Posts Tagged ‘Rahu’

Sky as a bridge: Transmission of Indian astronomy to China, Korea and Japan

Posted in Blogs (Articles) on April 5th, 2014 by Rajesh Kochhar – Be the first to comment

Rajesh Kochhar

Abstract

(Please write to me if you want the full text.)

Ancient cultural tradition of the Indian subcontinent (India for short) is characterized by a combination of three important factors: (i) antiquity, (ii) continuity, and (iii) interaction with the outside world. I discuss how astronomical knowledge was transmitted from India to China and thence to Korea and China. I point out that not only a study of Indian inputs is essential for a proper understanding of Chinese history of science but also Chinese response can be of great help in understanding developments within India through firm chronology.

 

What are Rahu and Ketu?

Posted in Blogs (Articles) on August 31st, 2012 by Rajesh Kochhar – Be the first to comment
  • Rahu and Ketu are two astro-mythological terms of Vedic vintage which underwent change and expansion of meaning in 6th century CE.
  • Contrary to many statements in print and on the internet, the Rgveda does not mention Rahu. In the Rgveda, eclipses of the Sun and the Moon take place when they are swallowed by an asura named Svarbhanu.
  • The Atharvaveda onwards, the eclipse-causing demon is called Rahu. In the Buddhist Pali literature, the Sun and the Moon successfully appeal to Buddha to rescue them from Rahu.
  • In the vast Mahabharata text, believed to have been by-and-large frozen in 4th century CE, Rahu is the eclipse-causing demon.
  • Unlike Rahu which was a proper noun exclusively associated with eclipses, ketu in this period was a common noun denoting a number of related phenomena rather than a particular event. Ketu, in plural stood for comets, meteors and the like. It has even been suggested that at places ketu denotes sunspots.
  • Astro-mythology changes after Aryabhata (born 476 CE) whose influential text Aryabhatiyam propounds the mathematical theory of eclipses. Note that this is a first for India not the whole world.
  • According to this theory, eclipses take place when the Moon is at one of the nodes of its orbit. The movement of these nodes can be calculated mathematically so that it now became possible to predict eclipses.
  • The movable part of the cosmos, what is now recognized as the solar system comprised two class of objects: planets (graha) and calamities (utpata)Since the planets could be mathematically  described, they represented cosmic order and were source of comfort.
  • In contrast, objects like comets appeared from nowhere without warning and thus cause of concern.
  • Aryabhata’s work transferred eclipses from the category of utpata to that of the grahas.Since  eclipses could be mathematically predicted, the two lunar nodes were designated grahas. Since they were not real, they were called shadow planets.
  • Varahamihira names these shadow planets. The ascending node was called Rahu and the descending node Ketu. Note that since the two nodes are 180 degrees apart, naming one would have been sufficient. But both were included so that the number of planets could be fixed at nine, considered to be a powerful and mysterious number.
  • While, for Rahu it was a re-definition of his old role, for Ketu it was a new assignment. It continued to be used in the old sense of comets, meteors, etc.
  • To sum up, when we seek to interpret the terms Rahu and Ketu in the old literature, we must first check what the time period is. Before 6th century, Rahu and Ketu are NOT planets. Rahu is a demon and Ketu a comet or a meteor. Beginning with 6th century CE, Rahu and Ketu become planets. In addition Ketu, continues to denote a comet or a meteor

Rahu and Ketu in mythological and “astronomological” contexts

Posted in Blogs (Articles) on August 13th, 2010 by Rajesh Kochhar – 2 Comments

Indian Journal of History of Science, Vol, 45, no.2, June 2010, pp. 287-297

Rajesh Kochhar

Abstract

Rahu and Katu were deployed as planetary deities in the sixth century CE immediately after the mathematical theory of eclipses was propounded by Aryabhata. Their literary credentials however go back to early Vedic times. Here our aim is to examine, in a joint mythological and astronomical-astrological (“astronomological”) context, how the textual meanings of Rahu and Ketu have evolved with time. There are clear stages in their evolutionary histories, which must be borne in mind while interpreting early references.

