preserved work of Sanskrit literature dealing with astronomy named Ṛgvedajyotiṣavedāṅga (V-III BC). This treatise describes the lunisolar Vedic calendar and explains the division of time, which are crucial due to the fact that one’s life in ancient India was centered around Vedic rites. In order for the ritual to be celebrated correctly, it was necessary to know the appropriate time for that, that is, to determine the propitious time for it drawing upon the position of moon and the sun in the (night)sky. The aim of the presentation is to show that Ṛgvedajyotiṣavedāṅga contains not only passages proving that astronomical observations were applied at those times, but also that some complex mathematical instructions were employed, especially on the division of time and the setting of meaningful moments of the day depending also on the position of the sun and the moon in the horizon. These times of the day, determined by the calculations and observations, were foundation for determining the appropriate time for the celebration of the Vedic ritual.