The legend of Rahu shows signs of internal development. Successor to the Rgvedic Svarbhanu, Rahu as eclipse-causing demon was reduced to a body-less head so that the swallowed sun or moon had an escape route. Rahu’s identification with the lunar ascending node represents an attempt to connect new scientific developments with traditional beliefs. Ketu, in contrast, was a dictionary word used to denote a variety of related phenomenon especially comets. The promotion of the head-less body as a demon represents expansion of mythology in the light of new scientific developments. Ketu was now given an additional entirely new role, creating avoidable confusion. Significantly, Ketu’s iconography represents efforts at reconciling its two disparate roles.

Key words: mathematical theory of eclipses, astrology, Vedic mythology, planetary deities, Buddhist mythology, astronomical omens, ritual

Ancient Indian perception of the moving cosmic environment two millennia ago was bipolar. Orbits of the seven geocentric planets (graha) by virtue of their predictability represented cosmic order, while phenomena like meteors, comets and eclipses which did not fit into any pattern were classified as utpata, portent or calamity. This world view is preserved in a Buddhist Sanskrit text, Sardulakarnavadana, the legend contained in which is known to have been translated in an abridged form into Chinese in 265 CE (Vaidya 199,p.xi) . As the 5th century CE came to a close, the status of eclipses was modified.

Mathematical theory of eclipses was propounded in India in 499CE by Aryabhata (born 476 CE) in his influential Siddhantic treatise simply known as Aryabhatiyam (See Ohashi 2009 for a recent review). According to this theory, solar and lunar eclipses occur when the moon is at either of its orbital nodes. These theoretical points move in a direction opposite to that of the planets and complete an orbit in the rather short period of 18.6 years. This development was immediately taken note of in astrological literature, which classified the two nodes as planets, implying that they were now amenable to mathematics. Since they were hypothetical they were dubbed shadow planets. The 6th century CE text Brihajjataka (2.2-3) by Varahamihira (died 587 CE) includes Rahu and Ketu in the list of planets, and even gives their synonyms: Tamas, Agu and Asura for Rahu; and Shikhi for Ketu (Rao 1986, p.76), which however never gained currency. The two nodes are 180 degrees apart so that specifying one fixes the other. It would thus have sufficed to include just one of them. Both were listed no doubt to bring the planetary number up to nine which was considered sacred.

If new words had been coined to designate the two nodes, matter would have rested there. But both Rahu and Ketu are terms of Vedic vintage. The term Rahu had previously been used as a proper noun and exclusively in connection with eclipse so that its deployment represents an attempt at integrating new scientific developments with ancient tradition. On the other hand Ketu was merely a common noun employed variously but never in association with eclipse. Here then was an old term which was given an entirely new identity, representing expansion of mythology in the light of new scientific developments.

It is not uncommon to see even earlier references to Rahu and Ketu being interpreted in terms of their later status. This is unfortunate, because it distorts the history of the evolution of “astronomological” thought. The new coinage is advisedly used in preference to the extant terms astronomical and astrological to avoid backdating the present differentiation into earlier times when they would have been essentially seen as one. Our aim is to investigate how the textual meanings of the terms Rahu and Ketu have evolved with time. We must keep in mind some notable features of the available source material. Most texts remained open for a long time and were contributed to by generations of authors. There is no reason to expect or demand internal self- consistency from them. The texts were often composed in metrical poetry and were meant for a select audience. Very often the meaning assigned to a particular word depends on the context in which it is used.

An important source of information on ancient India is the Mahabharata which was expanded over a long period of time to include matter that went beyond the description of the Bharata battle which it had originally set out to describe. The astronomical content of the Mahabharata is consistent with Vedic astronomy in that it marks sky positions with the help of bright stars or star groups known as naksatra. The Mahabharata is not familiar with the twelve zodiacal signs which make their appearance in post-Mauryan India in about the first century BCE at Baudha Gaya where they are depicted on the railing pillars (Kane 1975, p. 598). Given the size and the nature of the contents of the Mahabharata it is reasonable to assume that if zodiacal signs had been introduced into India when the Mahabharata text was still open they would have found their way into it. We thus conclude that the Mahabharata text had been closed by about 1st century BCE (Kochhar 2000, p.56). This is an important datum. At one place the Mahabharata (Vanaparva 188. 87-88) does say that “when the moon, the sun and Jupiter in Tisya come together in one rasi, krta age will begin”. The term rasi is used here in the general sense of a portion of sky, not in the precise sense of a zodiacal sign.

The Mahabharata does not make any reference to the week days either. There is no unanimity on the epoch when they were introduced into India. Varahamihira, already referred to, in his other works , Pancasiddhantika and Brihatsamhita, mentions week days while quoting authorities who had lived much earlier . From this it has been inferred that week days were introduced into India in the first century CE(Kane 1975, pp. 680-1). A more plausible case has been built by Markel (1991) to suggest that the week made its appearance in India only in forth century CE.

Vedic Rahu and Ketu

The Rgveda does not know of Rahu. Rgveda (5.40:5-9) describes how Svarbhanu, son of an asura, pierced the sun “through and through with darkness”. The eclipse caused great distress among observers: “All creatures looked like one who is bewildered, who knoweth not the place where he is standing”. The sun himself appealed to Atri: “Let not the oppressor with this dread, through anger, swallow me up, for I am thine, O Atri”. In response, “By his fourth sacred prayer Atri discovered Surya concealed in gloom that stayed his function”. “The Brahmana Atri, as he set the press-stones, serving the Gods with praise and adoration, established in the heavens the eye of Surya, and caused Svarbhanu’s magic arts to vanish. The Atris found the Sun again, him whom Svarbhanu of the brood of Asuras had pierced with gloom. This none besides had the power to do.” (Griffith 1896, p. 255) .The Atris were prominent contributors to the Rgveda. The whole of the fifth mandala is authored by them. The passage quoted above is mentioned and embellished at a number of places in the Vedic literature :Tandya Brahmana (4.5.2; 4.6.13; 6.6.8; 14.11. 14-15; 23.16.2), Gopatha Brahmana (8.19), Satapatha Brahmana (5.3.2.2), and Sankhayana Brahmana (24.3) ( Dikshit 1896, Vol.1, p.58; Kane 1975, pp. 241-242). What the Atris probably did was to chant mantras while the eclipse lasted. The Rgvedic description is significant. An eclipse was seen as the demon’s work in disrupting the cosmic order. Propitiation was needed to restore that order.

Dikshit (1896, Vol. 1, p. 57) while translating a passage from the Rgveda renders Svarbhanu as Rahu and goes on to give its meaning as the lunar ascending node. Similarly Kane (1975, p.569), while discussing a reference in the Maitrayani Upanisad, equates Rahu and Ketu with the ascending and descending node respectively. Svarbhanu’s career as an asura did not last long. It is not clear when and how Svarbhanu made way for Rahu, who appears for the first time, and as the sun’s enemy, in Atharvaveda (19, 9-10). Chandogya Upanisad (8.13) makes an interesting analogy: The “soul that has acquired true knowledge is said to shake off the body after casting off all evil” like “the moon becoming free from the mouth of Rahu” (Kane 1975, p.569).The Pali Buddhist sources refer to the moon and the sun freeing themselves from the clutches of Rahu by invoking Buddha’s name (Candima Sutta, Samyutta-nikaya 2.9; Suriya Sutta, Samyutta-nikaya 2.10).

Mahabharata (Bhismaparva 13.39-45) uses both Svarbhanu and Rahu as interchangeable names. Rahu is a graha, 12000 yojanas in diameter, bigger than both the moon (11000 yojanas) and the sun (10000 yojanas). Rahu had to be bigger than the sun and the moon so that it could grab them. Note that the term graha here carries the sense of a grabber and not that of a body in orbit. In course of time, the name Svarbhanu came to be de-stigmatized so much so that a son of Lord Krsna was given the name (Mani 1975, p. 778).

Atharvaveda (13.16-24) employs Ketu to mean ray of light. These nine verses are taken from Rgveda (1.50.1-9) in the same order and more or less in the same form. They are also found “in one or more other Vedic texts” (Whitney 1905, Vol.2, p.722). More typically Ketu meant combination of fire and smoke. The Atharvaveda passage (19.9.10) quoted above refers to Dhumaketu as an epithet of mrtyu [death]. It either means a comet or literally as “smoke-bannered” to the smoke rising from a funeral pyre (Whitney 1905,Vol. 2, p. 914). Atharvaveda (11.10.1-2, 7) uses Ketu in the plural, as arunah ketavah [ruddy Ketus]. Here the reference seems to be to comets or meteors. Varahamihira’s Brihatsamhita, composed in 6th century CE but containing much older material, quotes a still earlier astronomer Garga on a class of 77 comets, called Aruna, which are dark red in colour (Bhat 1981,Vol. 1, p.138).

Puranic Rahu and Ketu

If the demon Rahu devours the sun or the moon to cause an eclipse, how do they become visible again? The answer is provided by the well – known story samudramanthana (churning of ocean), described in Mahabharata, Visnupurana and elsewhere. In the story, the demon Rahu’s head is chopped off, which survives. It is the Rahu head which causes an eclipse. Since the rest of the body is missing, there is an escape route for the sun and the moon. Note that the name Rahu now belonged to the body-less head. The head-less body would remain unclaimed, till the 6th century CE; see below. Brhatsammhita (5:1-3) while narrating this story also refers to a prevalent alternative belief that Rahu is of a serpentine form with only the head and the tail. The ancient Iranian text Bundahishn talks of goshir, an eclipse-causing serpent. It is not clear whether Varahamihira is referring to the Iranian legend or an un-recorded Indian one. Al Biruni writing in the 11th century reserves the name Rahu for the dragon’s head and calls the tail Ketu (Sachau 1888, Vol. 2, p.234).There were some half-hearted attempts to relate eclipses to predictable phenomena. Thus it was speculated that an eclipse took place when five planets get together (Brihatsamhita 5.17)

Mahabharata (Adiparva 65. 11-12, 31) names Kasyapa as the father and Simhika as the mother of Rahu, who is at times designated Simihkeya after her. His three other real brothers are also mentioned, their given names, Sucandra, Candraharta and Candrapramardana, all being associated with moon. Kasyapa from another wife Danu had 34 named sons including one called Ketuman (not Ketu).Curiously the names Surya, Candramas and Svarbhanu figure in the list (Adiparva 65.22-26).These 34 demons are thus Rahu’s half brothers. This naming is an exrecise in meaningless creativity. This association may have an astronomical basis which does not seem to have been noted before. Varahamihira in his Brihatsamhita (3.7; 11.22) mentions a class of 33 comets known as Tamaskilakas (dark shafts), called children of Rahu. They were noticed by the 11th century astronomer and chronicler Al-Biruni also. Described as black, and shaped like a crow or a beheaded man or a sword, or bow and arrow, they are always in the neighbourhood of the sun and the moon. It is likely that this category include sunspots (Bhat 1981, pp.25-26). An ancient authority quoted by Varahamihira on Tamaskilaka is Garga, who figures in Mahabharata also as an astronomer and advisor ( Mani 1975, p. 280). He may well have been responsible for constructing a myth about 34 half-brothers of Rahu out of the description of Tamaskilakas. It is noteworthy that from independent considerations Garga has been place at about 100 BCE (Kane 1975, p.681), the epoch we have assigned to the closure of the Mahabharata.

Inverted astronomy in Mahabharata

The Mahabharata talks about the prevalent astronomical knowledge albeit often in an inverted manner. It will be useful to inspect the context in which these references were made.

When the two rival armies stood confronting each other, and the Bharata war looked imminent, last ditch efforts were made to avert it by appealing to the ineffectual king Dhrtarastra whose villainous sons were widely held responsible for bringing things to such a pass. To convey the enormity of the sense of impending genocide, the king was told that in anticipation of the war the natural order had already broken down. The effect was heightened by the fact that the so-called eye witness account was brought to the sightless king by his own biological father. The revered Ved Vyasa tells Dhrtarastra (Bhismaparva 3.46) as follows.

Cows are giving birth to asses; and elephants to dogs. Sons are enjoying sexual pleasures with their mothers. Idols of gods are laughing, vomiting blood, feeling sad, and falling off their pedestals on their own. Animals are being born with three horns, four eyes, five feet, two urinary organs, and two tails. Women are giving simultaneous birth to four –five girls, who immediately start singing, dancing and laughing. Trees are flowering out of season. Lotus and water-lily are blossoming on tree tops. Even koel, peacock and parrot are making fearsome sounds. There is a downpour of blood and bones from the sky.”

The imagined weirdness of the world in anticipation of the fratricidal war was extended to the skies as well. “Arundhati well known for her devotion to her husband Vasistha has left him behind. [The reference here seems to be the star pair in Ursa Major rather than to individuals.] Dawn and the dusk look like as if they are on fire. Vyasa tells Dhrtarastra that he could not make out the difference between day and night, because the sun, moon and the stars all were burning bright throughout. This is a fearsome sign. Although it was the Kartika full moon night, the moon was not visible; its luster had given way to fire.

It is in this background that even the more-reasonable sounding descriptions of celestial phenomenon should be seen. A recurring theme is the reference at various places in the Mahabharata to Rahu, as if the occurrence of an eclipse was at par with holocaust on earth. “Rahu has seized the sun” (Bhismaparva 3.11). “Rahu is approaching the sun” (Bhismaparva 141.10).”Rahu swallowed the sun most untimely” (Salyaparva 55.10). “Rahu eclipsed the sun and the moon simultaneously” (Asvamedhaparva 76. 15, 16, 18). Meteors (ulka) and earthquakes are also similarly invoked. As part of the celestial foreboding it is stated that a very dangerous Dhumaketu has overcome the naksatra Pusya. This will bring destruction to both sides. (This ill-omen appears in the 4th century CE Buddhist text Sardulakarnavadana as well; see below).

Continuing, his listing of ill omens, Ved Vyasa tells Dhrtarastra that the sveta graha (white planet) has transgressed Citra, while the parusa graha (harsh planet) has established itself between Citra and Svati (Bhismaparva 3.11, 16). The translators have exercised their own discretion in rendering these terms. Sveta graha has been left untranslated (Sathe et al. 1985, p.39) or equated with Ketu (Ganguli 1884-1896, Book 6, p.12). Parusa graha has been identified with Rahu by one translator ( Ganguli 1884-1896, Book 6, p.12) and with Ketu by ANOTHER (Sathe et al. 1985, p.39).. The arbitrariness is obvious. As we have argued it would be anachronistic to associate Rahu and Ketu with a planet in pre-Varahamihira times.

Greek astronomical elements made their documented appearance in India in 149 CE when a Greek astro-text was translated into Sanskrit by Yavanesvara. It was versified in 269CE by Sphujidhvaja under the title Yavanajataka (Pingree, p. 1959). The versification was a significant development, because it signifies assimilation of Greco-Babylonian elements into Indian tradition. And yet, Vedic astronomical tradition remained extant even after the introduction of Yavana texts, as can be seen from passages in Sardulakarnavadana, already referred to. “Irrespective of the naksatra, when the sun or the moon is seized by Rahu, the king along with his subjects comes to pain.” “Irrespective of the naksatra when Ketu enters the moon, the neighbouring enemy king gets the upper hand.” “When Dhumaketu establishes itself in the Pusya naksatra, then defeat in enemy’s assault from all four directions is guaranteed” (Vaidya 1999, p. 374, couplets 462,463, 466). As we have already noted, Dhumaketu in Pusya as a bad omen is mentioned in the Mahabharata also. It is significant that Ketu and Dhumaketu are listed separately and along with Rahu under utpata.

Once the mathematical theory of eclipse was propounded, Rahu ceased to be an utpata; its predictability however did not remove the fear associated with it. On the other hand, Ketu as comet continued to be an utpata. Brihatsamhita assigns separate chapters to a discussion on eclipses under the heading Rahu and on comets under Ketu. Brihatsamhita does not mention Ketu in the context of eclipse. As mentioned earlier, it is Varahamihira’s other text Brihajjataka which twins Ketu with Rahu as the eclipse-causing shadow planets, introducing the concept of navagraha. Ketu was now given a brand new identity; the torso which had been lying lifeless after the detachment of the Rahu head was now resurrected and named Ketu.

We have argued that inclusion of the demon Rahu in the list of mathematically tractable planets took place after 499CE. Support for this conclusion comes from iconographic data. The “ first surviving depiction of Rahu occurs in a relief of the ‘Churning of the Ocean’ carved over the façade of the doorway of cave-temple number nineteen at Udayagiri in the Vidisha district of Madhya Pradesh, which can be dated to ca. A.D.430-450. Earliest known representations of Rahu as a member of the planetary deities are those on two stone lintels, 100cm by 20cm, originally from the villages of Nachna and Kuthara in the Panna district in the Bundelkhand region of Madhya Pradesh, most likely sculpted during the reign of the Uccakalpa king Jayanatha (r. ca. A.D.490-510)” ( Markel 1990, pp.11-13). If the assigned dates are correct, it is remarkable that Rahu’s planetization occurred within a decade of Aryabhata’s theory. Ketu as a planetary deity appears in about 600 CE or a little later, in Uttar Pradesh. In the eastern state of Orissa, Ketu was not counted in until the tenth century, which thus had only eight grahas till then (Markel 1990, p.21). One wonders whether it was from Orissa that Rahu as Yahu travelled to Burma as one of the eight nats (spirits).

Astronomical literature employs the term Rahu in connection with eclipse but in a number of ways. Aryabhata does not use either Rahu or Ketu; he and following him many others refer to a node as pata. Brahmagupta (b.598CE) in his long career displays signs of intellectual evolution. Taking a position contrary to Aryabhata, he in his Brahmasphutasiddhanta, prepared in 628 CE, expresses his faith in the demon Rahu as the cause of eclipse . Al Biruni noted this (Sachau 1888,Vol. 2, p.110). His later text, Khandakhadyaka (665 CE), however, calculates eclipses in a matter-of-fact way employing the technical term pata and without naming Rahu or Ketu (Chatterjee 1970, pp. 80-85).

The 689 CE astronomical handbook Karanaratna by Devacarya (Shukla 1979) uses Rahu to denote the eclipse shadow (2.2) as well as the ascending node (e.g.1.15). Significantly, at one place (1.13) the latter is called Rahumukha (Rahu head). A tersely written basic astronomical text will have no reason to mention Ketu. As comet, meteor or the like Ketu lay outside the scope of theory while as descending node it would be redundant once the ascending node Rahu or pata was mentioned.

In later Iranian (and Arabic) mythology the ascending node Rahu and the descending node Ketu become the head and the tail of the dragon Al –Djawzahr. Ketu as comet is not forgotten; he figures as al-Kayd (Hartner 1965). Rahu and Ketu as part of mathematical astronomy were introduced into China during the Tang dynasty (618-907CE), but with modified meaning. While Rahu was retained in the sense of the lunar ascending node, Ketu was used as a designation for lunar apogee (Niu 1995)

The imagery and iconography of Rahu and Ketu have evolved over time, with the latter having been more difficult to conceptualize. While Rahu has been well-defined since the days of the samudramanthana story, Ketu had in the sixth century CE the eclipse role thrust upon him in addition to the cometary ( and not the other way round as Neugebauer (1957, p.211) suggests).

The tradition of eclipse calculation has continued uninterrupted till relatively recent times. A copper plate inscription tells us about the grant of a village by the Kalachuri king Ratnadeva II to an astronomer , Jagannatha by name, for correctly predicting the lunar eclipse of 1128CE. He knew two Siddhantas and succeeded where other astronomers in the court failed. Hence the reward ( Mirashi 1933-34,p.161).Seven centuries later, a Pondicherry-based traditional astronomer calculated for the benefit of John Warren the lunar eclipse of 1825 May 31-June 1, with the help of shells, placed on the ground, and from tables memorized “by means of certain artificial words and syllables”. The results were remarkably accurate for the time. There was an error of +4 minutes for the beginning, -23 minutes for the middle and -52 minutes for the end (Neugebauer 1983, p.436). Traditional almanacs still use old algorithms for their planetary position calculations, but have taken to using modern methods for calculating eclipses as a concession to the greater time consciousness of the present times.

To sum up, the terms Rahu and Ketu have been continuously in use since the early Vedic times, but their meaning has not remained static. Rahu was an eclipse-causing demon whose name was confined to the severed head in the samudramanthana story. In the sixth century CE, Rahu was identified with the ascending node of lunar orbit and designated the eighth planet.

From the earliest time till the sixth century CE, Ketu was not a proper noun but a dictionary word used to denote phenomena like comets and meteors. This meaning continued later as well. But in the sixth century CE, Ketu was made into a proper noun by identifying it with the descending node of the lunar orbit and designating it the ninth planet. The headless body of the demon left behind from the samudramanthana days was retrospectively named Ketu. This evolutionary sequence needs to be kept in mind while interpreting textual references. More specifically, identification of Rahu or Ketu with a planet in a text prior to Varahamihira would be an exercise in anachronism.

I thank Yukio Ohashi, K.T.S. Sarao, B.V. Subbarayappa, K. Ramaubramaniam and Michio Yano for help and useful conversations.

References

(To help place an author’s work in context, date of original publication is cited in the text. For convenience, date of translation or reprint, mostly facsimile, is added.)

Bhat, M. Ramakrishna (1981) Varahamihira’s Brihat Samhita (Delhi: Motilal Banarasidass).

Chatterjee, Bina (1970) The Khandakhadyaka of Brahmagupta with the commentary of Bhattotpla, Vol. I. ( Delhi: Motilal Banarasidass).

Dikshit, Sankar Balakrishna (1896) History of Indian Astronomy (English translation by R.V. Vaidya, Pt I,1968; Pt II, 1981. New Delhi: India Meteorological Department).

Ganguli, Kisari Mohan (1884-1896) Mahabharata of Krishna-Dvaipayana Vyasa ( on-line)

Griffith, Ralph T. H. (1896 ) The Hymns of the Rgveda ( Reprint, Delhi : Motilal Banarasidass, 1973).

Hartner, W. (1965) “ Al-Djawzahar”. In :Encyclopedia of Islam,Vol.2 ( Leiden: Brill), pp.501-502.

Kane, Pandurang Vaman. (1975) History of Dharmasastra, Vol. 5 (Poona: Bhandarkar Oriental Research Institute).

Kochhar, Rajesh (2000) The Vedic People (Hyderabad: Orient Longman).

Mani, Vettam (1975) Puranic Encyclopaedia (Delhi: Motilal Banarasidass).

Ohashi, Yukio (2009) “The mathematical and observational astronomy in traditional India”. In: Science in India, Vol. 13, Pt.8 (ed. J.V. Narlikar) (New Delhi: Viva Books), pp 1-88.

Markel, Stephen (1991) “The genesis of the Indian planetary deities”. East and West, Vol. 41. pp. 173-188)

Markel, Stephen (1990): The Imagery and Iconographic Development of the Indian Planetary Deities Rahu and Ketu”. South Asian Studies, 6:9-26.

Mirashi, V.V. (1933-34) Epigraphia India, Vol. XXII, 159-165.

Neugebauer, Otto (1957) “Notes on Al-Kaid”. J. Amer. Oriental Soc., 77, 211-215.

Neugebauer, Otto (1983) Astronomy and History : Selected Essays ( New York : Springer-Verlag).

Rao , Bangalore Suryanarain (1986) Varahamihira’s Brihat Jataka ( Delhi : Motilal Banarasidass, Reprint 2008).

Sachau, Edward C. (1888) AlBeruni’s India, ( 2 vols reprinted as one , Delhi : Atlantic Publishers)

Sathe, Shriram: Deshmukh, Vijaya; and Joshi Prabhakar ( 1983) Bhartiya Yuddha: Astronomical References ( Pune : Shri Babasaheb Apte Smarak Samiti).

Shukla, Kripa Shankar (1979) Karana-Ratna of Devacarya ( Lucknow : Lucknow University).

Vaidya, P. K. (ed.) (1999) Divyavadana ( Darbhanga: Mithila Institute).

Whitney, William Dwight (1905) Atharva-veda-samhita, 2 vols. (Cambridge, USA: Harvard University).

Yano, Michio (2003)”Calendars, astronomy and astrology” .Blackwell Companion to Hinduism (ed.:Cavin Flood)( Oxford: Blackwell)